Spectroscopy of Neutron�Rich Nuclei Produced

in the Spontaneous Fission of ���Cf

by

Michael Wilhelm Simon

Submitted in Partial Ful�llment

of the

Requirements for the Degree

Doctor of Philosophy

Supervised by

Professor Douglas Cline

Department of Physics and Astronomy

The College

Arts and Sciences

University of Rochester

Rochester� New York

����

ii

To my Parents

iii

Curriculum Vitae

The author was born in San Diego� California on October �� ����� He attended

the University of California� Berkeley from ��� to ��� and worked at the UCB

Earthquake Engineering Research Center and Fire Research Laboratory from ��� to

����� He attended San Francisco State University from �� to ���� and graduated

with a Bachelor of Science degree in Physics in ����� During his enrollment he per

formed research on superconducting tunnel junctions under the direction of Professor

Roger Bland� He entered the graduate physics program at the University of Rochester

in the fall of ����� He was awarded the Graduate Student Teaching Award in ����

and received the Master of Arts degree in Physics in ����� His dissertation research

was carried out at the Nuclear Structure Research Laboratory under the direction of

Professor Douglas Cline�

iv

Acknowledgments

The research presented in this thesis represents not only my e�ort� but also the

contributions of many people� I would like to extend thanks to all those involved�

I would like to thank rst my advisor� Dr� Douglas Cline� for his continued support

and encouragement� I would also like to thank Dr� ChingYen Wu for his a continued

interest in this work and for innumerable useful discussions� Thanks are also due

to the other members of the research group� Dr� Rich Ibbotson and Dr� Matt

Devlin deserve thanks for their contributions and e�orts in the ���Ho experiment�

The contributions of Robert Gray and Carl Welch in the development of CHICO and

during experiments are also gratefully acknowledged�

Thanks are also due to the collaborators at LBNL and LLNL� Dr� Kai Vetter�

Dr� A� O� Machiavelli� Dr� I� Y� Lee� Dr� Ken Gregorich� Dr� Steve Asztalos�

and Dr� R� W� MacLeod contributed signi cantly by insuring that the CHICO plus

GAMMASPHERE experiments were successful� I would also like to thank Dr� Jacob

Gilat for his careful work with the data and for many discussions� Discussions with

Dr� John Rasmussen are also gratefully acknowledged� Dr� Mark Stoyer deserves

thanks for his e�orts in suggesting the experiment� providing the ssion source� and

assistance during the course of this research�

The support o�ered by the sta� at the Nuclear Structure Research Laboratory

was invaluable� Thanks are due to Chris Long� Clint Cross� Ray Teng� Dave Munson�

and Eileen Pullara�

Finally� I would like to thank my family and many friends for their support�

v

Abstract

A new experimental technique has been developed for the spectroscopic investiga

tion of the neutronrich products of ���Cf�SF�� The chargedparticle detector CHICO

was coupled to the Gedetector array GAMMASPHERE and a thin ssion source

was used allowing the collection of highstatistics� highfold � ray data in kinematic

coincidence with the recoiling ssion partners� The selectivity provided by this tech

nique allows the � rays to be assigned unambiguously to the heavy or light ssion

partner� The added sensitivity allows many rotational bands to be extended to � ���h� and a sensitivity to nuclei produced with a yield of �� ����� ssion was achievedby massgating the � ray spectra�

The chargedparticle detector CHICO was developed for this experiment and for

studies utilizing other binary reactions� such as Coulomb excitation� transfer and

fusion ssion reactions� The detector covers a total solid angle of ��� sr and has

a time resolution of ��� ps� resulting in a mass resolution of �m�m��� for beam

experiments� or mass units for spontaneous ssion�

This technique was used to set limits� in agreement with shell model predictions�

on the E� decay of the ���

�level in ���I� Rotational bands in ���������������Mo� ���Ru�

�����������Nd� �����������Sm were extended to higher spin� Band crossings were observed

in the ground and � band in ���Mo� The � band of ���Ru shows continued tri

axial behavior at higher spin� The yrast rotational bands in �������������������Pd were

extended and rotational bands built on the lowlying isomeric levels in �������Pd were

newly identi ed� The behavior of the observed band crossings in the ground and

isomer bands of �������Pd � when compared to the neighboring �������Rh and cranked

shell model calculations indicate that the predicted change from prolate to oblate

shapes in the neutronrich Pd does not occur before ���Pd�

In a separate experiment� the lifetimes in ���Ho of the K � �

�ground band� up to

spin ��

��h� and K � ��

�band� up to spin �

�

��h� were measured by the recoildistance

method� The extracted matrix elements con rm earlier Coulomb excitation results�

and indicate that the K � ���

�� vibrational band has a deformation � ��� larger

than the ground band�

vi

Contents

List of Tables ix

List of Figures x

� Introduction �

� Theory and Models �

��� Microscopic Models of the Nucleus � � � � � � � � � � � � � � � � � � � ������ Spherical Shell Model � � � � � � � � � � � � � � � � � � � � � � � ������ Deformed Shell Model � � � � � � � � � � � � � � � � � � � � � � �

��� Collective Rotations and Vibrations � � � � � � � � � � � � � � � � � � � ������ Coupling of Single Particle Motion and Rotations � � � � � � � ��

��� Band Crossings � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� Phenomenological Classi cation of Rotational Bands � � � � � ��

� Experimental Techniques and Equipment ��

��� Introduction � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� GAMMASPHERE � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� The CHICO Detector � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

����� Design Requirements � � � � � � � � � � � � � � � � � � � � � � � ������� CHICO Description � � � � � � � � � � � � � � � � � � � � � � � � ������� PPACs � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� Electronics � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� Position Measurement and Calibration � � � � � � � � � � � � � ������� Time Measurement and Particle Identi cation � � � � � � � � � ������� Performance of GAMMASPHERE with CHICO � � � � � � � � ��

��� Summary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� ���Cf Spontaneous Fission Experiment Description ��

��� Introduction � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� The Experiment � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

����� The Fission Source � � � � � � � � � � � � � � � � � � � � � � � � ��

vii

��� Thick Source Data � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� Analysis � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

����� Mass Measurement � � � � � � � � � � � � � � � � � � � � � � � � ������� Gammaray Analysis � � � � � � � � � � � � � � � � � � � � � � � ��

��� Gammaray Spectrum Analysis � � � � � � � � � � � � � � � � � � � � � ����� Selectivity � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

����� Mass Gating � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� Selectivity Provided by the Doppler Correction � � � � � � � � ������� HK Measurement � � � � � � � � � � � � � � � � � � � � � � � � ������� Observation of Levels at Higher Spins and Excitation Energy � �

��� Summary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� Neutron h���band structures in the neutron�rich Pd �

��� Introduction � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� �������Pd Ground Bands � � � � � � � � � � � � � � � � � � � � � � � � � � ����� Isomeric bands in �������Pd � � � � � � � � � � � � � � � � � � � � � � � � ����� �����������Pd � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� �������Rh � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� Discussion � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� Summary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

Lifetime measurement of ���I �

��� Matrix Elements from ���Te � � � � � � � � � � � � � � � � � � � � � � � ���� Shell Model prediction of the ��

�

�level lifetime in ���I � � � � � � � � � �

��� Measurement of the ���

�level lifetime in ���I � � � � � � � � � � � � � � �

� High Spin Results ��

��� ���Ru � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� ���������������Mo � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� ���������������Nd � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� �����������Sm � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� Summary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

Conclusion ���

Bibliography ���

A Lifetime Measurement of low�lying levels in ���Ho ���

A�� Introduction � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���A���� The Coulomb Excitation Experiments � � � � � � � � � � � � � ���A���� Intrinsic Moments of Bands in ���Ho from InBand Matrix El

ements � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���A���� Motivation for the Lifetime Measurement Experiment � � � � � ���

viii

A�� The RecoilDistance Lifetime Experiment � � � � � � � � � � � � � � � � ���A���� Experimental Method � � � � � � � � � � � � � � � � � � � � � � ���A���� Lifetime analysis � � � � � � � � � � � � � � � � � � � � � � � � � ���

A�� Matrix elements derived from the lifetime measurement � � � � � � � � ���A���� Ground Band Matrix Elements � � � � � � � � � � � � � � � � � ���A���� K���

�

�InBand Matrix Elements � � � � � � � � � � � � � � � � ���

A���� K����

�Band to Ground Band Matrix Elements � � � � � � � � ��

A�� Summary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���

B Gammasphere Calibration ���

B�� Energy and E�ciency Calibration � � � � � � � � � � � � � � � � � � � � ���

ix

List of Tables

��� Logic tables programmed into the Programmable Logic Unit �PLU�used to de ne the rst level trigger� The �Forward only� sectionrefers to experiments with inverse kinematics� �Forward and Backward� would be used for experiments with a projectile with less massthan the target� A valid particle signal is given only if one of theconditions is met� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� Contributions to the time resolution for �� MeV ���Dy on a ����g�cm�

���Sn target� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� Selection criteria for a thin ssion source isotope� � � � � � � � � � � � ��

A�� Quadrupole moments and deformations of the K��

�ground band and

the K����

�� ��

�� bands of ���Ho measured by Coulomb excitation� � � ��

A�� ���Ho Ground Band Lifetimes � � � � � � � � � � � � � � � � � � � � � � ���A�� ���Ho K���

�Band Lifetimes � � � � � � � � � � � � � � � � � � � � � � � ���

x

List of Figures

��� Nuclei populated in ���Cf�SF� which have been studied spectroscopically� �

��� Schematic view of part of the GAMMASPHERE array �from ������ � ����� Sectional view of CHICO� The target chamber housing the PPACs and

the pressure window is on the right� The transmission lines carryingthe signals from the PPACs to the ampli er boards can also be seen�The length of the assembly is �� cm� � � � � � � � � � � � � � � � � � � ��

��� Crosssection view of the CHICO target chamber� The heavy linesshow the vacuum envelope containing the gas volume� � � � � � � � � � ��

��� One half of CHICO coupled with one half of GAMMASPHERE� � � � ����� Assembly of an individual PPAC� The asymmetrically segmented an

ode and the cathode board with the attached Lexan spacer are shown� ����� Front and back of a cathode board� � � � � � � � � � � � � � � � � � � � ����� Schematic for ideal and current threelayer cathode board delay lines� ���� Schematic for twolayer cathode board delay lines� � � � � � � � � � � � ����� Simulation of the response of the two and three layer cathodeboard

delay lines� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������ Schematic of the acquisition and trigger electronics� � � � � � � � � � � ������ Segmentation of Anode Pairs� Coplanar anode pairs �frontfront and

frontback� are segmented in a way to uniquely de ne the � of thereaction plane� For example� if the large section of both anodes trigger�then the reaction plane is in � slice �� � � � � � � � � � � � � � � � � � � ��

���� Scattering angle position spectrum� The various features of the position spectrum are discussed in the text of Section ������ � � � � � � � � ��

���� Calibration of the front counter theta positions� The heavy lines �experimental data� are t to the calculated angular correlations �lightlines� for a given reaction to obtain the � calibration coe�cients forthe front counter� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

���� Calibration of the back counter theta positions using the ���Cf�SF�data� The heavy line is the position measurement and the light line isthe t to the data� � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

xi

���� Particle identi cation� Measurement of the timeof�ight di�erenceand scattering angles allows the two scattering solutions to be cleanlyseparated� The time di�erence for the two solutions is ��� ns at ���

�channel ���� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������ Measured mass spectrum from the reaction ���Sm � ���Cm at MeV� ������ GEANT simulation of the e�ect of CHICO on the peak e�ciency of

GAMMASPHERE for � rays emitted at the target location� � � � � � ���� GEANT simulation of the e�ect of CHICO on the peaktototal ratio

of GAMMASPHERE for � rays emitted at the target location� � � � � ��

��� Schematic of the ssion experiment setup� The PPAC array �CHICO��is shown with two representative GAMMASPHERE Ge detectors andthe ssion source� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� The mass division between the ssion partners can be uniquely mappedfrom the timeof�ight di�erence of the recoiling nuclei and angularposition of the ssion axis� � � � � � � � � � � � � � � � � � � � � � � � � ��

��� Position spectrum from the ���Cf�SF� experiment� The solid line showsthe expected solidangle dependence of the yield� Above ��� the yielddrops due to target e�ects� � � � � � � � � � � � � � � � � � � � � � � � � ��

��� Measured Mass Resolution� The measured mass for individual nucleiare projected by setting double gates on � ray transitions� The relativeintensities of the mass distributions are not to scale� � � � � � � � � � � �

��� E�ect of heavy�light Doppler correction on raw � data� This gureshows the results of a simulation of the raw line shape and the lineshapes after the complimentary Doppler corrections are applied� � � � ��

��� Measured � ray energy resolution in the thin source ���Cf�SF� experiment� The e�ect of detector noise� counting statistics and Dopplerbroadening are included� � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� The multiplicity distribution �normalized to the number of triple events�and number of unpacked triples from clean � rays events from the thinsource ���Cf�SF� experiment� � � � � � � � � � � � � � � � � � � � � � � � ��

�� Observation of ���Dy in ���Cf�SF�� The top gure shows the groundrotational band of ���Dy� The bottom gure shows the coincident transitions in ��Ge� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� The top gure shows a gated spectrum from the thin source data� Thebottom spectra is with the same applied gates in the thick source data� ��

���� Delayed � ray �isomer� spectrum� � � � � � � � � � � � � � � � � � � � � ����� Total energy and multiplicity in ���Cf�SF�� � � � � � � � � � � � � � � � ������ � ray spectra with the �light� applied Doppler correction gated on the

total energy and multiplicity regions shown in Figure ����� The top gure is from the higher total energy region and the lower gure isfrom the lower total energy region� � � � � � � � � � � � � � � � � � � � ��

xii

���� Using a thin source eliminates Dopplerbroadened line shape problemsand allows observation of levels with shorter lifetimes and high spin�The spectrum on the right ���� is from ���Cm in a KCl crystal andshows the e�ect Dopplerbroadening has for higher lying transitions� � ��

��� Spectra double gated on the ���� and ��� � rays in the thin �upper�and thick �lower� source data � � � � � � � � � � � � � � � � � � � � � � ��

��� ���Pd level diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� ���Pd level diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���� Systematics of �h��

�band heads in the odd Pd isotopes� � � � � � � � � ��

��� Identi cation of ���Pd isomer band� The top spectra �a� is from thelight Doppler shifted thin source ���Cf�SF� data� The middle spectra �b� is from an asymmetric cube from the thin source ���Cf�SF�data with the Te coincident transitions projected out� The bottom �c�spectra is from a thick source experiment ���� ��� � � � � � � � � � � � ��

��� The average masses of the Te ssion partners calculated from the �� ��� Te transitions in coincidence with the Pd� This was used to identifythe mass number of the isomeric Pd bands� � � � � � � � � � � � � � � � ��

��� Even Pd band crossings � � � � � � � � � � � � � � � � � � � � � � � � � ���� ���Pd level diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� ���Pd level diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������ ���Pd level diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������ ���Rh level diagram ���� � � � � � � � � � � � � � � � � � � � � � � � � � ������ ���Rh level diagram ���� � � � � � � � � � � � � � � � � � � � � � � � � � ������ ���Pd single particle routhians for neutrons in an oblate shape� � � � � ������ ���Pd single particle routhians for neutrons in an prolate shape� � � � ������ ���Pd single particle routhians for protons in an oblate shape� � � � � ����� ���Pd single particle routhians for protons in an prolate shape� � � � � ����� The aligned angular momentum of the ground bands of ���Rh and

���Pd and the ���

�isomer band in ���Pd ����� � � � � � � � � � � � � � � ��

��� The aligned angular momentum of the ground bands in ���Rh� ���Pd�and ���Pd� and the

�

�isomer band in ���Pd� � � � � � � � � � � � � � � �

���� The aligned angular momentum of the ground bands of �����������Pdand the

�

�isomer band in ���Pd� � � � � � � � � � � � � � � � � � � � � �

��� ���Te level diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���� ���I level diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��� ���I spectrum � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ����� GEANT calculation of the peake�ciency away from the center of

GAMMASPHERE ��� � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� Level diagram for ���Ru� New levels added from the present work areshown as thick lines in the level diagram� � � � � � � � � � � � � � � � � ��

xiii

��� The left gure shows the RTR model predictions for the energy levelsof the � band as a function of the � shape parameter� The right gureshows the value of the shape parameter � extracted from the leveldiagram� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

��� Level diagram for ���������������Mo� New levels observed in the presentwork are shown as thick lines� � � � � � � � � � � � � � � � � � � � � � � ��

��� Kinetic and dynamic moments of inertia for the ground bands of ���������������Mo� ����� Kinetic and dynamic moments of inertia for ���Mo ground and even

and odd spin sequences of the �band� � � � � � � � � � � � � � � � � � ����� Level diagrams for the ground bands of ���������������Nd � � � � � � � � ���� Kinetic and dynamic moments of inertia for the ground bands of ���������������Nd� ��� Level diagrams for the ground bands of �����������Sm � � � � � � � � � � ������ Kinetic and dynamic moments of inertia for the ground bands of �����������Sm����

A�� Level diagram for ���Ho� The matrix elements connecting the levelsshown were measured in the Coulomb excitation experiments ��� ��The level energies are given in KeV� � � � � � � � � � � � � � � � � � � � ���

A�� Schematic of the RecoilDistance Lifetime Experiment � � � � � � � � � ���A�� Lifetime of the ��

�GSB level measured from the ��

�GSB�

�GSB transition���

A�� Lifetime of the ���K���

�level measured from the ��

�K���

��

�GSB

transition � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���A�� Lifetime of the ��

�K���

�

�level measured from the ��

�K���

��

�GSB

transition � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���A�� Ground Band E� matrix elements from the Coulomb excitation work

and from the RecoilDistance lifetime measurement� � � � � � � � � � � ���A�� Ground Band M� matrix elements from Coulomb excitation work and

RecoilDistance lifetime measurement � � � � � � � � � � � � � � � � � � ���A� E� matrix elements for K���

�� from �J�� inband transitions � � � � ��

A�� K����M� inband matrix elements � � � � � � � � � � � � � � � � � � � ���

A��� E� �J�� matrix elements connecting the K����band to the ground

band � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���A��� E� �J�� matrix elements connecting the K���

�band to the ground

band � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���A��� M� matrix elements connecting the K���

�band to the ground band � ���

B�� Energy Calibration curve for GAMMASPHERE� � � � � � � � � � � � � ���B�� Intrinsic � ray energy resolution for GAMMASPHERE � � � � � � � � ���B�� Relative e�ciency curve for GAMMASPHERE� � � � � � � � � � � � � ���B�� BGO calibration spectra� The spectrum shown is the sum of all the

BGO elements of the GAMMASPHERE array� � � � � � � � � � � � � � ���

�

Chapter �

Introduction

The study of neutronrich region of the nuclear landscape is expected to yield

new and interesting physics� New features such as modi cation of the nuclear shell

structure and new excitation modes ensuing from the weak binding of the neutrons

are expected in the extremely neutronrich region� These prospects motivate the

study of the largely unexplored region of neutronrich nuclei�

There is a paucity of production mechanisms which populate the very neutronrich

nuclei� The ssion products of the actinides provide access towards this mass region

that is di�cult to access by other experimental techniques� The spontaneous ssion

�SF� of ���Cf� the process used in this work� populates the mass regions centered

around � A � ��� and � A � ��� with Z � �� and Z � ��� respectively� These

nuclei lie on the neutronrich side of the valley of stability� and nuclei with up

to �� additional neutrons beyond their heaviest stable isotope are produced with

enough yield for spectroscopic study �see Figure ����� In addition� the ssion products

are populated to moderate spins� with rotational bands observed up to spin �� �h�

Various nuclear reaction mechanisms have been used to populate neutronrich nuclei�

Deep inelastic ��� �� and heavyion transfer reactions ��� have been used to create

neutronrich nuclei� but the current sensitivity of the � ray detector arrays limits the

observation of nuclei to those which are � � neutrons beyond the stable isotopes� Therotational bands in the nuclei in the A � ��� region populated by these reactions

also have been observed to spins around �� �h to �� �h� Induced ssion and fusion

�

Figure ���� Nuclei populated in ���Cf�SF� which have been studied spectroscopically�

ssion reactions also can populate neutronrich nuclei in the same mass region as

spontaneous ssion� but the additional energy brought into the system results in more

neutron emission and� hence� the production of less neutronrich nuclei� Medium and

relativistic energy nuclear fragmentation ��� �� �� have been used to create beams

of neutronrich nuclei but� because of the large recoil velocities and low intensities

produced� it is currently not possible to perform prompt spectroscopy of high spin

states with these beams� The current possibilities for studying neutronrich nuclei by

reaction mechanisms largely do not overlap with the region populated in spontaneous

ssion�

The neutronrich nuclei produced in ssion have been a rich eld of study that has

progressed by the development of a variety of experimental techniques and detectors�

Because of the numerous nuclei produced in spontaneous ssion and� therefore� the

large number of � rays emitted during the deexcitation of these nuclei� the selectiv

�

ity provided by these experimental methods are essential in ssion product studies�

Even the earliest spectroscopic study of ���Cf�SF� suggesting that the spectroscopy

of individual ssion products was feasible ��� employed the technique of detecting

the ssion fragments in coincidence with the � rays� The coincident detection of the

ssion partners and deexcitation � rays along with a measurement of the kinetic

energy of the ssion partners provided the possibility of assigning the � ray peaks

to the heavy or light ssion partner and provided a mass measurement for the nuclei

emitting the � ray� Another early experiment �� �� utilized these methods� in addition

to using two � ray detectors� to identify the rotational bands of �� light and �� heavy

ssion partners populated with the largest yield� The use of multiple � ray detectors

allowed the observation of these bands up to spins of �h and illustrated the utility

of � ray coincidence techniques in ssion product spectroscopy�

The most signi cant recent advance in the study of these neutronrich ssion

products has been the development of high resolution � ray detector arrays� The

latest generation of these arrays� such as GAMMASPHERE and Euroball� provide

high e�ciency allowing the collection of highstatistics data sets where three or more

� rays are detected in coincidence for a ssion event� The sensitivity imparted by

these high e�ciency arrays and the selectivity provided by the highfold collection of

� rays has extended the region of ssion products that can be studied and increased

the observation of deexcitation cascades to higher spins and excitation energy� In

certain cases rotational bands up to spin �� �h have been observed with these arrays�

Experiments using these arrays have been performed with sources that are thick with

respect to the recoiling ssion products� that is the ssion products are stopped in the

source material� The information gathered in these experiments comes primarily from

the analysis of the coincidence relationships of the � rays� These arrays have opened

up the spectroscopic study of these otherwise di�cult to populate nuclei� Interesting

physics that has been produced from these studies include the identi cation of new

regions of quadrupole and octupole deformed nuclear shapes� shape coexistence� and

contributed to the study of shell structures around the doublely magic ���Sn region

�see� for example� ���� and references therein��

The next suggested experimental advance for the study of ssion products is the

�

coupling of the techniques of coincident ssionproduct detection with the collection

of highfold � ray data� This requires using a thin ssion source and large solidangle

ssionfragment detector system compatible with the large � ray detector arrays�

The bene ts of this type of experiment combine the additional selectivity of the

mass information and association of the � rays to either the light or heavy ssion

partner with the selectivity provided by the � ray coincident technique� This type

of experiment is expected to allow observation of levels in the neutronrich nuclei at

even higher spin and excitation energy� The possibilities for studying the neutron

rich nuclei produced in the spontaneous ssion of ���Cf using high statistics data

combining the particle� coincident technique and highfold � ray data are explored

in this work�

This thesis begins with a description of the theoretical models used in the in

terpretation of the results of the thin source ssion experiment� Next� the ����

chargedparticle detector system� CHICO� is described� The development of CHICO

comprises a major component of this thesis� CHICO when used in conjunction with

GAMMASPHERE provides a powerful new facility for nuclear spectroscopy� This

combination has been used in studies using elastic and quasielastic reactions and

other binary processes� such as fusion ssion and spontaneous ssion� the latter being

the focus of this thesis� The present thin source ���Cf�SF� experiment and a discus

sion of the selectivity provided by coupling a ssionfragment detector with the latest

generation of large � ray detector arrays then is presented� followed by the results

obtained utilizing this new technique�

�

Chapter �

Theory and Models

��� Microscopic Models of the Nucleus

����� Spherical Shell Model

The observance of special properties in nuclei with �magic� number of neutrons

or protons� occurring at �� � ��� ��� �� and ��� ����� suggests that the nucleus has a

shell structure analogous to that of the atomic electrons� Experimental evidence for

shell closures occurring at these magic numbers include the singleparticle separation

energies� which are the energy required to remove the least bound nucleon from the

nucleus� Nuclei with a magic number of neutrons or protons are more strongly bound

and have larger separation energies than their neighbors with additional nucleons�

Unlike the electrons in the shell model of the atom� which are in�uenced by a

strong central force created by the Coulomb potential� the nucleons experience a

potential that originates from the interaction with all the other nucleons� This can

be described by a mean eld� V �r�� which is commonly modeled with a WoodSaxon

or harmonic oscillator form� With this type of average potential� the nucleons are

treated as being independent of each other� This approach is validated by the long

mean free path of the nucleons caused in part by the Pauli Exclusion Principle� The

�

Hamiltonian for the nucleons in the singleparticle shell model is given by

Hi�r� �

�� �h�

�m�� �V �r�

�i�r� � �ii�r� �����

This description still does not reproduce the observed shell closures at magic num

bers of neutrons or protons� A spinorbit �L�S� term of the appropriate strength

must be included in the potential V �r� for the calculated energy levels to agree with

experimental results� The projection of the angular momentum� lz� and spin� sz� are

no longer good quantum numbers since they do not commute with singleparticle

Hamiltonian which includes the spinorbit term� The levels are characterized by the

radial quantum number n� the orbital angular momentum quantum number l� the

spin quantum number s� the total angular momentum j� and its projection jz� The

terminology of the atomic shell model is frequently used in labeling orbitals with

the quantum number l��������������� with the letters s� p� d� f� g� h��� � This descrip

tion assumes that the single particle orbitals are completely independent� The full

spherical shell model includes a residual twobody interaction�

The spherical shell model is successful in predicting certain properties of nuclei in

regions near closed shells� The spins� parities and transition rates of excited particle

hole and single particle states can be calculated with this model� and ground state

spins and parities can also be explained� Nuclei further from the closedshell re

gions show compelling evidence for deformed shapes� For these regions� a spherical

potential is no longer convenient� and a deformed potential provides a more useful

representation�

����� Deformed Shell Model

In the midshell regions there is considerable evidence for stable deformation of

the nuclear shape� such as large quadrupole moments of the ground state of nuclei

and the presence of rotational bands� These features are not conveniently reproduced

with the spherical shell model� and a more e�ective approach is to assume that the

nucleons are e�ected by a deformed average potential� The model of the nucleus

described by a quadrupoledeformed harmonic oscillator potential was considered

�

rst by Nilsson �����

The dynamics of the nucleons is described by a threedimensional anisotropic

harmonic oscillator with a Hamiltonian

H� � � �h

�M�� �

M

����

xx� � ��

yy� � ��

zz�� �����

where the coordinates refer to a body xed frame� With the assumption of axial

symmetry� the symmetric axis is taken� by convention� to be the zaxis� A deformation

parameter� � can be introduced giving

��� � ��

x � ��y � ��

�� ��� �

�

� �

�����

��z � ��

�� ���� �

� �

�����

and ��� � is de ned in a manner as to conserve volume� The eigenstates for the

axial symmetric case solved in the cylindrical coordinate system are characterized by

the quantum numbers nz� n�� ml� where ml is the projection of the particle angular

momentum onto the symmetry axis� The energy of the eigenstates is given by

�� � �h��

� �N �

�

�

��

�N

�� nz

�������

with N � nz��n�� j ml j� This equation shows that the deformation causes splittingof levels with the same N and di�erent nz� The quantum numbers characterizing the

Nilsson levels are �Nnzml� � where � ml � ms is the projection of the angular

momentum onto the symmetry axis�

The full Nilsson Hamiltonian includes a spinorbit term L�S and a L� term to

account for de ciencies in the assumption of a harmonic oscillator form of the poten

tial� With the inclusion of these terms� nz� n�� and ml are no longer good quantum

numbers� For large deformations� however� the contributions of these terms are small

compared to the e�ect of the deformation� and the levels can be characterized by the

quantum numbers of the anisotropic harmonic oscillator�

��� Collective Rotations and Vibrations

Nuclei exhibit collective behavior that can be modeled neglecting the microscopic

structure� The separation of macroscopic collective motion and microscopic single

particle degrees of freedom is justi ed in the adiabatic limit� where the collective

motion is slow compared to the frequency of the single particle motion� The collec

tive motion at low excitation energy largely is related to surface motion and� hence�

collective models of the nucleus begin with a description of the nuclear shape�

The nucleus can be modeled as a body having a distinct surface with a radius R

de ned by

R��� �� � R�

��� � �X

���

�X����

����Y����� ��

A �����

where R� is the radius of a sphere with the same volume� For this expansion� the ���

term ensures volume conservation and the ��� terms x the center of mass location�

The lowest order of interest �� � �� describes a quadrupole deformation� Here the

ve space xed parameters ��� can be reduced by an appropriate rotation to two

real parameters� a�� and a��� describing the nuclear shape in the intrinsic frame� and

� Euler angles describing the orientation of the nucleus� A quadrupole deformed

nuclear shape can be represented in the body xed frame using the HillWheeler

coordinates ����� and �� de ned by

a�� cos��� �����

a�� �p�sin��� ����

� a��� � �a��� �����

where describes the magnitude of the quadrupole deformation and � � in the region

�� � � � ���� describes the amount of asymmetry with respect to the principle axis�

In its intrinsic frame� the collective motion of the nucleus can be described by the

collective Hamiltonian ����

Hc � V �� �� ��

�

Xi

Ji�� ����i �

�

�B��

!� �B�� ! !� ��

�B��

� !�� ������

where J i are the moments of inertia� �i are the angular velocities� and B��� B�� � B��

are the mass parameters for the � � � coupled� and � vibrations� respectively�

The wave function in the space xed coordinate system for a nucleus described by

�

the Bohr Hamiltonian can be separated into intrinsic and rotational components by

"I�M �

XK

��IK�� ��jIKM � ������

where ��IK are the solutions to the Bohr Hamiltonian with angular momentum I�

with projection K onto the symmetry axis� and � are all the other quantum numbers

of the intrinsic motion� The rotational component is de ned by

jIKM � �

s�I � �

��DI�

MK� � ������

where DI�

MK� � are the Wigner functions� and represent the Euler angles� The

wave function "I�M � has angular momentum I and a projection� M � of the angular

momentum onto the zaxis�

The most common collective degrees of freedom for a quadrupoledeformed nucleus

are rotation� vibration� and � vibration� These modes of excitation are common

to deformed nuclei and typically have energies less than the pairing gap� and� hence�

are important in describing the lowlying spectral features of deformed nuclei� The

features can be illustrated by solutions to a simpli ed expansion of the Bohr Hamilto

nian� as in the RotationVibration model ����� that assumes axial symmetry ������

and neglects terms which explicitly couple the rotational� and � vibrational de

grees of freedom� In this case K remains a good quantum number and the sum in

equation ���� reduces to a single term� Also� the intrinsic part of the wave func

tion �I�K separates in and � and the wave function in the space xed frame can be

written as

"I�MK � jn� � jn� � jIKM � � ������

with the energies of the eigenstates given by

EKn�n� � �h��

�n� �

�

�

�� �h��

�n� � � �

jKj�

���h�

�J �I�I � ���K��

������

The level diagram suggested by equation ���� illustrates some general features of

the spectra of deformed nuclei� States of di�erent intrinsic structure� here described

��

by di�erent number of vibrational quanta� n� and n� � can be the basis of rotational

bands with level spacing described by the I�I ��� relation� In general other types of

intrinsic states also can be the basis for rotational bands� such as singleparticle and

particlehole states�

����� Coupling of Single Particle Motion and Rotations

In a simple macroscopic picture� the nucleus is treated as a rigid body subject to

vibrational and rotational motion� A realistic microscopic model necessarily needs to

include the e�ect a rotating nuclear potential has on the single particle orbitals� For

example� the lowlying levels of rotational bands deviate from the predicted I�I � ��

level spacing� This can be understood as a reduction of the pairing energy and

partial alignment of the angular momentum by the Coriolis interaction of nucleon

pairs coupled to zero angular momentum� These e�ects cause a gradual increase in

the moment of inertia as the rotational frequency increases and� hence� the observed

deviation from the I�I��� spacing� At higher rotational frequencies the Coriolis force

is strong enough to overcome the pairing energy and align the angular momentum of

the nucleons along the rotational axis�

One method of taking into account the e�ect of rotation on single particle motion is

the cranking model proposed by Inglis ����� In this model the singleparticle potential

of the xed nuclear shape of the form V �r� t� � V �r� �� ���t� t � �� is rotated about

a space xed axis� The explicit time dependence of the space xed Hamiltonian is

removed by a unitary transformation U � ei�Jxt into the body xed frame� The single

particle Hamiltonian� h�� in the body xed frame then is related to the Hamiltonian

in the space xed frame� h�t�� by

h� #" � �h���� �Jx� #" ������

with h��� � Uh�t�U�� and #" � U"� and the energies ��i� of the singleparticle

orbitals in the body xed frame are related to the energies �#�i� in the space xed

frame by

�i � #�i � � � #"jJxj#" � � ������

��

The rotation has the largest e�ect on orbitals having large j� the total angular mo

mentum of the orbital� and small � the projection of the singleparticle angular

momentum on the nuclear symmetry axis� values� The excitation energy of these

levels are reduced in energy with increasing � as they are aligned along the rotational

axis�

��� Band Crossings

In deformed nuclei� excited rotational bands are built on microscopic structures

di�erent than the ground state con guration and therefore can have moments of

inertia that di�er from the ground band� The energy levels of the rotational bands

follow the approximate relation E�I� � E��� � h�

�JI�I � ��� where E��� is the band

head energy� Bands with larger moments of inertia eventually will cross bands with

lower moments of inertia in the I versus E plane� This means that� at the crossing

point� members of the crossing bands with the same spin will have approximately

the same energy� The residual interaction repels the states at the band crossing and

causes band mixing near the crossing point� The deexcitation proceeds along the

yrast line� which is the sequence of spins with lowest energy for a given spin�

The deexcitation cascade of � rays re�ect the change of the structure of the nu

cleus at the crossing point� For weak interactions between the crossing bands� the

properties of the observed rotational sequences can change dramatically over a small

range of spin� This change can be demonstrated by plotting the moment of iner

tia against the rotational frequency� The increase in moment of inertia at the band

crossing corresponds to a decrease in rotational frequency of the nucleus� and for weak

interactions between the bands the moment of inertia has a characteristic �s� shape�

����� Phenomenological Classi�cation of Rotational Bands

The low spin energy levels of rotational bands in deformed nuclei can be described

to rst order by the rigid rotor result

E ��

�J�� �

L�

�J � with L� � �h�I�I � �� ������

��

The moment of inertia �J � and frequency of rotation ��� for a rotational band can bede ned from the level energies in analogy with classical relations� The kinetic �J ����

and dynamic �J ���� moments of inertia are de ned �Ref� ����� for example� as

J ��� ��

�

dE�I�

d�I��

������I � ���h�

E�

�����

J ��� �

�d�E�I�

�dI��

��

��h�

�E�

������

for I � I�� transitions� with E� � E�I��E�I���� where the di�erential quantitiesare approximated by discrete di�erences� The rotational frequency of the nuclei can

be de ned by ���

� �

pI� �K�

J ����pI� � I � ��K�

E�

��I � ���h ������

The component of the angular momentum� K� directed along the symmetry axis

is subtracted from the total angular momentum in the calculation of the rotational

frequency� �� since it does not contribute to the collective rotation perpendicular to

the symmetry axis of the nuclear core� Plots of the rotational frequency� �� versus the

moments of inertia� J ��� and J ���� are very sensitive to deviations in the rotational

sequence of levels�

The aligned angular momentum� ix���� which is the amount of angular momentum

perpendicular to the symmetry axis of the deformed nucleus beyond the contribution

of the rotating core� also can be calculated from the level energies� The moment of

inertia of the ground band can be expanded as a function of the rotational frequency

� as

Jg � J ���� � J ���

� �� ������

where J ���� and J ���

� are obtained from a t to the data� and are called the Harris

parameters ����� The contribution to the angular momentum of the rotating nuclear

core is then

�hIref��� � �J ���� � J ���

� ���� ������

��

and the aligned angular momentum is given by

ix��� � I���� Iref��� ������

The aligned angular momentum� ix� is useful for interpreting the behavior of the

moment of inertia� J ����

��

Chapter �

Experimental Techniques and

Equipment

��� Introduction

Recent developments of large � ray detector arrays� such as GAMMASPHERE �����

have led to new advances in nuclear physics� The large gains in both the � ray de

tection e�ciency and the resolving power achieved with these arrays has enabled the

discovery and study of a variety of new physics �see� for example� ���� �����

The coupling of these � ray detector arrays with auxiliary detectors further ex

pands their versatility� For example� the coincident detection of deexcitation � rays

with the detection of the scattered and recoiling nuclei from heavyion reactions per

formed using thin targets is a powerful method for studying the nucleus� Gamma ray

spectra from thick target experiments can su�er from Dopplerbroadened line shapes�

occurring for transitions which have lifetimes comparable to the stopping time of the

nuclei in the target� In thin target experiments the nuclei recoil into vacuum and the

Dopplerbroadened line shapes can be eliminated� Since the velocities of the nuclei

are appreciable� on the order of �� of the speed of light� the � rays emitted from the

nuclei in �ight have associated Doppler shifts� By measuring the timeof�ight dif

ference along with the scattering angles of the nuclei it is possible to reconstruct the

kinematics of the reaction and to distinguish the targetlike from the projectilelike

��

nuclei for two body reactions� Measurement of the scattering angles and velocities

of the reaction products allows the � ray energies to be corrected for the Doppler

e�ect on an eventbyevent basis� resulting in spectra with sharp � ray peaks and the

ability to assign the � rays to the targetlike or projectile like nucleus�

The particle� ray coincidence technique has applications to the study of Coulomb

excitation� nucleon transfer� and ssion� With large solid angle particle detectors it

is possible to concurrently measure scattering angles and � ray yields over a range of

scattering angles� For Coulomb excitation experiments this is equivalent to measur

ing � ray yields for varying Coulomb excitation strength� giving information on the

B�E�� values of the excited levels ����� The scattering angle information also can be

used to select reactions that occur near the grazing angle� selectively enhancing the

transfer channels ����� The coincident � rays can be used to identify the correlated

reaction products determining the number of nucleons transfered� The application of

the particle� ray coincidence technique to the study of neutronrich nuclei resulting

from spontaneous ssion is discussed in detail in Chapter ��

To fully utilize the particle� ray coincidence technique with the new powerful

� ray detector arrays� a large solidangle particle detector� CHICO �Compact Heavy

Ion Counter�� was developed at the University of Rochester as part of this thesis�

This chapter describes the equipment used in these types of thin target experiments

with a particle detector coupled to a large � ray detector array� A brief descrip

tion of GAMMASPHERE is given� and a more extensive discussion of the design

considerations� physical description� and performance of the CHICO detector also is

presented�

��� GAMMASPHERE

GAMMASPHERE is a spherical array of ��� large volume ���� cm diameter x

cm length� highpurity Ge � ray detectors� The Ge detectors are mounted on

two movable hemispheres� allowing access to the reaction region at the center of

the array� A schematic diagram of part of the GAMMASPHERE array is show in

Figure ���� The distance from the center of the array to the Ge detector faces is ��

��

cm� constraining the size of any auxiliary detectors�

The factors contributing to the power of GAMMASPHERE are the gains achieved

from the high granularity� Compton suppression� and large solidangle coverage of the

array� and the performance of the individual detectors� The key features of the indi

vidual detectors are their e�ciency� energy resolution� and peaktototal ratio� Each

of the detectors is made of ntype Ge crystal with about a ��� detection e�ciency for

a � ray entering the Ge crystal� and ��� keV energy resolution for a ���� MeV � ray�

The Ge crystals are surrounded by BGO �bismuth germanate� Compton suppressors

which allow rejection of events where the full energy of the � ray is not deposited in

the Ge crystal due to Compton scattering� The peaktototal ratio� the number of

counts in the � ray peak divided by the total counts in the spectrum� is improved by

the Compton suppression from ���� to ��� for a ���� MeV � ray �����

The peak e�ciency� the probability of detecting the full energy of a � ray in one

of the detectors of the array� depends on the solid angle covered by the Ge detectors�

The solid angle coverage by Ge of the array� with the full complement of ��� Ge

detectors� is about ��� of �� sr� resulting in a total peak e�ciency of ���� for the

detection of a ���� MeV � ray by the whole GAMMASPHERE array� The individual

detectors subtend an angle of about ��� viewed from the target location at the center

of the array� The small solid angle of each detector reduces summing errors� where

two � rays hit the same detector� and reduces Doppler broadening of the � ray line

shapes�

The high peak e�ciency of GAMMASPHERE allows the collection of highstatistics

highfold � ray data� where many � rays are detected in coincidence� The highfold

events can be �unpacked� to increase the statistics for events with lower fold� for

example a �fold event contains �� distinct �fold events� Multiple gates on � ray

transitions can be set on highfold events� allowing speci c features of complex � ray

spectra to be selected and enhanced�

��

γγ

γ

BGO Suppressor Plug

Ge Detector

BGO SuppressorShield

LiquidNitrogenDewar

Detector Electronics

HevimetShield

SupportHemisphere

PMTubes

Gamma-raySource

Figure ���� Schematic view of part of the GAMMASPHERE array �from ������

��� The CHICO Detector

����� Design Requirements

There are several factors constraining the design of a heavyion detector to be used

successfully in conjunction with GAMMASPHERE� The detector design and perfor

mance obviously should address the experimental requirements for the physics being

studied� Furthermore� coupling of the heavyion detector with GAMMASPHERE

constrains the physical size and symmetry of the detector� and requires that the de

tector is designed to have a minimal impact on the performance of GAMMASPHERE�

The primary purpose of the heavyion detector is to gather enough information

from the involved nuclei to reconstruct the kinematics of the event� For beam experi

ments� the measurement of the scattering angles of both targetlike and projectilelike

nuclei de ne the momenta of the nuclei through the relation derived from conservation

�

of momentum� with the assumption of twobody kinematics�

P��� �P�sin������

sin��� � ��������

where P� is the momentum of the beam� P� and P� are the momentum of the nuclei�

and �� and �� are the scattering angles� Resolution of polar scattering angles to �� is

more than su�cient to calculate the momenta of the nuclei since other e�ects� such

as the size of the beam spot� produce comparable errors in the angle measurement�

The scattering angles of the nuclei completely de ne the momenta for twobody

reactions but� in practice� do not uniquely identify the targetlike and projectilelike

nuclei over the full range of scattering angles� The two scattering solutions can be

resolved with inclusion of a measurement of the di�erence in timeof�ight of the

nuclei from the target to the particle detectors� For the geometry of the CHICO

detector� the minimum �ight path from the target to the detectors is about �� cm�

and for experiments run near the Coulomb barrier the separation in timeof�ight

di�erence for the two solutions is typically on the order of nanoseconds� Therefore to

resolve the two solutions over all scattering angles it is critical to use detectors with

subnanosecond time resolution�

Parallel plate avalanche counters �PPACs� ���� are ideally suited for a detector

of this type� They can be designed with su�cient angular resolution and typically

have time resolutions around ��� ps �FWHM�� PPACs have other attractive features

for this application� The individual detectors can handle particle detection rates

around ���k�sec� leaving experimental detection rates limited only by the acquisition

electronics� The PPACs are resistant to radiation damage� can run for months with

good stability� and the detection threshold for heavy ions can be adjusted to the

experiment� This last feature is especially important for ���Cf ssion studies since

the �decay rate is about �� times the ssion rate it is important to tune the PPACs

to be insensitive to the � particles� The PPACs also have a relatively simple light

mass design and are constructed of low Z materials so they do not strongly scatter

� rays� and hence do not degrade the performance of GAMMASPHERE�

The symmetry chosen for the particle detector is dependent on the symmetry

of GAMMASPHERE� For certain experimentally measurable quantities� such as the

��

excitation of the nuclei as a function of the scattering angle �or equivalently the

impact parameter�� or � ray angular distributions� it is useful to sum spectra that

originate from sets of � ray detectors with similar angular position with respect to

particle scattering angles� To maximize the number of spectra that can be summed�

minimizing the total number of spectra to analyze� the particle detector should have

the same symmetry as the Ge detectors of GAMMASPHERE� The � ray detectors

of GAMMASPHERE are arranged with pentagonal symmetry� but since the particle

detector needs to have an even number of detectors to e�ectively collect binary particle

coincidences� CHICO was designed with the least common multiple of �� azimuthal

sections�

����� CHICO Description

The CHICO detector consists of �� separate trapezoidal parallel plate avalanche

counters �PPACs�� There are two essentially identical assemblies� each of which

houses �� of the PPACs arranged in a truncated cone coaxial with the beam direction

�Figures ���� ����� Figure ��� shows the half of the CHICO detector installed in one

half of GAMMASPHERE� The PPACs� their segmented anodes� and their delay line

cathodes are described in Section ������ The two assemblies are joined along the

� � ��� plane �with respect to the beam direction�� The forward assembly has an

active � range from ��� to ��� and the back assembly has an active � range from

��� to ���� An individual PPAC covers an azimuthal width of ��� and there is a

dead region of � in � between each of the PPACs� giving ��� of � coverage for both

the forward and back assemblies� The total angular coverage is � ��� sr� or about

��� of the total solid angle� About ��� of the total solidangle is lost to the dead

space between the PPACs� another �� is lost along the joint between the two halves�

and �� is lost at the beam entrance and exit ports� The PPACs are positioned with

the normal at an angle of ��� with respect to the beam axis and the minimum �ight

path� from the center of the target to the midpoint between the anode and cathode

in the PPACs� is ��� cm�

The housing for the PPACs is a ��� mm ������� in� thick aluminum hemisphere

��

Figure ���� Sectional view of CHICO� The target chamber housing the PPACs andthe pressure window is on the right� The transmission lines carrying the signals fromthe PPACs to the ampli er boards can also be seen� The length of the assembly is�� cm�

shell with a ���� cm ��� in� diameter� The PPACs are mounted to xtures epoxied to

the inside of the hemisphere� The epoxy used was Hysol EA ������NA� manufactured

by Dexter Aerospace Materials Division� and was chosen for its high shear and peel

strength with aluminum� The wide end of the PPACs are seated in a ring glued along

the diameter of the hemisphere which also provides the Oring seal with the pressure

window� The pressure window consists of a conical frame covered with ��� �m thick

Mylar �����g�cm��� and serves to contain the detector gas from the target chamber

volume� All �� PPACs for each half of the detector sit in a common gas volume� A

��

Figure ���� Crosssection view of the CHICO target chamber� The heavy lines showthe vacuum envelope containing the gas volume�

collimator can also be mounted in the target chamber� The tungsten collimator has a

��� mm ����� in� diameter entrance hole and a ��� mm ���� in� exit hole and holds a

gold foil with a ��� mm ������ in� diameter hole ���� cm �� in� from the target� The

collimator has no more than ��� transmission for a ��� keV � ray which may arise

from excitation of the gold foil by the beam�

The target ladder can hold four targets at one time and is designed so the targets

can be switched without opening the detector� The ladder is mounted on a ��� mm

������ in� thick ring that has the same diameter as the hemisphere� with an Oring

on each side� This thin ring of the target ladder assembly completes the vacuum

��

Figure ���� One half of CHICO coupled with one half of GAMMASPHERE�

seal between the two halves of the CHICO detector� Two separate target ladder

assemblies have been constructed� one of which allows the targets to be retracted into

a box to facilitate handling of radioactive targets� Both target ladders are insulated

so a bias voltage up to �� kV can be applied to suppress the emission of secondary

electrons�

��

����� PPACs

The essential elements of each PPAC comprise a thin lm anode plus a cathode

circuit board� A diagram of an individual PPAC assembly is shown in Figure ����

The anode� made of approximately ��� �g�cm� thick stretched polypropylene with

an approximately �� �g�cm� aluminum coating� is segmented into two electrically

isolated sections and is glued to a ��� mm ������ in� thick G�� frame� The signals

from the anode and cathode are carried to the ampli ers by a stripline transmission

line which has four �� ohm impedance traces on a central plane shielded on either

side by ground planes� The PPAC end of the transmission line is forked allowing two

of the traces to connect to the cathode board and two of the traces to the segmented

anode� The anode traces on the transmission line also carry the bias voltage �����V� to the PPAC anode�

A ��� mm ������ in� thick Lexan spacer separates the anode from the cathode� The

spacer is slotted along the sides so the detector gas can circulate to the active region

of the PPAC� preventing degradation of the detector performance over time due to

radiation damage of the gas� The azimuthal width of the spacer is ��� and ��� for the

anode frame� The spacer has a smaller opening angle to prevent edge e�ects� where

the aluminized polypropylene is glued to the anode frame� from causing an electrical

discharge to the cathode� The azimuthal width of the active area of the PPACs

�de ned by the spacer� is constant� so the total geometric � acceptance remains

constant at �� over the entire polar range of the full detector assembly�

The cathode board is a three layer circuit board� shown in Figure ���� The active

side �front� of the cathode board� where the particles are detected� is segmented into

�� wide traces of constant polar angle �� Each of the traces is connected to one tap

of a delay line which is mounted on the back side of the cathode board� The delay

line has a delay of � ns per tap and is made of passive delay chips manufactured

by Rhombus Industries� The traces on the active side of the board are connected

to the delay line on the back of the cathode board by platedthru holes which are

located near the edge of the board� The third �middle� layer is a ground plane located

between the delay line side and the active side of the cathode� The ground plane acts

��

Figure ���� Assembly of an individual PPAC� The asymmetrically segmented anodeand the cathode board with the attached Lexan spacer are shown�

to capacitively decouple the traces of the delay line on one side of the board from

the sensing traces on the active side of the board� The addition of the ground plane

considerably improves the performance of the delay line�

The delay line can be modeled with inductors and capacitors as shown in Figure

���� An ideal delay line� without any capacitive contribution from the cathode board�

would have the values speci ed by the delay chips� which are L���� nH for the

inductors and C���� pF for the capacitors� giving a delay of tdelay �pLC�� ns

per tap� The threelayer board can be modeled by the addition of the capacitance

between the traces and the ground plane� calculated to be about � pF at each tap�

These capacitances are in parallel with the delay line capacitances� changing the value

of C� to about �� pF� and increasing the delay per tap to ����� ns� The cathodeboards from the previous generation of Rochester heavyion detectors ���� ��� were

of a similar design� except they did not have a ground plane separating the delay line

��

Figure ���� Front and back of a cathode board�

from the sensing traces� Since these older cathode boards have no ground plane� there

is no additional capacitance between the traces and ground �C���� pf�� However�

the traces connecting the platedthru holes along the edge of the board to the delay

chips capacitively couple� with a capacitance calculated to be � pF� to several of the

nearest taps of the delay line via the sensing traces on the active side of the board�

This old design of cathode boards can be modeled as shown in Figure ���

The performance of these various con gurations were simulated using the program

SPICE ���� The simulation modeled the application of a voltage impulse approxi

mating an actual signal �a Gaussian shape with a FWHM of � ns� at one end of

the delay line and calculated the pulse shape after propagating to the other end of

the delay line� The results are shown in Figure ���� The only signi cant di�erence

between the signals propagated down the ideal delay line and the three layer board

delay line �not shown� is a small di�erence in overall delay caused by the additional

��

Figure ���� Schematic for ideal and current threelayer cathode board delay lines�

Figure ��� Schematic for twolayer cathode board delay lines�

capacitance present at each tap of the delay line for the three layer board� The dif

ference between the two and three layer boards is more signi cant� The addition of

the ground plane increases the output pulse height and decreases the output pulse

rise time� This results in a better signal to noise ratio and a better time resolution

for the cathode signals and� hence� a more accurate position measurement�

��

0 20 40 60 80Time (ns)

0

0.5

1

Am

plitu

de (

Arb

itrar

y un

its)

Simulated Response of 3−layer Cathode Board

ideal delay linewithout ground plane

Input pulse output pulse

Figure ���� Simulation of the response of the two and three layer cathodeboard delaylines�

����� Electronics

Ampli ers

Compact ampli er boards ���� were designed at the Nuclear Structure Research

Laboratory speci cally for use with the CHICO detector� Each PPAC has a dedicated

ampli er board with two anode channels and two cathode channels� The physical

size of the boards was kept small� ���� cm by ��� cm� allowing them to be housed

in the detector assembly as close to the detectors as possible to reduce electronic

noise pickup� The ampli ers are based on cascadable microwave ampli cation chips�

simplifying the design and construction� The circuit boards are threelayer boards�

with the signal traces on the middle layer shielded by the ground planes� Since the

acquisition electronics require negative inputs with pulse heights on the order of a

Volt� the anode ampli cation chain is noninverting with a total gain of ���� and the

cathode ampli cation chain is inverting with a gain of ���� The ��� MHz bandwidth

of the ampli ers ensures that the rise times of the pulses are not degraded during

�

ampli cation� Each of the ampli er channels also has an associated energy signal�

created by inductive picko� from the time signals� useful for performing diagnostics

on the detectors during an experiment�

Acquisition Electronics

A schematic gure of the acquisition electronics is shown in Figure ����� Standard

NIM and CAMAC modules are used to extract and digitize the time information from

the ampli ed anode and cathode signals� The time picko� signals from both the

anodes and cathodes are converted to logic pulses by Tennelec Model ��� Constant

Fraction Discriminators �CFDs�� These units extract timing information from the

input pulses by providing a NIM standard logic output pulse when the input signal

reaches a xed fraction of the maximum input pulse height� The logic timing signals

then travel through ��� ns of delay cables and are regenerated and converted to ECL

standard logic pulses by ���� LeCroy discriminators� The ���� discriminators have

two outputs� one which passes the signal on to the timetodigital converters �TDCs��

and the other which can be used in conjunction with scalar units to monitor signal

rates during an experiment� The TDCs are a combination of the LeCroy ���� Fast

Encoding and Readout TQCs �FERETs� and the LeCroy model ����B Fast Encoding

Readout ADCs �FERAs�� The charge outputs from the FERETs are further delayed

by ��� ns and fed into the FERAs� where the signals are digitized and stored until

read into the data stream� The FERETs are run in a common stop mode� The

FERETs are fast modules with little dead time and are gated at the rst level trigger

rate� The charge outputs are started in the individual channels of the FERETs upon

receipt of the timing signal from the ���� LeCroy discriminators and are stopped at

the end of the gate signal� The FERAs also require a gate signal� but since these are

relatively slow devices they are gated at the nal trigger rate�

The gates for the FERETs are provided by a LeCroy model ��� Programmable

Logic Unit �PLU�� This unit provides a �exible method of generating a valid event

�or gate� signal and can be programmed to accommodate various experimental con

ditions� The anode signals of the full PPAC array are summed by quadrant �front

��

Figure ����� Schematic of the acquisition and trigger electronics�

��

Front Front Back BackRight Left Right Left

Forward � � � �only

� � � �Forward � � � �and � � � �

Backward � � � �� � � �

Fission � � � �� � � �

Table ���� Logic tables programmed into the Programmable Logic Unit �PLU� usedto de ne the rst level trigger� The �Forward only� section refers to experiments withinverse kinematics� �Forward and Backward� would be used for experiments with aprojectile with less mass than the target� A valid particle signal is given only if oneof the conditions is met�

right� front left� back right� back left� after the CFDs� and these summed signals are

the inputs to the PLU� The PLU checks if a valid event occurred according to the

appropriate tables �see Table ���� and provides the rst level trigger signal if the con

ditions are met� The second level trigger is built by requiring a coincidence between

the rst level trigger and a valid � ray event� which is provided by the GAMMA

SPHERE electronics� The nal level trigger is the sum of the second level trigger

and a scaled down rst level trigger� The scaled down rst level trigger represents a

fraction of all the particle events� regardless of any � ray requirement� and provides

a means of normalizing the � rays yields to the total cross section of a reaction� This

nal trigger is used to gate the FERAs and to inform the GAMMASPHERE data

acquisition that the event should be read and entered into the data stream�

����� Position Measurement and Calibration

The detector was designed to measure both the polar ��� and azimuthal ��� angles

�with respect to the beam direction� of the scattered nuclei� The � measurement is

��

Figure ����� Segmentation of Anode Pairs� Coplanar anode pairs �frontfront andfrontback� are segmented in a way to uniquely de ne the � of the reaction plane�For example� if the large section of both anodes trigger� then the reaction plane is in� slice ��

provided by the segmentation of the anodes� A �binary� scheme was implemented�

similar to previous generations of Rochester heavyion detectors ���� ���� to reduce

the number of electronic channels necessary for the given resolution� The anodes are

segmented into two sections covering ��and �

�of the �angle subtended by the individ

ual PPACs� Twobody kinematics demand that the scattered beamlike and recoiling

targetlike nuclei are coplanar� so the combination of large and small segment in

which the reaction products are detected de ne the �slice in which the reaction

plane lies �Figure ������ The �resolution is � ���� and is limited by the angularwidth of the smaller of the two anode segments� which is ����� The �measurement is

de ned by the geometry of the detector and combination of the anodes in which the

nuclei are detected�

The � angle measurement is obtained from the signals read out of the delay line

on the cathode board� The signal generated in the cathode by the incident heavy

ion travels both directions down the delay line� The time di�erence between the

two ends of the delay line determines the location of the event along the delay line�

��

10 20 30 40 50 60 70 80Scattering Angle (Degrees)

0

500

1000

1500C

ount

s

Position Spectrum86

Kr + 63

Cu @265MeV

Figure ����� Scattering angle position spectrum� The various features of the positionspectrum are discussed in the text of Section ������

An example of the position measurement is shown in Figure ����� This spectrum

contains events in which the target and projectile nuclei were detected in coincidence

in the reaction ��Kr on ��Cu at a lab energy of ��� MeV� The peaks in the spectra

correspond to theta slices of the cathode board indicating that the position resolution

is about ��� The dip in the position spectrum near ��� is the shadow of a support rib

in the pressure window� which subtends ��� The dip in the spectrum at ��� results

from the coincidence particledetection requirement since this is the scattering angle

for Kr when the Cu is blocked by the support rib in the opposite PPAC� Also present

in the position spectrum is the maximum scattering angle of ��� for the Kr nuclei�

The sharp cuto� at ��� is from a mask to eliminate small angle scattering events�

The cuto� beyond ��� is also a result of coincidence requirement� re�ecting that the

��

0 20 40 60 80 100Counter #4 (Degrees)

0

20

40

60

80

100

Cou

nter

#9

(Deg

rees

)144

Sm+248

Cm

162Dy+

118Sn

Figure ����� Calibration of the front counter theta positions� The heavy lines �experimental data� are t to the calculated angular correlations �light lines� for a givenreaction to obtain the � calibration coe�cients for the front counter�

Kr is masked below ����

The position measurement for an individual PPAC can be calibrated using the

physical limits and the shadow of the support rib as reference points� A more precise

calibration can be performed by relying on the angular correlation of the scattered

reaction products in beam experiments� The position measured in one PPAC is

plotted against the position measured in the opposing PPAC� and these curves are

then t to the calculated angular correlations� There are two curves in these types of

plots corresponding to either the projectilelike or targetlike nucleus arriving in one

of the PPACs� There is one unique angle where the curves cross� de ned in the lab

frame by�

�cross � cos���

�

s� �

mproj

mtarg

������

wheremproj andmtarg are the mass of the projectile and target� respectively� Matching

this point in the data to the calculated value de nes a family of possible calibration

coe�cients� Since the angular correlations can be relatively featureless �as can be

seen for the ���Sm � ���Cm reaction in Figure ������ it may not be possible to pick

��

0 20 40 60 80 100Counter #10 (Degrees)

80

100

120

140

160

180

Cou

nter

#15

(D

egre

es)

Figure ����� Calibration of the back counter theta positions using the ���Cf�SF� data�The heavy line is the position measurement and the light line is the t to the data�

the calibration coe�cients unambiguously� Adding a second data set with mproj and

mtarg chosen so that �cross is signi cantly di�erent provides a method of choosing the

correct values for the calibration� For this experiment the position calibration was

performed using the reactions ���Sm � ���Cm and ���Dy � ���Sn� A leastsquares t

including both data sets then was performed to extract the calibration for each of the

� pairs of PPACs in the front array�

The back array of PPACs �� � ���� were calibrated in a similar manner� except

instead of using beam on target data� the thin source ssion data was used� The

ssion fragments leave the source colinearly� so the sum of the polar angles of their

�ight direction must add to ���� The calibrations for the back PPAC positions can

then be t referenced to the front PPAC positions� An example of this is shown in

Figure ����� Again� a leastsquares t was performed for each of the �� frontback

pairs of PPACs� but with the coe�cients for the front PPACs xed by the beam on

target calibration�

��

Figure ����� Particle identi cation� Measurement of the timeof�ight di�erence andscattering angles allows the two scattering solutions to be cleanly separated� Thetime di�erence for the two solutions is ��� ns at ��� �channel ����

����� Time Measurement and Particle Identi�cation

The targetlike and projectilelike nuclei can be identi ed if they are detected

in coincidence by plotting the scattering angle against the timeof�ight di�erence

��TOF �� An example of this is shown in Figure ����� The mass of each nucleus can

also be calculated with the assumption of twobody kinematics by

m� ��TOF��� � �d��P��Mtot

�d��P�� � �d��P�������

where �TOF��� is the timeof�ight di�erence for the left and right nucleus� and d� and

d� are the length of the �ight path for the left and right nucleus� respectively� The

momenta of the left and right nuclei �P���� are given by Equation ���� A calculated

mass spectrum is shown in Figure ���� for the reaction ���Sm � ���Cm at a lab energy

of MeV�

The resolution of the timeof�ight di�erence measurement is about ��� ns� The

various experimental factors contributing to the time resolution for a typical beam

��

50 100 150 200 250 300 350Mass (amu)

0

5000

10000

15000

20000

Cou

nts

Mass Spectrum144

Sm + 248

Cm @888 MeV

144Sm

248Cm

12amu14amu

Figure ����� Measured mass spectrum from the reaction ���Sm � ���Cm at MeV�

experiment� in this case a beam of �� MeV �lab energy� ���Dy on a ����g�cm� ���Sn

target� can be calculated and are shown in Table ���� Typical values for the energy

�Estrag� and angle ��strag� straggle of the beam and ejectile nuclei as they pass through

the target material are shown� along with their contribution to the time resolution�

The location of the reaction within the target material also e�ects the time of �ight�

since the beam and scattered nuclei lose energy as they pass through the target

material� This contribution to the time resolution is listed in Table ��� under �Target

Thickness�� The largest contribution to the time resolution uncertainty is the beam

spot size� Because of the short �ight path ���� cm� to the detectors� the � mm beam

spot subtends about �� with respect to a given point on the detectors� The energy of

the scattered nuclei varies rapidly enough with scattering angle for this to be the major

contribution to the time resolution� The resolution of the electronics can be measured

from the �selfgated� time� which should yield a narrow peak� The time measurement

is �self gated� for the particle which ful lls the valid event requirement� for instance

the second particle to reach the counter when looking for coincidences� The average

��

Time Resolution �ns�

Measured Width ����

EstragDy ���MeV� �����Sn ����MeV� �����

�stragDy ������ �����Sn ������ �����

Target thickness ����

Beam spot ��mm� ����

Electronic Resolution ����

Intrinsic Resolution �����

Table ���� Contributions to the time resolution for �� MeV ���Dy on a ����g�cm�

���Sn target�

width for the �selfgated� time peak is ��� ns� The intrinsic timedi�erence resolution�

after unfolding all of these contributions� is about ���ps� or ���ps for a single PPAC�

���� Performance of GAMMASPHERE with CHICO

The impact of CHICO on the response characteristics of GAMMASPHERE is an

important consideration when coupling these two detectors� The CHICO detector was

designed to have as little mass as possible within the scattering chamber of GAMMA

SPHERE to minimize scattering and absorption of � rays� Simulations modeling the

in�uence of CHICO on the response of GAMMASPHERE were performed ���� using

the Monte Carlo code GEANT ����� The peak e�ciency �Figure ����� and the peak

tototal ratio �Figure ���� for GAMMASPHERE were modeled with and without

�

0 500 1000 1500 2000γ−Ray Energy (keV)

0

10

20

30

40

Pea

k E

ffic

ienc

y (%

)

GEANT Simulation of Peak Efficiency

GAMMASPHERE aloneGAMMASPHERE + CHICO

Figure ����� GEANT simulation of the e�ect of CHICO on the peak e�ciency ofGAMMASPHERE for � rays emitted at the target location�

the presence of CHICO� The peak e�ciency simulation over predicts the performance

of GAMMASPHERE� giving a value of ���� compared to the measured value of

����� The simulation shows that the presence of CHICO decreases the peak e�ciency

of GAMMASPHERE by about ���� from ���� to ����� for a ���� MeV � ray� The

simulations reproduce the measured peaktototal ratio of ��� quite accurately for a

���� MeV � ray and indicate that the in�uence of CHICO reduces the peaktototal

ratio from ���� to ������ that is ����

��� Summary

A heavyion detector was constructed which can be used with GAMMASPHERE�

The detector measures scattering angles of the reaction products over a solid angle of

��� sr with �� resolution and timeof�ight di�erence with ��� ps resolution� This in

formation can be used to identify the targetlike and projectilelike nuclei� reconstruct

the kinematics of each event� and perform the Doppler correction on the � rays on an

��

0 500 1000 1500 2000γ−Ray Energy (keV)

30

40

50

60

70

80

90

100

Pea

k to

Tot

al (

%)

GEANT Peak to Total Simulation

GAMMASPHERE aloneGAMMASPHERE + CHICO

Figure ���� GEANT simulation of the e�ect of CHICO on the peaktototal ratio ofGAMMASPHERE for � rays emitted at the target location�

eventbyevent basis� The masses of the nuclei can be resolved to �m�m � ��� The

detector has a minimum amount of mass within the GAMMASPHERE scattering

chamber� and hence minimally degrades the response characteristics of GAMMA

SPHERE� The design of the detector included development of compact highgain

ampli ers and a strip line transmission line� allowing the ampli ers to be placed

within the detector housing� reducing problems with electronic noise� The develop

ment of threelayer cathode boards yielded improved position resolution�

The detector has become an important part of the GAMMASPHERE program

and has been used to study a variety of physics by various reactions including the

Coulomb excitation and production of neutronrich nuclei in the mass ���� region viatransfer reactions ��� ���� searches for doubleoctupole phonon strength in ���Pb ����

��� and �Zr ����� a feasibility study of populating transuranic nuclei via heavyion

transfer ����� population of the neutronrich nuclei in the �� � A � �� region using

a fusion ssion reaction ����� a study of Kforbidden transitions in ��Hf by Coulomb

excitation ���� and spontaneous ssion of ���Cf�SF�� described in the present work�

��

Chapter �

���Cf Spontaneous Fission

Experiment Description

��� Introduction

As mentioned in the introduction� spontaneous ssion provides a method for the

study of neutronrich nuclei� The technique of using the latest generation of large

� ray detector arrays in conjunction with a ssionfragment detector expands the

research opportunities for the study of properties of neutronrich nuclei produced

in spontaneous ssion� In previous experiments using these large � ray detector

arrays� thick ssion sources were used which stopped the recoiling ssion fragments

within the source � ���� ��� ��� ���� for example�� The stopping times of the recoiling

ssion products in the source are on the order of � ����� seconds� Transitions with

lifetimes on the order of the stopping times su�er Doppler broadening� limiting the

observation of highspin transitions� The data collected in these experiments comprise

highstatistics highfold � rayevents� By using a ssionfragment detector with these

large � ray detector arrays additional information and selectivity can be achieved�

In the present experiment the heavyion detector CHICO was coupled to the � ray

detector array GAMMASPHERE and a thin ssion source was used� allowing the

the ssion fragments to recoil into vacuum and be detected in coincidence with the

deexcitation � rays of the ssion products� The additional information gained from

��

Figure ���� Schematic of the ssion experiment setup� The PPAC array �CHICO�� isshown with two representative GAMMASPHERE Ge detectors and the ssion source�

the coincident detection of the ssion fragments with their deexcitation � rays results

in greater selectivity and provides a means of extracting more information from each

ssion event� The mass division can be measured� allowing the sorting of the copious

� rays by mass region� and provides a means of assigning the � rays to either the

heavy or light ssion partner� Since the ssion partners recoil into vacuum� the

problem of Doppler broadened line shapes is eliminated� allowing the observation of

levels at higher spin and excitation energies� The experimental method� analysis� and

selectivity achievable with this technique are described in this chapter�

��� The Experiment

The experiment was conducted using GAMMASPHERE at Lawrence Berkeley

National Laboratory� The experimental setup �Figure ���� comprises the CHICO

��

detector� GAMMASPHERE �both described in Chapter ��� and a �thin� �� �Ci

���Cf spontaneous ssion source that allows the ssion fragments to leave the source�

Details of the source and choice of spontaneously ssioning isotope are discussed is

section ������

The CHICO detector detects the recoiling ssion fragments� measuring the time

of�ight di�erence and direction of the fragment�s �ight� GAMMASPHERE coinci

dently measures the energy and direction of the deexcitation � rays emitted by the

ssion fragments� The experiment was conducted with � Ge detectors installed in

GAMMASPHERE� Graded absorbers made of ����� mm ������ in�� Cu and Ta foil

were placed over the � ray detectors and ���� mm ������ in�� Pb absorbers were

placed over the BGO detectors to attenuate xrays� Events with two particles and at

least � � rays were collected at a rate of � ���� events�second� The experiment ran

for about � hours in which total of � �� ��� events were recorded�

����� The Fission Source

Selection of the proper spontaneous ssion source material is critical to the suc

cess of this type of thin source experiment� The choice of a suitable spontaneously

ssioning isotope is limited by availability and isotopic properties such as the halflife

and strength of the spontaneous ssion decay branch� Previously� thick source exper

iments with large � ray detector arrays have been performed with ���Cm ����� ��� for

example�� ���Pu ���� and ���Cf ���� ���� A primary consideration in the selection of

isotope for thin source is the amount of source material needed since the ssion frag

ments need to be able to leave the source material without appreciable energy loss�

The amount of ssioning isotope needed is proportional to the halflife and inversely

proportional to the ssion branchingratio� These quantities� along with the mass of

material needed for a source with the strength as used in the present experiment� are

shown in Table ����

Of these� ���Cf is the most suitable for a thin source� A ���Cf source of su�cient

strength is essentially massless� with about �� nanograms of isotope needed� A source

of the same strength made from ���Cm would require about � milligrams of material�

��

isotope � ��

BRSF ��� ���� mass �g� for a �k�sec source���Pu ���� ��� y ���� ���� ������Cm ��� ��� y ���� ���� ��� �������Cf ����� y ���� �� ��� ����

Table ���� Selection criteria for a thin ssion source isotope�

making it marginal since too much energy would be lost by the ssion fragments

passing through the source material� A ���Pu source of the same strength would be

unusable since the ssion fragments would not make it out of the �� g of requiredsource material�

The ssion source used in this experiment consisted of �� �Ci of ���Cf electro

plated to a region about � cm in diameter on a ��� �g�cm� Ni foil� The source was

mounted in CHICO with a �� �g�cm� carbon foil covering the ssion material to

prevent selftransport of the ���Cf� The nickel and carbon foils are thin enough to

allow the ssion fragments to leave the source� The source was produced by Mark

Stoyer at Lawrence Livermore National Laboratory�

��� Thick Source Data

Some of the data presented in this thesis� the Rh level diagrams and Pd spectra

in Chapter � and the ���I spectrum in Section ���� is from a thick source ���Cf�SF�

experiment ���� ���� This experiment was performed with a �� �Ci ���Cf source

sandwiched between two ��� mil Ni foils and two � mil thick Al foils� The experiment

was performed with GAMMASPHERE with �� Compton suppressed Ge detectors

and a total of ��� �� triple or higher fold � ray coincidence events were collected�

��� Analysis

The measured quantities in the thin source experiment are the timeof�ight dif

ference of the ssion partners and the Doppler shifted energies of the � rays� This

��

section describes how the relevant quantities� the mass division between the ssion

partners and the transition energies are extracted from the experimental data�

����� Mass Measurement

The average value of the total kinetic energy released for a given mass division

�TKE�MH �ML��� and its standard deviation ��TKE�MH �ML�� in spontaneous ssion of

���Cf are well measured quantities ���� ��� ��� ���� The TKE�MH �ML� can be used

to calculate the initial recoil velocities of the emitted ssion fragment pairs� With the

inclusion of experimental considerations� such as energy loss of the recoiling ssion

fragments in the target material and geometric variation of the �ight path length�

the experimentally measured timeof�ight di�erence can be used to deduce the mass

division and nal velocities of the ssion fragments on an eventbyevent basis� Rather

than using an iterative algorithm analyzing each event separately� where the initial

mass division is guessed� then corrected for energy loss e�ects� and repeated until

convergence� which would be computationally time consuming� the timeof�ight

di�erence as a function of mass division and ssion axis orientation was calculated

�as described below� and stored in a lookup table� The quantities important to the

subsequent analysis� the nal velocities of the ssion fragments� mass division� and the

time of the ssion� t� with respect to the detected coincidence� can then be retrieved

based on the measured timeof�ightdi�erence and ssion axis orientation�

For binary ssion events� the initial velocities of the two ssion fragments can be

calculated� Conservation of momentum constrains the two fragments to have equal

and opposite momenta� The kinetic energies �KEH�L�� velocities �vH�L�� and timeof

�ight di�erence ��TOF � of the complimentary heavy and light fragments with masses

MH and ML� respectively� are given by�

KEH�L �ML�H

ML �MH

TKE�MH �ML� �����

vH�L �

vuut�ML�HTKE�MH �ML�

�MH�L��ML �MH������

��

�TOF �dL��L� �L�

vL� dH��H � �H�

vH�����

where d��� �� is the �ight path length which is dependent� due to the geometry of the

detector� on the orientation of the ssion axis�

The recoiling ssion fragments travel either through the ����g�cm� Ni backing

foil� or the ���g�cm� carbon cover foil during their �ight to the particle detectors�

The fragments will loose some of their kinetic energy as they travel through the

material� e�ecting their nal recoil velocities� The amount of energy lost depends

on both the nuclear charge and velocity of the ssion fragments and the amount of

material through which they pass� For a given mass division the nuclear charge ZH�L

of the heavy and light fragments were assumed to be proportional to the masses�

ZH�L �MH�L

MH�MLZtot where MH �ML sums to ��� amu� the nuclear mass of

���Cf�

and Ztot is the total nuclear charge of �e� The amount of backing foil or cover foil

material that the ssion fragments travel through is inversely proportional to the

cosine of the angle of ssion axis� The energy loss was calculated using the program

ENELOSS ���� The nal velocities of the ssion fragments were then calculated by

subtracting the energy lost in the nickel backing foil or carbon cover foil from the

initial kinetic energies KEH�L given in Equation ����

The �TOF depends on the �ight path distance d��� �� of the fragments� which in

turn depends on the geometry of the detector and the � and � angle of the ssion

axis� For the geometry of CHICO the distance from the target to the PPAC is given

by

d��� �� �d�

cos���sin����� � sin���cos�����cos���������

where d� is the distance from the target to the PPACs along the normal ���� cm�

and �� is with respect to the centerline of a given PPAC�

Figure ��� shows the dependence of the calculated masses on the timeof�ight

di�erence and angular orientation of the ssion axis� The timeof�ight di�erence

maps into a unique mass division for a given �� � orientation of the ssion axis� At

large angles� above about ���� there is signi cant energy loss in the target material

and the coincidence particle detection e�ciency drops �see Figure �����

��

0.0 20.0 40.0 60.0 80.0Theta

−35.0

−25.0

−15.0

−5.0

5.0

15.0

25.0ΔT

OF

(ns)

Map of T.O.F to Mass500μg Ni Backing and 20μg C Cover foil

60

80

120

160

200

180

140

100

Mass of forward fragment

Figure ���� The mass division between the ssion partners can be uniquely mappedfrom the timeof�ight di�erence of the recoiling nuclei and angular position of the ssion axis�

The resolution of the mass measurement based on the timeof�ight is about

mass units �FWHM�� The resolution was measured by gating the � ray spectra on

transitions in speci c nuclei and projecting the measured mass for these events� An

example of the mass measurement based on the timeof�ight di�erence is shown in

Figure ����

����� Gammaray Analysis

Doppler Correction

The ssion fragments leave the source with velocities on the order of a few percent

of the speed of light� The measured energies of the � rays emitted during the �ight

��

0 10 20 30 40 50 60 70 80 90Theta (deg)

0

5000

10000

15000

Fission Position Spectrum

Figure ���� Position spectrum from the ���Cf�SF� experiment� The solid line showsthe expected solidangle dependence of the yield� Above ��� the yield drops due totarget e�ects�

of the ssion fragments are appreciably Doppler shifted and need to be transformed

back to their rest frame to extract the transition energies� The transformation of the

� energies to their rest frame is given by

E � E ��� cos���p��p

�� ������

where E is the true transition energy in the deexciting nuclei�s rest frame� E � is

the energy measured in the lab frame� ��p� is the angle between the ssion fragment

velocity vector and the direction of the emitted � ray in the lab frame� and � vc�

The timeof�ightdi�erence measurement provides the velocities of the fragments� as

discussed in section ������ The angle between the emitted � ray and the direction

of travel of the nuclei� ��p� � is known since the orientation of the ssion axis ��p�

�p� is measured by CHICO� and the direction of the � ray ���� ��� is measured by

GAMMASPHERE� The angle ��p� is given by

cos���p�� � sin��p�sin����cos��� � �p� � cos��p�cos���� �����

�

70 90 110 130 150 170Mass (amu)

252Cf SF Mass Spectrum

144Ba

134Te

Total Mass Yield

FWHM=8 amu

Figure ���� Measured Mass Resolution� The measured mass for individual nuclei areprojected by setting double gates on � ray transitions� The relative intensities of themass distributions are not to scale�

where �p� �p and �� � �� are the direction of travel of the nuclei and � ray� respectively�

The � ray line shapes in the raw spectra are broad and �at due to the Doppler

shift� Sharp � ray line shapes are recovered by performing the Doppler correction

on an eventbyevent basis� It is not known a priori whether a detected � ray was

emitted from the heavy or light ssion partner and� hence� it is not determined

whether the Doppler correction should be performed for the heavy or light nucleus�

In the application of the heavy �light� Doppler correction to the data set� the sharp

� ray line shapes are recovered for the heavy �light� nuclei�s � rays� and the light

�heavy� nuclei�s � ray line shapes are broadened further� A simulation of the e�ect

of the correct and incorrect Doppler correction is shown in Figure ����

�Ray Resolution

The � ray resolution is an important quantity for experiments of this type� The

analysis relies heavily on examining the � ray coincidence relationships both from

��

440 460 480 500 520 540 560γ−ray Energy (keV)

0

1000

2000

3000

Cou

nts

Light fragment γ−ray

Raw line shapeLine shape after’’heavy’’ Doppler shift

Line shape after’’light’’ Doppler shift

Figure ���� E�ect of heavy�light Doppler correction on raw � data� This gure showsthe results of a simulation of the raw line shape and the line shapes after the complimentary Doppler corrections are applied�

individual nuclei and correlated ssion pairs by setting gates on speci c � rays� Since

there are over one hundred daughter nuclei populated in the spontaneous ssion of

���Cf� each of which may have ��� distinct transitions� there will be transitions indi�erent nuclei which have nearly the same energy� Gates on � rays which overlap

with �spurious� nuclei will introduce false correlations� It is necessary to check that

the energy resolution is optimized to reduce this problem�

The fullwidthhalfmaximum �FWHM� of the � ray peaks can be described with

the function

FWHM � �A�� � A�

��pE�� � A�

��E���

�

� �����

where A� is related to the noise in the detector and ampli er� A� is related to the

counting statistics of the charge collection within the � ray detectors� and A� is

related to the Doppler broadening of the � ray peaks ����� For situations where the

��

deexciting nuclei have no recoil velocity� such as in thick target experiments or the

use of � ray calibration sources� the term A���� The measured resolution along with

the contributions from each of the terms in Equation ��� for the ssion experiment

is shown in Figure ��� and the intrinsic resolution for GAMMASPHERE is shown in

Figure B��� The noise and counting statistics terms for the ssion experiment and

calibration sources show good agreement� The � ray energy resolution for the ssion

experiment is dominated by the Doppler broadening term�

Primary contributions to the Doppler term A� of Eqn� ��� in the ssion experiment

are the angle uncertainty in the direction of the � ray due to the opening angle of the

� ray detector and the variation in the total kinetic energy� �TKE� for a given mass

division� The statistical variation in total kinetic energy of the ssion products in

spontaneous ssion of ���Cf is on the order of �� MeV out of �� MeV� leading to a

variation of about �� in fragment velocity� or about ���� variation in the Doppler

corrected energy of the � rays� The Doppler corrected energy also is dependent on

the angle between the direction of travel of the � ray and the ssion fragment and is

described by the relation

dE

E� sin��p��d�p� ����

The � ray detectors have an opening halfangle of � �� ����� rad�� For typical recoilvelocities of � ����� the error in the Doppler corrected energy due to the angle

uncertainty is about ���� for � ray detectors located at ��� to the ssion axis� where

the solidangle is a maximum� These contributions account for nearly all of the

degradation of resolution� and for the current experiment cannot be improved upon�

��� Gamma�ray Spectrum Analysis

The development of large � ray detector arrays allows highfold detection of high

multiplicity � ray events� The coincidence relationships between � rays in these high

fold events carry the information used in construction of level diagram and identi

cation of correlated nuclei� Examination of the coincidence relationships of � rays

from the same nucleus determines the decay sequences of that nucleus� from which

��

0 500 1000 1500 2000E (keV)

0

5

10

15

FWH

M (

keV

)

Fission Data γ−ray ResolutionFWHM=(A1

2+A2

2(E

1/2)

2+A3

2(E)

2)

1/2

Total FWHMFission DataA1=1.21 (Noise)A2=0.0657 (Counting)A3=0.0059 (Doppler)

Figure ���� Measured � ray energy resolution in the thin source ���Cf�SF� experiment�The e�ect of detector noise� counting statistics and Doppler broadening are included�

the level diagram can be deduced� The coincidence relationships among � rays from

partner nuclei can identify which reaction products are correlated� In the case of this

thin source ssion experiment� the � rays for either the heavy or light ssion part

ner can be selected by means of the Doppler correction� as shown in section ������

The level diagrams for the ssion products can be constructed by examination of

coincident � rays with the same applied Doppler correction� The identi cation of

correlated ssion partners is performed by using the correlations between � rays with

complimentary applied Doppler corrections�

The analysis of � ray coincidence relationships is performed by sorting events with

three or more � rays into threedimensional histograms� or cubes� where the axis of

the cube represent the energy of the � rays� For events with more than three � rays�

all subcombinations of � � � triples are �unpacked� from the higher order ntuples

and histogrammed� The � ray correlations can then be studied by setting gates on

two axis of the cube and projecting onto the third axis� The multiplicity distribution

��

0 5 10 15Clean γ multiplicity

10−8

10−6

10−4

10−2

100

102

Cou

nts/

# of

Tri

ples

Clean γ−Ray Multiplicity Distribuiton

raw multiplicitiesunpacked triples

Figure ���� The multiplicity distribution �normalized to the number of triple events�and number of unpacked triples from clean � rays events from the thin source���Cf�SF� experiment�

of clean � rays and number of unpacked triples for the thin source ssion experiment

is shown in Figure ���� The largest contribution of triples to the histogram is from

unpacked fourfold � ray coincidences�

Symmetric Cubes

The symmetric cubes are created by histograming the unpacked � � � events

with the same type of Doppler correction� either heavy or light� applied to each of

the � rays� In practice� the � ray triples are ordered in energy before histograming

�E��� E��

� E��� and each � ray triple is only histogrammed once� This requires

only one sixth of the storage space needed compared to a cube where all permutations

are histogrammed� and still carries the same information� The gating and display

software LEVITR ���� used in the analysis of the symmetric cubes performs the

necessary unfolding of the one sixth cube when gates are applied to the cube�

��

The symmetric cubes were used for developing the level diagrams for the nuclei

populated in the present thin source ���Cf�SF� experiment� The events that are useful

for developing the level diagrams are those with which three or more � rays originate

from the same nucleus� Gating the cubes on known transitions in a speci c nucleus

projects out coincident transitions of the possible decay sequences which include the

gated transitions� The � ray triples can have one� two� or three of the � rays emitted

by the partner of the nucleus of interest� but these events are not observed in the

projected spectra since the application of the Doppler correction broadens the line

shapes of the � rays from the partner nuclei to a level near the background�

Asymmetric Cubes

Asymmetric cubes are data structures which have two axis that are symmetric�

where the � rays have the same type of applied Doppler correction� and the third axis

where the � ray has the complimentary Doppler correction applied� A given � ray

triple is histogrammed three times� once with each � ray of the triple histogrammed

along the asymmetric axis and the other two along the symmetric axes� The pair of

� rays histogrammed along the symmetric axes are again ordered by energy �E���

E��� before histograming to save storage space�

Analysis of the � ray coincidence relationships from the thin source data between

two correlated nuclei was performed with asymmetric cubes� Setting gates on transi

tions in a nucleus along the symmetric axes projects out transitions from the partner

nuclei� This procedure can be used to identify the nucleus of origin for unknown de

cay sequences� If the partner nuclei can be identi ed� then� since the nuclear charge

is conserved in the ssion process� at least the charge of the nucleus from which the

gated transitions originated can be identi ed�

Background subtraction

There are several sources of background in the � ray spectra� The Compton sup

pression in the GAMMASPHERE Ge detectors does not remove all of the Compton

scattering events� re�ected in the peaktototal ratio of ���� There are also statistical

��

� rays from decay of nuclei populated in the quasicontinuum region which do not

give discrete � ray peaks� For the thin source ssion experiment� � rays which are

histogrammed with the wrong Doppler correction also contribute to the background�

In the analysis of the symmetric cubes the software package LEVITR subtracts

a background built from the crossproducts of lowerdimensional projections of the

threedimensional histograms� The threedimensional background is de ned as

Bijk ��

T�Mijbk �Mikbj �Mjkbi�

��

T ���Pibjbk � biPjbk � bibjPk � bibjbk� �����

where T is the total number of counts in the histogram�M is the total twodimensional

projection of the cube� P is the total onedimensional projection of the cube onto one

axis� and b is the background drawn under the total projection P ����� For the sym

metric cubes� the three twodimensional projections� M� and the total projections� P�

and the � dimensional total background� b� are the same regardless of which direction

the projections are taken�

A background subtraction was implemented based on Equation ��� for the analy

sis of asymmetric cubes� The background for spectra projected from the asymmetric

cubes use the same method� except the two dimensional projections� total projections�

and backgrounds are di�erent depending on which direction the projections are taken�

Performing a background subtraction in the analysis of asymmetric cubes is impor

tant since the background from events histogrammed with the wrong combination of

Doppler corrections is three times as large as for the symmetric cubes�

�� Selectivity

����� Mass Gating

The measurement of the mass division of the ssion partners provides additional

selectivity and enhances the ability to study nuclei produced with low yield� The

� ray data can be histogrammed with gates set on the measured masses of the s

sion fragments� Selecting � rays from speci c mass regions reduces the � ray �back

��

ground� of the nuclei which are not of current interest which allows observation of

weak transitions which might otherwise be obscured�

As an example� the prompt � rays from ���Dy were observed in a massgated spec

tra of the thin source ���Cf�SF� �Figure ���� ���Dy is produced in ���Cf�SF� at a level

of ��� ���� of the total mass yield ����� The yrast band was observed by summing

multiple doublegates on the yrast transitions� The yrast band of ���Dy has been pre

viously identi ed to a spin of ���h in the �n transfer reaction ���Sn����Dy����Dy����Sn

performed using CHICO in conjunction with GAMMASPHERE ���� The same gates

used to produce the top spectrum in Figure �� with a symmetric cube were applied

to an asymmetric cube to project out the ssion partner � rays� Two � rays from

the Dy ssion partner Ge were observed to be in coincidence� con rming that the

observed rotational band belongs to Dy�

����� Selectivity Provided by the Doppler Correction

The application of the Doppler correction allow the � rays to be assigned unam

biguously to either the heavy or light ssion partner� and� with the application of

appropriate � ray gates� spectra which include sharp � ray peaks from only one nu

cleus can be generated� In the thick source experiments� since the � rays are emitted

after both the ssion partners come to rest in the source material� it is not possible to

identify from which nucleus the � ray originates without relying on the systematics of

the � ray coincidence relationships� The thick source spectra gated on � rays of one

particular nucleus brings back not only coincident � rays from that nucleus� but also

� rays from the several partner nuclei� Setting gates on symmetric cubes from the

thin source data� where the applied Doppler correction broadens the � ray line shapes

from the partner nuclei� provide spectra which have � rays only from the nucleus of

interest� The resultant spectra are more straight forward to interpret� Spectra with

the same gates on transitions in ���Mo from the thick source and thin source data are

shown in Figure ����

The Doppler correction in conjunction with the geometry of CHICO provides a

method of separating � rays from prompt decays from � rays emitted after decays of

��

0 200 400 600 800 1000 1200 1400−100

0

100

200

−13

47 82

Ge

−93

8 82

Ge

0 100 200 300 400 500 600 700 800 900 1000−100

0

100

200

300

400

−17

7 4+

⇒2+

−27

7 6+

⇒4+

−36

4 8+

⇒6+

−44

9 10

+⇒

8+

−52

6 12

+⇒

10+

−59

6 14

+⇒

12+

166Dy (4.9x10

−5/fission)

Figure ��� Observation of ���Dy in ���Cf�SF�� The top gure shows the groundrotational band of ���Dy� The bottom gure shows the coincident transitions in ��Ge�

isomeric levels� The prompt � rays which are emitted during the ��� ns �ight of the ssion partners are seen as sharp peaks in the � ray spectra only after the Doppler

correction is applied� After the nuclei implant in the PPACS� the emitted � rays are

observed as sharp peaks in the spectra only if no Doppler correction is applied since

the nuclei no longer have a recoil velocity� Figure ���� shows a � ray spectrum with

no Doppler correction applied�

��

0 100 200 300 400 500 600 700 800 900

0

10000

20000

30000

104Mo Transitions−

144 B

a 2+

−0+

−14

4 Ba

4+−

2+

−14

4 Ba

6+−

4+

−14

4 Ba

8+−

6+

−14

2 Ba

2+−

0+

−14

2 Ba

4+−

2+−

144 B

a 8+

−6+Thick Source

0

2000

4000

6000

8000

104Mo

−10

4 Mo

2+−

0+

−10

4 Mo

4+−

2+

−10

4 Mo

8+−

6+

−10

4 Mo

10+−

8+

−10

4 Mo

12+−

10+

−10

4 Mo

14+−

12+

Thin Source

−G

ate

Figure ���� The top gure shows a gated spectrum from the thin source data� Thebottom spectra is with the same applied gates in the thick source data�

����� HK Measurement

GAMMASPHERE can perform as a high e�ciency sum spectrometer� The BGO

crystals in the Ge detectors used for the Compton suppression can also be used as

highe�ciency lowresolution � ray detectors� The BGO crystals were calibrated �see

Section B� and the total energy and multiplicity of the ssion events were recorded�

The total energy included �clean� � rays� Compton scattered events� and BGO only

events� The total energy and multiplicity �HK� and the projections are shown in

Figure �����

�

0 500 1000 1500 2000Energy (keV)

0

10000

20000

Isomeric Transitions

Figure ����� Delayed � ray �isomer� spectrum�

The HK information can be used to gate the � ray spectra� A di�erence in relative

intensities of peaks in spectra gated on di�erent HK regions would indicate that the

total � ray energy and multiplicity is dependent on the mass division between the

ssion partners� Two spectra gated on the regions shown in Figure ����c are shown

in Figure ���� and there are di�erences between these spectra� This selectivity can

be used to study the dynamics of the ssion process� but lies beyond the scope of this

thesis�

����� Observation of Levels at Higher Spins and Excitation

Energy

The use of a thin source makes it possible to observe transitions at higher spins

and excitation energies than with the thick source experiments� In the thick source

��

0 10 20 30 40 50 60 70 80 90MeV

Energy ProjectionC

ount

s

0 10 20 30 40 γ−ray Multiplicity

100

102

104

106

108

Cou

nts

Total Multiplicity Projection

Figure ����� Total energy and multiplicity in ���Cf�SF��

��

0 200 400 600 800 1000Energy (keV)

0

1e+06

2e+06

3e+06

4e+060 200 400 600 800 1000

0

5000

10000

15000

20000

H−K Gated γ−ray Spectra’Light’ Doppler Correction

High energy gate

Low energy gate

Figure ����� � ray spectra with the �light� applied Doppler correction gated on thetotal energy and multiplicity regions shown in Figure ����� The top gure is from thehigher total energy region and the lower gure is from the lower total energy region�

experiments� the recoiling ssion fragments slow down and stop in the source in�� ps�Gamma rays emitted during the slowing down process are Doppler shifted and� hence�

the line shapes of � rays from transitions with lifetimes comparable to the stopping

times are Doppler broadened� In the thin source experiment most of the � rays

are emitted while the ssion partners are recoiling at their full Coulombaccelerated

velocities� After the Doppler correction is applied� there is no lineshape broadening

��

450 550 650 750Energy (keV)

0

200

400

600450.0 550.0 650.0 750.0

0

200

400

600

800

12−10

14−12

16−14

18−16

20−1822−20

12−10

14−12

16−14

18−16

20−18

154Nd

152Nd

Figure ����� Using a thin source eliminates Dopplerbroadened line shape problemsand allows observation of levels with shorter lifetimes and high spin� The spectrum onthe right ���� is from ���Cm in a KCl crystal and shows the e�ect Dopplerbroadeninghas for higher lying transitions�

as for recoiling fragments in a thick source� Sharp lineshapes for transitions with

lifetimes on the order of the � � ps stopping time are recovered� Spectra showing

transitions from the same isotopes observed in the thick and thin source experiments

are shown in Figure ����� and the e�ect of the Doppler broadening can be seen in

the thick source spectra� Typically in the thin source data the level spectrum can be

extended by two or more levels� allowing observation of levels with spin up to ���h

and excitation energies of � � MeV� The extension of rotational band structures is

seen not only for the yrast bands� but also for the more weakly populated side bands�

Level diagrams that have been extended are shown in Chapter ��

��

�� Summary

A technique of studying ssion products of ���Cf�SF� using a large solidangle

particle detector array �CHICO� with the latest generation of � ray detector arrays

�GAMMASPHERE� was developed� In this experiment� highstatistics data con

sisting of highfold � ray events along with the timeof�ight of the ssion partners

were collected� The additional information provided by the coincident detection of

the ssion products provides selectivity and sensitivity beyond what is possible with

thick ssion source experiments� The timeof�ightdi�erence provides a means of

measuring the masses of the ssion products with a resolution of � amu� The

mass information can be used to gate the � ray spectra allowing the study of nuclei

produced with low yield� A detection sensitivity to a yield of � ����� ssion was

achieved�

Since the ssion products recoil freely into vacuum� the deexcitation � rays emit

ted during the �ight of the ssion products need to be Doppler corrected� This allows

the � rays to be unambiguously assigned to either the heavy or light ssion product�

The resultant spectra are cleaner� since they contain � rays from only one species�

either heavy or light� of ssion product� Levels at higher spins and excitation en

ergies are observable in this experiment than in the thick source experiments since

the � ray lineshapes are not Doppler broadened due to the stopping times of ssion

products in the source� Rotational bands can typically be extended by a few levels�

��

Chapter �

Neutron h��

�band structures in the

neutron�rich Pd

��� Introduction

The neutronrich nuclei Pd are in a region of the nuclear landscape where interest

ing shaperelated properties occur� For example� the lowlying energy level structure

and measured � ray branching ratios of neutronrich Ru are consistent with stable

triaxial quadrupole deformations ���� ���� Also� the even mass neutronrich Pd and

Mo nuclei have a lowlying �� bands indicating the importance of the � shape pa

rameter� Theoretical calculations of the ground state shapes for the neutron rich Pd

predict a shape change from prolate to oblate with increasing neutron number� Cal

culations of the quadrupole potential energy landscape using the NilssonStrutinsky

method� with the cranked WoodsSaxon average potential and a monopole pairing

residual interaction� show that these nuclei could have shallow minima making them

susceptible to � vibrations or even stable triaxial deformation� and that minima at

both prolate and oblate shapes might exist ����� This calculation predicts a shift

in the ground state shape from prolate to oblate with increasing neutron number

for the even mass Pd beyond ���Pd� Calculations using the nite range liquid drop

model predict the shift from prolate to oblate shapes to occur at mass ��� for the

Pd ���� ���� Experimentally observed properties of the neutronrich nuclei provide a

��

means of testing the predictive power of the various models�

Since the neutronrich Pd isotopes are unstable to decay� direct measurements

of the shaperelated properties� such as the E� matrix elements along with their

relative phase� are currently not experimentally feasible� The highspin behavior of

the yrast rotational bands� however� can be used to deduce the shape properties of

the ground state con gurations� The highspin behavior of the palladium nuclei in

this region has been studied recently by a variety of reactions� Heavyion fusion

evaporation reactions were used to populate ������Pd and the neighboring ��Ag �����

deepinelastic reactions were used to investigate ���Pd ���� and ������Pd were studied

via a fusion ssion reaction ����� While the above reaction mechanisms allow some

selectivity of the resultant nuclei� there is a limit to how far from stability toward

the neutron rich side that these reactions can reach� Population of the neutronrich

Pd currently relies on either spontaneous or induced ssion of a heavy nucleus� The

levels of neutronrich Pd observed via induced ssion have been observed through the

decay of Rh ���� ��� ��� and hence have yielded little information on the high spin

behavior� High spin states in neutron rich �����������Pd have been observed in previous

���Cf�SF� experiments using the high e�ciency of large � ray arrays ���� ���� The

highspin properties of these nuclei are of interest since the band crossings can be

observed� giving evidence of the nuclear shape�

As noted in Ref� ����� the yrast band structures of �����������Pd are similar� hav

ing band crossings of nearly identical moments of inertia� The authors of Ref� ����

attribute the rst band crossings in these nuclei to the alignment of a ��g ��� pair

based primarily on comparison to cranked shell model calculations performed with

the assumption of oblate shapes predicted by the nite range droplet model ����� This

conclusion was made without the bene t of either the observation of the completion

of the back bend� from which the total aligned angular momentum can be measured�

or knowledge of rotational bands in neighboring odd A nuclei� both of which can be

used to deduce the type of orbital involved in the alignment� In subsequent work� the

properties of the rotational bands based on �h���levels observed in the odd neighbor

ing nuclei ������Pd have con rmed the ��h����� nature of the band crossings observed

in the even �������Pd ground state bands ����� implying prolate shapes for these nu

��

clei� Since the moments of inertia are so similar for �����������Pd� the discrepancy in

the identi cation of the orbitals responsible for the band crossing in ���Pd calls into

question the proposed ���� ��g ��� nature of the band crossings in �������Pd�

In the present work rotational bands in the odd neutron �������Pd and odd pro

ton �������Rh ���� have been identi ed� as well as additional levels in the eveneven

�����������Pd� The band crossings in these rotational bands give evidence that the

aligning nucleons occupy ��h����� orbitals� Comparison with cranked shell model

calculations suggest that �������Pd nuclear shapes are prolate for the ground state

con gurations�

��� �������Pd Ground Bands

The lowlying levels ��� MeV� of ���Pd have been identi ed previously in decay

of ���Rh ����� The ground state of ���Pd was assigned a spin and parity of ��

�based

on the properties of its decay to ���Ag ����� with a con guration based on a mixture

of the spherical shell model neutron states �d��and �g

������ Other levels and spin

assignments observed in Ref� ���� and relevant to this work� are at ��� and ��� keV�

The level at ��� keV �with no previous spin or parity assignment� decays directly to

the ground state and also by a ��� keV � ray to the level at ��� keV� The ��� keV

level has been assigned a spin and parity of �

�and its decay to the ground state is by

an M� transition ����� The ���� ���� and ��� keV transitions are also observed in both

the thick and thin ssion source data sets� Gates on these transitions in the thick

source data clearly show the coincidence of these lines with several of the Te ssion

partners �Figure ����� The coupled bands shown in the level diagram �Figure ����

were constructed by relying on the � ray coincidence relationships elucidated by

setting various combinations of double gates in the thin source data cubes� The spin

assignments for these levels are tentative and are based on the probable spin of �

�

assigned to the ��� keV level in Ref� ���� and on the decay pattern of the band� The

highest spin and excitation energy observed for this band is ���at ���� MeV�

The construction of the ground band of ���Pd from transitions seen in ���Cf�SF�

is similar to the method described for ���Pd� The low lying levels are known from

��

0 500 1000−100

0

100

200

300

400

500

−13

4 Te

2+→

0+−13

5 Te

15/2

−→

11/2

−

−13

5 Te

11/2

−→

7/2−

−13

6 Te

2+→

0+

−13

6 Te

4+→

2+

−13

6 Te

6+→

4+

−13

4 Te

4+→

2+

Thick Source−

113Pd transitions

0 500 1000

0

50

100

150

200

113Pd

189.7−265 keV Double Gate

Thin Source

−11

3 Pd

13/2

+→

9/2+

−11

3 Pd

11/2

+→

9/2+

−11

3 Pd

19/2

+→

15/2

+

−11

3 Pd

17/2

+→

13/2

+

−11

3 Pd

13/2

+→

11/2

+

Figure ���� Spectra double gated on the ���� and ��� � rays in the thin �upper�and thick �lower� source data

decay of ���Rh ���� ���� The adopted ground state spin of ���Pd was assigned to be��with positive parity in Ref� ���� based on odd Pd systematics� but Ref� ���� assigns

a spin of ��� In the present work we will assume the more recent value of �

�for this

level� Levels decaying to the ground state which are observed both in decay and

ssion are at �� keV and �� keV� The �� keV level decays to the �� keV level

with the emission of a ��� keV � ray� By setting gates in the ssion data on the ����

��

0.75 50.75 100.750

2000

4000

6000

Ene

rgy

(keV

)

113Pd

81

464

1035

1757

2587

3479

4437

5509

190

716

1345

2029

(9/2+)455

1032

1679

2343

(13/2+)

1072

958

892

830

722

571

383

(17/2+)684

629

526

(21/2+)

664

647

577

6719

(5/2+)(9/2−)

(13/2−)

(17/2−)

(21/2−)

(25/2−)

(29/2−)

(33/2−)

(37/2−)

0.4 s (7/2+)

(11/2+)

(15/2+)

(19/2+)

1210

(41/2−)

2705(23/2+)

676

Figure ���� ���Pd level diagram

�� keV � cascade depopulating the �� keV level� other coincident transitions are

observed� Again� the coincidence relationships used to identify members of the band�

and the observed intensities were used to order the transitions within the band� Only

one signature of this band was seen� and the band was observed to a presumed spin

of ��and an excitation energy of ��� MeV�

��� Isomeric bands in �������Pd

The odd palladium nuclei beyond ���Pd are known to have a negative parity band

built on a decoupled �h���orbital �see Figure ����� As the neutron Fermi level rises

with increasing neutron number� the band head energy drops� reaching a minimum

at ���Pd� just past the middle of the neutron shell� These negative parity band heads

become isomeric for ��Pd and beyond� The spins for the band heads are ���

�through

���Pd� whereas the most probable spin for the band head changes to �

�for ���Pd

and ���Pd ����� The decay of these isomeric levels is strongly hindered with respect

�

65 115

0

2000

4000E

nerg

y (k

eV)

115Pd

641

791

938

3120

3911

4849

89

483

1062

1806

2690

3686

4758

128

468

956

1483

1962

2479

1072

996

884

744

579

394

516

479

518

489

340

(33/2+)

(29/2+)

(17/2+)

(13/2+)

(11/2+)

(21/2+)

(25/2+)

(9/2+)

(3/2+)(9/2−)

(13/2−)

(17/2−)

(21/2−)

(25/2−)

(29/2−)

(31/2−)

50 s (5/2+)

Figure ���� ���Pd level diagram

to Weisskopf singleparticle estimates� for example the hindrance factor for the M�

decay of the �

�isomeric level in ���Pd to the ground state is ��������� The authors of

���� suggest that large shape di�erences between the ground state and isomeric state

could be the cause of these large hindrance factors� possibly providing evidence to

the predicted minima for prolate and oblate shapes in this region�

The decay of these isomeric levels in �������Pd have been observed in isotopes

separated after induced ssion ���� ���� The separation process in these experiments

requires time on the order of tenths of milliseconds� so the prompt � rays feeding the

isomers were not observed� Experiments observing the prompt � rays can be used

to identify the bands feeding these isomeric levels� For example� heavyion induced

ssion in conjunction with prompt � ray spectroscopy has been used to observe the

rotational bands based on the isomers in ������Pd ����� In the present work the

rotational bands based on the ground state and the isomeric state in �������Pd have

been identi ed by prompt spectroscopy of ���Cf spontaneous ssion products�

The rotational band built on the isomeric con gurations in �������Pd were observed

��

0

500

1000

150011/2−

11/2−

11/2−

11/2− 11/2− 11/2−

ν11/2 band head101

Pd

103Pd

105Pd

107Pd 109

Pd 111Pd

113Pd

115Pd

(9/2−) (9/2−)

0

1000

2000

Odd Pd Isomer band

107Pd

109Pd

111Pd

113Pd

115Pd

Mid

−Sh

ell

101Pd

103Pd

105Pd

Figure ���� Systematics of �h���band heads in the odd Pd isotopes�

in both the thick source and thin source data sets in the present work� Because of

the long half life of the band heads� their decay to the ground state is not observed in

the spontaneous ssion experiments� and no transitions were observed linking these

bands to the ground band� Assignment of these bands to Pd isotopes are based on the

coincidence with � decays from Te� the partner nuclei in ���Cf�SF�� and assignment

to either ���Pd or ���Pd is based on the average mass of the Te partners�

Spectra resulting from gates on the transitions in the isomer band in ���Pd in the

thick source data show the coincidence of the ssion partner Te � rays �Figure ���c��

The spectrum resulting from the same gates in the thin source data� where the Pdlike

Doppler shift has been applied� is shown in Figure ���a� In thin source data the ���Pd

band is observed to a spin of ���� Higher spins are observed in the thin source data

since the Doppler broadening of the line shapes due to the stopping times of the ssion

fragments� as happens in the thick source experiment data� is eliminated� Because

of the Doppler correction� the Te gamma ray peaks are broadened and di�cult to

observe in this spectrum� The coincident partner � rays can be recovered from the

thin source data by using �asymmetric cubes�� where events with three or more � rays

are sorted with a �light� �Pdlike� Doppler shift on two of the axis and a �heavy�

��

0 500 1000

0

2000

4000

6000

Thick Source

−13

4 Te

2+→

0+

−13

5 Te

15/2

−→

11/2

−

−13

5 Te

11/2

−→

7/2−

−13

6 Te

2+→

0+

−13

6 Te

4+→

2+

−13

6 Te

6+→

4+

−13

4 Te

4+→

2+

−11

3 Pd

830

keV

−11

3 Pd

722

keV

−11

3 Pd

571

keV

−11

3 Pd

383

keV

0

1000

2000

3000

Te projection (thin source)

−13

5 Te

15/2

−→

11/2

−

−13

5 Te

11/2

−→

7/2−

−13

4 Te

6+→

6+

−13

6 Te

4+→

2+

−13

6 Te

2+→

+

−13

4 Te

20 →0+

−13

6 Te

6+→

4+

−13

4 Te

4−→

2−

0

1000

2000

3000

113Pd (thin source)−

383

−57

1

−72

2

−83

0

−89

2

−95

8

−10

72

Figure ���� Identi cation of ���Pd isomer band� The top spectra �a� is from the lightDoppler shifted thin source ���Cf�SF� data� The middle spectra �b� is from an asymmetric cube from the thin source ���Cf�SF� data with the Te coincident transitionsprojected out� The bottom �c� spectra is from a thick source experiment ���� ���

�Telike� Doppler shift on the third axis� Setting gates on the two symmetric axis

then projects out the � rays of the heavy �Telike� partner� The spectrum shown in

Figure ���b shows such a projection of the ssion partner Te � rays in coincidence

with the ���Pd �

�band transitions from the thin source experiment data�

The assignment of the isomer bands to either ���Pd or ���Pd is accomplished by

��

taking a mass weighted average of the �� � �� transition intensities of the even Te

partner nuclei� Since the Te isotopes have isomers up to ����ns� this was done withthe thick source data� The time window for collecting � rays for the thick source

experiment was � �s� long enough so that the �� � �� yield represents the true

mass yield since decays of levels populated below the isomeric level� decays that

bypass the isomeric levels� and decay chains that are trapped in the isomeric levels

and subsequently decay all are collected within this time� The Doppler corrected

thin source data do not provide yields representing the mass production when there

are levels with long lifetimes in the decay chain since only the � rays emitted during

�ight are recovered� The average masses of the Te partner nuclei for �������Pd are

shown in Figure ���� and the isomeric bands were assigned to �������Pd based on the

relatively smooth dependence of Te mass with increasing Pd mass� The spins were

assigned assuming that the transitions are �J�� as for a decoupled band� following

the systematics in the lighter odd Pd isotopes� These isomer bands are actually yrast�

so they are expected to be strongly populated in ssion� The isomer band in ���Pd

was observed up to a spin of ���at ���� MeV and the band in ���Pd up to a spin

of ���at ��� MeV� The ordering of the � rays within the bands were based on the

observed intensities of the � ray peaks�

��� �����������Pd

The yrast bands of �����������Pd were previously identi ed to spins of ���h� ���h�

and ���h� respectively� in thick source experiments observing � rays from spontaneous

ssion of ���Cf ����� The level diagrams were extended to ground band spins of ���h�

���h� and ���h� with the addition of � vibrationallike bands up to spins �h� ���h� ���h�

respectively� and negative parity bands were observed in ���Pd up to spin ���h and up

to spin ���h in ���Pd �����

The level diagrams for �����������Pd based on this work agree with those of ���� ���

with one exception and a few additions� In ���Pd the ��� � ��� transition is assigned

an energy of ��� instead of ����� keV� and the yrast bands are extended to spin ���h

in these three nuclei� A probable negative parity band for ���Pd also is reported�

��

110 111 112 113 114 115 116 117 118Pd Mass (amu)

132

133

134

135

136

137

Te

Mas

s (a

mu)

Identification of Pd Isomer Bands

Figure ���� The average masses of the Te ssion partners calculated from the �� � ��

Te transitions in coincidence with the Pd� This was used to identify the mass numberof the isomeric Pd bands�

The moments of inertia calculated from the transition energies for �����������Pd are

shown in Fig� ���� The most notable features of these moments of inertia are the

nearly identical nature and also a second band crossing observed in ���Pd�

��� �������Rh

The level diagrams �Figures ����� ����� for �������Rh were developed using the thick

source data and extended to higher spins with the thin source data ����� The tran

sitions in the Rh were identi ed based on their coincidence with transitions in their

ssion partners� the isotopes of iodine� and with levels seen in decay of ���Ru �����

The levels are ordered from � ray intensity and coincidence considerations� The

adopted ground state spins of �������Rh are �

�� based on the systematics of the odd

Rh nuclei ���� ���� and the ground state band spins and parities were assigned assum

ing the systematics of coupled �I�� bands� The ground band of ���Rh was observed

��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8hω

0

10

20

30

40

50

J 1

Even Pd Backbends

108Pd

110Pd

112Pd

114Pd

116Pd

Figure ���� Even Pd band crossings

349

884

1552

2321

3053

3601

4343

5244

6310

7523

736

1095

1362

2268

17582002

24822708

3142

3749

4482

2903

3452

0+

2+

4+

6+

8+

10+

12+

14+

16+

18+

20+

(2+)

(3+)(4+)

(5+)(6+)

(7+)

112Pd

349535

668

769

732

548

724

901

1006

1213

733

607

434549

310

239195

479746388

736

724

663

359

640

6261384

1157

822(5−)

(7−)

(9−)

(11−)

(13−)

(6−)

(8−)

Figure ��� ���Pd level diagram

��

333

853

1502

2218

2862

3446

4150

5013

6026

7178

2184

2600

3106

3739

4473

5255

6109

694

1011

1320

1630

1983

0+

2289

2904

3503

2+

4+

6+

8+

10+

12+

14+

16+

18+

20+

(2+)

(3+)

(4+)

(5+)

(6+)

(7+)

(9+)

(11+)

114Pd

333520

649

716

644

584

704

863

1016

1149

854

782

734

633

506416

599

615

659

619317 626

663468

679

361

889

1098

1331

694

(5−)

(7−)

(9−)

(11−)

(13−)

(15−)

(17−)

Figure ���� ���Pd level diagram

340

878

1560

2345

3094

3686

4398

5248

6197

738

1066

1374

1719

21001984

2437

2971

3631

4415

2277

2827

0+

2+

4+

6+

8+

10+

12+

14+

16+

18+

(2+)

(3+)

(4+)

(5+)

(6+)

116Pd

340538

682

785

749

592

712

850

823

784

660

534

453550

1106

877

160

293

328

653726

636

398

(5−)

(7−)

(9−)

(11−)

(13−)

(6−)

(8−)

714320+

823

Figure ����� ���Pd level diagram

��

492

1159

1933

2671

3300

4028

212

1384

2157

716

3049

3710

610

1020.1

1952

3327

2966

2652

2356

2114

0

14231375

7/2+

(11/2+)

(15/2+)

(19/2+)

(23/2+)

(27/2+)

(31/2+)

(9/2+)

(13/2+)

(17/2+)

(21/2+)

(25/2+)

(29/2+)

111Rh

Figure ����� ���Rh level diagram ����

up to a spin of ���

�and an energy of ��� keV� and the ground band of ���Rh was

observed up to a spin of ��

�and an energy of ���� keV�

The odd A nuclei �������Rh� with a nuclear charge of ��� have one proton less than

the neighboring eveneven �������Pd�

�� Discussion

Model independent information about nuclear shapes can be obtained from the

electric and magnetic transition matrix elements� which can be measured� for instance

by Coulomb excitation� However� in the regions of nuclides where the half lives are too

short to produce suitable targets� and where radioactive beams of su�cient intensity

have not yet been developed to perform such experiments� less direct evidence can

be used to provide information on the nuclear shape� The ordering and behavior

of the Nilsson orbitals of the nuclear core at high spins is sensitive to the nuclear

deformation� especially for the contrast between prolate or oblate shapes� Hence

��

113Rh

0

444

1076

1776

2471

3092

212

685

1321

2038

2724

3335

571

937

1285

1674

2134

2447

3134

(7/2+)

(11/2+)

(15/2+)

(19/2+)

(23/2+)

(27/2+)

(9/2+)

(13/2+)

(17/2+)

(21/2+)

(25/2+)

(29/2+)

Figure ����� ���Rh level diagram ����

identi cation of the orbitals which are occupied by the valence protons and neutrons

can provide model dependent information about the nuclear shape�

Identi cation of the orbitals responsible for the observed band crossings in �����������Pd�

whether the ��g ��� or ��h��

���pair are aligned� can answer the question of whether

these nuclei are still prolate or have changed to oblate deformation as predicted by

theoretical models ���� ���� Preliminary HFB cranked shell model calculations for

proton and neutrons levels in ���Pd for both prolate and oblate shapes are shown

in Figures ����� ����� ����� ����� The deformations used in these calculations are

from the calculated oblate and prolate minima for ���Pd in Ref� ����� The predicted

frequency for the ��h����� alignment is about ��� MeV��h for both prolate and oblate

shapes� The calculated proton alignments� however� are signi cantly di�erent for

oblate or prolate shapes� with the alignments occurring a frequencies of about ���

MeV��h or ��� MeV��h respectively� These frequencies are either below or above the

expected neutron alignments� so if the nature of the rst observed band crossings can

be deduced from the experimental data� this would suggest either oblate or prolate

��

0.0 0.1 0.2 0.3 0.4 0.5hω (MeV)

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Qua

si-n

eutr

on R

outh

ian

(MeV

)

β2=-0.250 β4=-0.090 γ= 0.0 N= 70116 OBLATE NEUTRONS(π,α) : solid=(+,+1/2), dotted=(+,-1/2), dash-dotted=(-,+1/2), dashed=(-,-1/2).

20-MAY-98 21:47:08 JIHIR, Oak Ridge, R.W.

Figure ����� ���Pd single particle routhians for neutrons in an oblate shape�

0.0 0.1 0.2 0.3 0.4 0.5hω (MeV)

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Qua

si-n

eutr

on R

outh

ian

(MeV

)

β2= 0.200 β4=-0.030 γ= 0.0 N= 70116PD PROLATE NEUTRONS(π,α) : solid=(+,+1/2), dotted=(+,-1/2), dash-dotted=(-,+1/2), dashed=(-,-1/2).

20-MAY-98 21:46:53 JIHIR, Oak Ridge, R.W.

Figure ����� ���Pd single particle routhians for neutrons in an prolate shape�

shapes for �����������Pd�

Information about the orbitals responsible for the observed band crossings can be

derived from aligned angular momentum� The adopted greference ����� with Harris

parameters of J������h�MeV and J�������h��MeV�� giving a constant alignment for

�

0.0 0.1 0.2 0.3 0.4 0.5hω (MeV)

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Qua

si-p

roto

n R

outh

ian

(MeV

)

β2=-0.240 β4=-0.080 γ= 0.0 Z= 46116PD OBLATE PROTONS(π,α) : solid=(+,+1/2), dotted=(+,-1/2), dash-dotted=(-,+1/2), dashed=(-,-1/2).

20-MAY-98 21:48:08 JIHIR, Oak Ridge, R.W.

Figure ����� ���Pd single particle routhians for protons in an oblate shape�

0.0 0.1 0.2 0.3 0.4 0.5hω (MeV)

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Qua

si-p

roto

n R

outh

ian

(MeV

)

β2= 0.200 β4=-0.030 γ= 0.0 Z= 46116PD PROLATE PROTONS(π,α) : solid=(+,+1/2), dotted=(+,-1/2), dash-dotted=(-,+1/2), dashed=(-,-1/2).

20-MAY-98 21:48:02 JIHIR, Oak Ridge, R.W.

Figure ����� ���Pd single particle routhians for protons in an prolate shape�

the S band of ���Pd� was used in the calculation of the aligned angular momentum� ix�

in Figures ����� ���� ����� The similarity of the band crossings through this region

�see Figure ���� justify the use of the same parameters for all these nuclei� The highest

j orbitals for the valence neutrons and protons� �h���and �g

�respectively� are the

��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8h− ω

−2

0

2

4

6

8

i x

111Rh 7/2

+ band

112Pd

111Pd 11/2

− band

Figure ����� The aligned angular momentum of the ground bands of ���Rh and ���Pdand the ��

�

�isomer band in ���Pd �����

likely candidates for causing the observed alignments since these are the most sensitive

to the Coriolis interaction� The maximal aligned angular momentum a ��h�����pair

can contribute is ���h and the maximum alignment a ��g ���pair can contribute is �h�

The amount of angular momentum aligned in �����������Pd �see Figs� ����� ���� �����

is close to �h� which does not conclusively rule out this being a ��g ��� alignment�

Thus blocking arguments must be used to identify the aligning orbital�

The band crossing in ���Pd was identi ed to originate from a ��h�����pair based

on the observation that frequency at which the alignment of the �h���isomer band

in ���Pd is delayed with respect to ���Pd ����� This observation is con rmed by the

behavior of the rotational band in ���Rh� shown in Figure ����� A band crossing is

observed occurring at the same rotational frequency as the band crossing in ���Pd�

implying that the unpaired valence proton occupying the g �orbital in the ground state

of ���Rh acts as a spectator and does not block the alignment� hence the possibility

of the alignment in ���Pd being caused by a ��g ���pair is excluded�

The behavior of the rotational bands in ���Pd and ���Rh con rm that the band

�

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8h− ω

−2

0

2

4

6

8

i x

114Pd

113Rh 7/2

+ band

113Pd 9/2

− band

113Pd gsb +

113Pd gsb −

Figure ���� The aligned angular momentum of the ground bands in ���Rh� ���Pd�and ���Pd� and the

�

�isomer band in ���Pd�

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8h− ω

−2

0

2

4

6

8

10

12

i x

116Pd

115Pd 9/2

− band

115Pd 3/2

+ band

114Pd

Figure ����� The aligned angular momentum of the ground bands of �����������Pd andthe

�

�isomer band in ���Pd�

�

crossing observed in ���Pd also is caused by the alignment of a ��h�����pair� The

aligned angular momentum for �������Pd and ���Rh are shown in Figure ���� In

���Pd the frequency of the band crossing in the isomer band built on the �h���orbital

is delayed by the unpaired valence neutron from about ��� MeV��h to ���� MeV��h�

For the rotational structures built on the ground state �which is a mixture of �d��and

�g ��� the crossing frequency ��� MeV��h is not delayed� Here the unpaired neutron is

in an orbital which does not e�ect the ��h�����pair alignment� In ���Rh the presence

of the unpaired valence proton in the g �orbital does not block the band crossing

from occurring either� which is consistent with the conclusion that the band crossing

in ���Pd is from a ��h����� pair�

The suggestion posed that the isomeric levels in the oddA Pd have prolate shapes

while the ground band shapes are oblate� based on the large hindrances of the isomeric

decays ����� makes blocking arguments based only on the oddA Pd bands inconclu

sive� If the ground state shapes of �����������Pd and �������Pd were oblate� the observed

alignment in the ground state bands of these nuclei would be caused by a ��g ���pair�

and comparison with the isomeric �h���bands would be incorrect� The blocking argu

ments presented here are supported by the observation that the unpaired g �proton

in �������Rh do not delay the alignments of their ground bands�

The aligned angular momentum for the ground band of ���Pd and the ground

and isomer band of ���Pd is shown in Fig� ����� The same arguments used for the

identi cation of the orbits responsible for the band crossing in ���Pd� based on the

behavior of the bands in ���Pd� can be used for ���Pd and ���Pd� The �h���isomer

band in ���Pd blocks the band crossing while the ground band con guration does

not� The crossing frequencies in ���Pd of both the ground band and isomer band

are di�erent than the lighter Pd and Rh� The isomer band delays the neutron pair

alignment to a rotational frequency of about ���� MeV��h� compared to ���� MeV��h in

�������Pd� The alignment of the ground band alignment in ���Pd occurs at about ����

MeV��h� well below the crossing frequency observed in the ground bands of �������Rh�

���������������Pd�

�

�� Summary

New levels in the neutronrich Pd and Rh were observed in the prompt spec

troscopy of ssion products of ���Cf�SF�� Rotational bands based on the ground state

con guration and on the �

�or ��

�

�isomeric levels were identi ed in �������Pd� The

ground state bands of �����������Pd each were extended to spins of ���h A second band

crossing in ���Pd and a negative parity band in ���Pd� similar to bands in �������Pd�

were observed� Rotational bands built on the ground state con gurations of �������Rh

also also identi ed�

The behavior of the moment of inertia of these rotational bands identify the or

bitals responsible for the alignments observed in the yrast bands of �����������Pd� The

band crossings in the isomeric bands of �������Pd based on the �h���orbital are de

layed compared to the band crossings of the neighboring ���Pd and ���Pd� suggesting

a ��h����� character for these even Pd band crossings� The ground bands of �������Pd�

built on di�erent � con gurations� and the oddproton con guration of �������Rh ex

hibit band crossings at the same frequency as the even Pd� The Rh results con rm

that the band crossings are not caused by the alignment of a ��g ���pair� Comparison

to cranked shell model calculations suggest that since the aligning nuclei are ��h�����

the nuclear shapes for the even Pd are prolate� and the predicted shape transition

from prolate to oblate has not yet occurred up to ���Pd�

�

Chapter �

Lifetime measurement of ���I

The study of the nuclei near double shell closures is of fundamental interest since

the single particle structures in these regions are expected to be relatively pure con

gurations� The experimentally measured properties of the single particle structures

of the valence nuclei� where a few particles or holes are coupled to a double closed

shell core� give information on the basic single particle matrix elements and interac

tion between the pairs of nucleons in valence orbitals ����� There are few double shell

closures for heavy nuclei with A���� The region around ���Pb is the most accessible

experimentally� since it lies within the valley of stability� and has been well stud

ied� The other double closed shell regions� around �Ni� ���Sn� and ���Sn� are more

di�cult to study since they lie away from stability� The nuclei in the ���Sn region

are populated in ssion of actinide nuclei and have been studied via decay and by

prompt spectroscopy of ssion fragments�

With the development of new experimental techniques for producing and studying

neutronrich nuclei� the double closed shell region around ���Sn is being opened for

study� The application of the technique using powerful � ray arrays for the prompt

spectroscopy of spontaneous ssion �SF� products extends the possibilities for the

study of the single particle structures in this interesting region� beyond what is pos

sible from the study of decay products� Recent work analyzing ���Cm ssion in

cludes a study of the N�� isotones ����� the identi cation of the ��f �

��� multiplet

in ���Sn ����� and identi cation of single particle structure of ���Te and ���I with

�

supporting shell model calculations�

As more is learned about spectroscopy of the nuclei in the ���Sn region ����� and

as experimental techniques are re ned to measure more lifetimes in this region ����

it is possible to extract single shell and transition matrix elements� Predictions based

on these matrix elements can be made for lifetimes of transitions which have not

yet been measured� In this chapter the lifetime of the ���

�level in ���I is estimated

based on the singleparticle matrix elements extracted from previous measurements

in ���Te� and is compared to a lifetime measurement from the thin source ssion data�

�� Matrix Elements from ���Te

The nucleus ���Te has two valence protons outside a ���Sn core� The yrast excited

states of ���Te� shown in the level diagram in Figure ���� have been interpreted to be

single particle structures ����� Levels based on proton con gurations include ��� ���

�� levels belonging to a ��g �

��� multiplet� a ��� level belonging to a �g

��d�

�� multiplet�

and ��� �� and �� levels belonging to a �g �� h��

�� multiplet� Higher lying single

particle structures involve excitation of the ���Sn core�

The lifetimes of the ��� and �� members of the g��

�

multiplet� and the �� level have

been measured in the decay of ���Sb ���� Assuming a pure �g ��� con guration�

the B�E�� values extracted from the ��� and �� lifetimes can be used to determine

the onebody matrix element � g �

�jjE�jjg �

��� The �� level decays via an E� to the

��� member of the g��

�

multiplet and the ��� member of the �g �

�� d �

�� multiplet� The

B�E�� values for these transitions can be used to extract the � g �

�jjE�jjh ��

�� and

� d �

�jjE�jjh ��

�� onebody matrix elements� The calculation of the matrix elements

below is carried out assuming that all the wave functions are a pure con gurations�

which may not be entirely true� For example� in calculations by the authors of

Ref� ���� yielding results which reproduce the experimental data well� impure wave

functions were used� and the contributions from con gurations other than g���

for the

ground state were ��� and less than �� for the other members of the �g���

multiplet�

The measured B�E�� from Ref� ��� are�

�

134Te

0

127915771691

2398

4014429945634557

5080

56225805

6525

6010

0+

2+4

+6+

1

6+

2

9−

7−

8−

πg2

7/2

πg7/2d5/2

πg7/2h11/2

πg2

7/2νf7/2h−1

11/2

8+

9+

10+

12+

13+

E3

Figure ���� ���Te level diagram

B�E��Ii � If �W�u�� �e�fm����� � ��� ��� ������� � ��� ���� ���

B�E��Ii � If �W�u�� �e�fm��

��� � ��� �� �������� � ��� �� ������

The �ray transition rates between twoparticle states can be calculated using the

wave functions for a mixed con guration �����

IiMi� ��j��IiMi

� �j � j��IiMi� ��j���IiMi

�����

IfMf� #��j��IfMf

� #�j � j��IfMf� #��j���IfMf

�����

In the case of the E� transitions from the �g �

��� multiplet� assuming these levels are

pure con gurations� the coe�cients � # � � � #� � � and the matrix element

�

reduces to

� If jjT ���� jjIi ��

p��Ii � ��

p��j � ��� � �jjjT�jj�j � W �jjIf�$ Iij� �����

The transition rate is then given by

B�E�$ Ii � If � ��If � �

�Ii � �� If jjT ���

� jjIi �� �����

� ���If � ����j � �� � �jjjT�jj�j �� W ��jjIf�$ Iij� �����

and from this the single shell matrix element � g �

�jjE�jjg �

�� can be calculated giving

Ii � If � g �

�jjE�jjg �

���efm��

��� � ��� ������ � ��� �����

The same procedure can now be applied to extract the shell model matrix ele

ment � g �

�jjE�jjh ��

�� from the ��� � ��� transition� In this case the disappearing

coe�cients in ����� are � � � � � for Ii and# � #� � � for If and the transition

matrix element is given by

� If jjT ���� jjIi � �

p��Ii � ��

p�p��j � �� � �jjjE�jj�j� � �����

W �jj�If�$ Iij�

� ��jjE�jj��

�� �

p�� � � � � g �

�jjE�jjh ��

�� ���������� �����

� ����� � g �

�jjE�jjh ��

��

� g �

�jjE�jjh ��

��� ����� efm� ����

The matrix element governing the E� transition ��� � ��� transition is � �g ��

d�����jjE�jj�g

��h��

��� �� The transition occurring is a proton moving from the h ��

�to

the d �

�orbital� The � d �

�jjE�jjh ��

�� matrix element can be extracted by recoupling

the components of the initial and nal wave functions�

�E��g

�

�� h

��

��

���

����

g

h

� � � �

�

�

�X�

p�� � � � ��p�� � � � ��W �gh�� � ���

����

g

h

�� � �

�

�X�

p����

p�� � � � ��W �gh�� � ��� � �jjE�jjh �

���

SSS

g �

�

� �g � d���jjE�jj�g � h�� � �p�� � �W �

�

�

��

��� � �

�

�� � d �

�jjE�jjh ��

�� �����

B�E�$ �g �

�h ��

��� � �g �

�d �

����� �

��

��� ���� � d �

�jjE�jjh ��

��� ������

� d �

�jjE�jjh ��

��� ����� efm� ������

�� Shell Model prediction of the ���

�level lifetime

in ���I

The identity of the yrast levels of the three valence proton nucleus ���I can be

described as the coupling of an additional g �

�proton to the singleparticle structures

of ���Te� The level diagram and underlying singleparticle structures for ���I are

shown in Figure ���� Using the single particle matrix elements calculated from ���Te�

the lifetime for this transition can be calculated� Again� it should be noted that the

assumption of pure con gurations is made� The calculations in Ref� ��� indicate that

the percentage of other components in the g���

con guration is about ��� except for

the ground state which has ��� Assuming the con gurations are pure� the ���

�is

��g���

�� h ��

�� and the �

�

�is ��g��

�

�� d d�

��

�E�

hg���

� h ��

�

i��

�

���

�

�

JJ

��

����

g

g

�

h

���

�

��

1994

1422

1134

0

365536893766

4241

4776

5328

5576

4380

7/2+

11/2+

15/2+

17/2+

19/2−

23/2−

21/2−

19/2+21/2+

23/2+

25/2+

27/2+

πg3

7/2

πg2

7/2d5/2

πg2

7/2h11/2

πg3

7/2νf7/2h−1

11/2

135I

E1 E3

Figure ���� ���I level diagram

�X�

p�� � ��

�� ��

p�� � �� ��W ��

��

�

��

�� �

��

���

JJ

������g

g

�

h

� �

��

� �g� � d� ���

�jjE�jj�g� � h� ���

� � �p�� � �W ��

��

�

��

�� �

��

�

�

�� � d �

�jjE�jjh ��

��

B�E�$ �g���

h ��

�� ���

� � �g���

d �

�� ���

�� ��

��� ����� � d �

�jjE�jjh ��

���

� ��� e�fm� ������

The transition energy is ���� keV� so the partial width can be calculated to be

% � ������ ��� eV� Assuming no other decay routes for the ���

�level� and pure

�

con gurations� the upper bound for this lifetime is�

� � ���� ns ������

�� Measurement of the ���

�level lifetime in ���I

The possibility of measuring the lifetime of the ���

�level in ���I is suggested from

the comparison of the thick source and thin source data� The � ray spectra from these

two data sets� with the same summed gates applied on the ��

� � ���

�� ��

�

� � ���

�� and

���

� � �

�transitions in ���I� are shown in Figure ���� The spectrum in Figure ���a

was obtained from the �prompt� � rays� that is the Doppler correction was applied�

so only the � rays emitted in�ight before the nuclei reach the PPACs are recovered�

The observed intensity of ���� keV E� transition deexciting the ���

�relative to the

���� keV E� transition depopulating the ��

�level in the thin source data is ��� that

of the thick source� The E� can be used to normalize the E� intensity for comparison

of the thick and thin source data� Transitions with E� multipolarity are faster than

transitions with E� multipolarity� and hence� the intensity of the E� transition should

include all of the population of the ��

�level� The lower E��E� intensity ratio in the

thin source data suggests that the lifetime of the E� transition might be long enough

that a signi cant fraction of the decay occurs after the nuclei implant in the PPACs�

which occurs after a calculated average timeof�ight of ���� ns� The intensities of

the prompt and delayed peaks can be used to measure the lifetime of the level�

The �delayed� component of the E� decay� that which decays after the nuclei

implant in the PPACs� was searched for in the thin source data by sorting the � rays�

without applying any Doppler correction� into a threedimensional histogram� The

resultant gated spectra should give sharp � ray peaks for transitions occurring after

the nuclei stop in the PPACs� The �delayed� intensity of the E� transition was then

obtained by applying the same gates as were applied as in generation of the prompt

���I spectra� There was no � ray peak observed at the expected energy of ���� keV�

but an upper limit on the intensity was obtained by a t at the expected location�

There is an apparent discrepancy in the intensity of the E� transition comparing

��

the thick and thin source data� The ratio of the total �prompt plus delayed� E�

intensity to E� intensity in the thin source data is less than in the thick source

data� Possible explanations for the di�erence in observed ratios are e�ciency and line

shape considerations� The reduced E� intensity in the thin source could result from a

decrease in peake�ciency of GAMMASPHERE as the nuclei recoil from the source�

To check this possibility the peake�ciency was simulated with the Monte Carlo

code GEANT ��� �Figure� ����� The simulation was performed for a ���� keV � ray

emitted at ���� ���� and ��� cm from the center of GAMMASPHERE� The simulation

was performed without the CHICO detector� but the relative e�ciencies are expected

to be similar �see Section ������� The peake�ciency is shown to remain relatively

�at over the �ight path of the nuclei� Other possible reasons for the discrepancy

between the two data sets are related to the � ray line shapes� In the thin source

data the angle between the � ray direction and recoil direction� used in calculating

the Doppler correction� assumes the nucleus is at the center of GAMMASPHERE� As

the nucleus travels from the source this angle is no longer correct� and the resultant

� ray peak after the Doppler correction would broaden� It is also possible that the

E� transition in the thick source has a component which is broadened due to the

stopping time of the recoiling fragment in the source resulting in a reduction in the

observed E� intensity� The broadening of the line shapes could result in lost intensity

in the gated spectra�

Since the di�erences in the E� intensity between the thick source and thin source

data are not well quanti ed� the lifetime of the E� transition was estimated using

the thin source data alone� The measured prompt and delayed intensities� Ip and Id�

respectively� can give the lifetime� � � through the relation

exp��t�� �

IdIp � Id

������

where t is the average time of �ight to the PPACs� The lifetime obtained for the

E� transition from the thin source experiment is ����������� ns� The high limit of the

measurement� ��� ns� is an upper bound on the lifetime since it is possible that some

of the intensity of the prompt peak is not observed due to experimental consider

ations� This value agrees well with the shell model prediction of ��� ns calculated

��

0 200 400 600 800 1000 1200 1400 1600 1800Energy (keV)

0e+00

1e+04

2e+04

3e+04

x10

135I Thick Source

E1

E3

0 200 400 600 800 1000 1200 1400 1600 1800

0

1000

2000

3000

4000

x10

135I Thin Source

E1 E3

Figure ���� ���I spectrum

0 5 10 15Distance from Center (θ=49 deg) (cm)

0.08

0.09

0.1

0.11

Pea

k E

ff.

Off Center Efficiency of GS1695 keV γ−ray,

Figure ���� GEANT calculation of the peake�ciency away from the center of GAMMASPHERE ���

��

in Section ���� Extraction of more quantitative information about this transition�

such as collective enhancement of the E� transition rate� requires a more accurate

measurement of the lifetime�

��

Chapter

High Spin Results

One of the advantages of performing spectroscopic studies of ���Cf�SF� products

with a thin source� as discussed in Section ������ is the ability to observe levels at

higher spins and excitation energies� By performing the Doppler correction on the

� rays emitted during the �ight of the ssion products� sharp line shapes can be

recovered for � rays emitted from levels which have lifetime on the order of � ps�

Extending rotational bands to higher spins allows the ability to study the nuclear

structure related properties� such as band crossings and shape properties� at higher

excitation energy� The purpose of this chapter is to illustrate the capabilities of this

technique by showing the results from a few nuclei�

�� ���Ru

The role of triaxiality in the structure of ���Ru has been discussed recently in the

literature���� ���� Some of the evidence for triaxial behavior in this nucleus is the

very low lying ��� state� the � ray branching ratios from the � band to the ground

band� and the staggered spacing of the levels in the �band� In the present work the

ground band has been extended to �� �h and �band has been extended from spin

��� to ��� �Figure ����� and the strong stagger continues at higher spin indicating

that the centroid of the shape parameter � remains nonzero� To extract a rough

value for the � shape parameter� the level structure of the �band was compared

��

−50.0 0.0 50.0 100.0

112Ru

0+2+

10+

5+

237

645

1190

1839

2563

3326

4118

4953

5829

6726

523

748

981

1235

1570

1840

2263

2534

3033

3291

3871

4096

4765

4952

5856

4+

6+

8+

10+

12+

14+

16+

18+

20+

2+

4+

6+

8+

12+

14+

3+

7+

9+

11+

13+

15+

17+

Figure ���� Level diagram for ���Ru� New levels added from the present work areshown as thick lines in the level diagram�

to the Rigid Triaxial Rotor �RTR� model predictions ���� The RTR model does

not include e�ects such as variable moment of inertia and as a consequence� the

predicted energies of the levels are higher than the observed levels� To correct for

this in comparing the observed level to the RTR predictions� ratios of di�erences in

energy of levels in the experimental spectra were compared to the same ratios from

the RTR model as follows�

E�I � ��� E�I�

E�I�� E�I� �� RTR�

E�I � ��� E�I�

E�I�� E�I� �� expt�����

The �value satisfying the equality were extracted� This analysis indicates that the

centroid of the � deformation ranges from ��� to ��� at higher spins� which is reduced

from ����� given by the RTR model based on the ratio of ��� ���� energies �Figure �����

��

10.0 15.0 20.0 25.0γ

0.0

5.0

10.0

15.0

Ene

rgy

(MeV

)

Rigid Tri−axial Rotor Model"γ"−band levels

16+

14+

15+

12+13+

10+11+

8+9+

2+3+4+5+

6+7+

17+

(Davydov, A.S. and G.F. Filippov (1958) NP 8)

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0Spin

0.0

5.0

10.0

15.0

20.0

25.0

30.0

γ (c

entr

oid)

112Ru

ΔE+/ΔΕ−

E(2+

2)/E(2+

1)

Figure ���� The left gure shows the RTR model predictions for the energy levels ofthe � band as a function of the � shape parameter� The right gure shows the valueof the shape parameter � extracted from the level diagram�

�� ��������������Mo

The neutronrich nuclei �������Mo have been observed in ���Cm�SF� up to spins of

�� �h and �� �h� respectively� in the ground band� and to a spin of �� �h in the � band

of ���Mo ���� The ground bands of ���������������Mo were extended to spins of �� �h�

�� �h� �� �h� and �� �h� respectively� by Zhu et al� ����� In the present work the ground

band for these nuclei were extended to spins of �� �h� � �h� �� �h and � �h� respectively�

and the � band of ���Mo was extended to �� �h� Zhu et al� noted that there was an

indication of a band crossing in ground band of ���Mo at spin �� �h� By extending

this rotational band by three levels the rest of the band crossing region is observed

�Figure ����� The band crossing also occurs in the odd and even spin sequences of

the �band �Figure �����

�� ���������������Nd

The ground state rotational bands of the neutronrich nuclei �����������Nd have been

observed to spins of �� �h in the spontaneous ssion of ���Cm ����� ���������������Nd also

��

102Mo

106Mo

108Mo

295.9

742.9

1321.1

2018.0

2790.1

3623.6

4502.2

171.1

521.6

1032.6

1687.4

2471.6

3368.8

4361.4

5410.8

6496.9

5347.2

4344.8

3402.5

2529.9

1752.5

1090.3

563.2

192.52+4+

6+

8+

10+

12+

14+

2+4+

6+

8+

10+

12+

14+

16+

18+

2+4+

6+

8+

10+

12+

14+

16+

−50.0 0.0 50.0 100.0

192

560

1079

1721

2455

3253

4114

5060

6112

7282

812

1214

1724

2326

3004

3766

4629

5591

1027

1475

2036

3396

4184

5063

2683

2305

2866

3573

4377

104Mo

0+2+

2+

4+5+6+7+8+

4+

10+

6+

12+

13+

14+

15+

16+

8+

3+

10+

12+

14+

16+

18+

9+

20+

11+

Figure ���� Level diagram for ���������������Mo� New levels observed in the presentwork are shown as thick lines�

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8h−ω [MeV]

10

20

30

40

J 1/h−

2 [M

eV]−

1

102,104,106,108Mo

Kinetic Moment of Inertia

102Mo

104Mo

106Mo

108Mo

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8h−ω [MeV]

20

40

60

80

100

120

J 2/h−

2 [M

eV]−

1

102,104,106,108Mo

Dynamic Moment of Inertia

102Mo

104Mo

106Mo

108Mo

Figure ���� Kinetic and dynamic moments of inertia for the ground bands of���������������Mo�

��

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8h−ω [MeV]

15

20

25

30

35

J 1/h−

2 [M

eV]−

1

104Mo Ground and γ−bandKinetic Moment of Inertia

104Mo γ−band (even)

104Mo γ−band (odd)

104Mo ground band

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8h−ω [MeV]

20

30

40

50

60

70

J 2/h−

2 [M

eV]−

1

104Mo Ground and γ−bandDynamic Moment of Inertia

104Mo γ−band (even)

104Mo γ−band (odd)

104Mo ground band

Figure ���� Kinetic and dynamic moments of inertia for ���Mo ground and even andodd spin sequences of the �band�

have been observed in ���Cf�SF� to maximum spins of �� �h ���� � �h ��� ��� ��

�h ���� and �� �h ���� respectively� The rotational bands in ���Nd and ���Nd have

been been extended to � �h and �� �h� respectively ���� In the present work� ���Nd

was also observed to a spin of �� �h� the ground bands of �������Nd were extended to

�� �h� and ���Nd was extended to �� �h� The transition energies from this work agree

well with those assigned in Ref� ���� except for the �� � � transition in ���Nd�

which this work indicates is ����� kev instead of ����� keV� The newly identi ed

levels with spin �� �h in �������Nd are the highest angular momentum yet observed

in spontaneous ssion products� The extended level diagrams for ���������������Nd are

shown in Figure ��� and the kinetic and dynamic moments of inertia are shown in

Figure ����

�� ����������Sm

The ground state rotational bands of �������Sm were identi ed in early spectro

scopic studies of ssion products to spins of � �h and �h� respectively ���� In more

recent work ��� the ground state rotational band in ���Sm was identi ed to a spin

of �� �h� and the bands in �������Sm were extended to �� �h� In the present work the

�

150Nd

152Nd

154Nd

156Nd

129.9

381.1

720.0

1128.9

1598.0

2119.0

2682.0

3274.1

72.4

236.3

483.3

805.1

1195.0

1647.2

2157.4

2721.5

3336.5

3998.9

4705.9

72.8

235.0

483.3

811.1

1211.6

1677.9

2203.2

2779.8

3399.9

4056.6

4745.3

66.9221.6

459.9

777.1

1168.1

1627.6

2150.9

2733.7

3372.4

4063.0

2+4+

6+

8+

10+

12+

14+

16+

2+4+6+

8+

10+

12+

14+

16+

18+

20+

22+ 22+

20+

18+

16+

14+

12+

10+

8+

6+4+2+ 2+

4+6+

8+

10+

12+

14+

16+

18+

20+

Figure ���� Level diagrams for the ground bands of ���������������Nd

0 0.1 0.2 0.3 0.4h−ω [MeV]

20

30

40

50

60

70

J 1/h−

2 [M

eV]−

1

150,152,154,156Nd

Kinetic Moment of Inertia

150Nd

152Nd

154Nd

156Nd

0 0.1 0.2 0.3 0.4h−ω [MeV]

0

50

100

150

J 2/h−

2 [M

eV]−

1

150,152,154,156Nd

Dynamic Moment of Inertia

150Nd

152Nd

154Nd

156Nd

Figure ���� Kinetic and dynamic moments of inertia for the ground bands of���������������Nd�

��

bands in �����������Sm were extended to spins of � �h� �� �h and � �h� respectively�

The level diagrams are shown in Figure ��� and the moments of inertia are shown in

Figure ���� The authors of Ref� ��� note that there is an indication of a band crossing

occurring in ���Sm at spin �� �h� The rapid change in the dynamic moment of inertia

at the higher observed spins in the present work shows that this band crossing does

occur�

�� Summary

The spectroscopic study of ���Cf�SF� ssion products using a thin source tech

nique� described in Chapter �� allows the observation of transitions occurring at higher

spin and excitation energy than is possible with the thick source technique� Rota

tional bands can typically be extended by one to three levels allowing the structure

of the nuclei to be studied at higher excitation energy�

The ground band of ���Ru was extended two levels to a spin of �� �h and the �

band was extended seven levels to a spin of �� �h� The staggered spacing of the energy

levels in the � band� when compared to the Rigid Triaxial Rotor model� indicate

that nonzero centroid of the � shape parameter evident a low spin persists at higher

spins�

The rotational bands in ���������������Mo were extended� with the ground band in

���Mo extended to a spin of �� �h� and the � band extended six levels to a spin of ��

�h� The high spin states in ���Mo allow the observation of the band crossing occurring

in the ground band� and indicate that the � band also undergoes a similar crossing�

The ground bands in �����������Nd and �����������Sm were also extend one to three

levels� �������Nd were extended to a spin of �� �h� which is currently the highest

observed angular momentum in spontaneous ssion products�

���

75.9

249.9

517.2

871.9

1307.8

1818.9

2400.3

72.8

3045.5

3741.1

240.0

498.2

842.1

1266.4

1765.7

2334.3

2967.3

3660.0

4407.8

70.6

232.5

482.6

813.5

1224.4

1706.9

2256.2

2866.7

3536.2

2+4+

6+

8+

10+

12+

14+

16+

18+

20+

18+

16+

14+

12+

10+

8+

6+4+2+ 2+

4+

6+

8+

10+

12+

14+

16+

18+

156Sm

158Sm

160Sm

Figure ��� Level diagrams for the ground bands of �����������Sm

0 0.1 0.2 0.3 0.4h− ω [MeV]

35

40

45

50

55

J 1/h−

2 [M

eV]−

1

156,158,160Sm

Kine tic Moment of Inertia

156Sm

158Sm

160Sm

0 0.1 0.2 0.3 0.4h− ω [MeV]

40

50

60

70

80

90

J 2/h−

2 [M

eV]−

1

156,158,160Sm

Dynamic Moment of Inertia

156Sm

158Sm

160Sm

Figure ���� Kinetic and dynamic moments of inertia for the ground bands of�����������Sm�

���

Chapter

Conclusion

This thesis consists of the development of a new method for studying neutronrich

nuclei produced in the spontaneous ssion of ���Cf� The technique involves coupling

a large solidangle chargedparticle detector system with a large � ray detector array

and using a thin ssion source� Greater sensitivity and selectivity is o�ered by adding

the particle� ray coincident technique to the highstatistics� highfold � ray data

collected by GAMMASPHERE� By detecting the ssion products� which recoil freely

into vacuum� the masses of the ssion products can be deduced� and the � rays can

be unambiguously assigned to either the heavy or light ssion partner� The mass

information can be used to select � rays from a speci c mass region making it easier

to analyze the resultant spectra� Regions of lowyield mass production also can be

selectively enhanced� The mass gating has been used to extend the spectroscopic

sensitivity to transitions from a nucleus produced at a level of less that � � ����

per ssion� Level diagrams can be extended to higher spins and excitation energy in

the thin source experiment since the line shapes for the � rays from these shortlived

transitions are not Doppler broadened� as in thick source experiments�

A major component of this work was the development of the chargedparticle

detector system� CHICO� The construction of this large solidangle detector capable of

handling high count rates was a necessary development enabling the thin source ssion

experiment to be carried out� The detector also extends the research opportunities

studying other binary reactions with GAMMASPHERE� CHICO in conjunction with

���

GAMMASPHERE has been used to study nuclear structure via Coulomb excitation�

transfer� and fusion ssion reactions� The detector comprises an array of �� parallel

plate avalanche counters �PPACs� covering an angular range of ��� � � � �� and

��� � � � ��� and ��� in � for a total solid angle of �� sr� The PPACs have

segmented anodes and a threelayer delay line cathode which provide an angular

resolution of ���� in � and �� in �� The timeof�ight di�erence of the reaction products

can be measured with ��� ps resolution allowing a mass resolution of �m�m��� for

beam reactions� and mass units for spontaneous ssion�

The added sensitivity and selectivity of this new technique was exploited in the

study of the neutronrich nuclei produced in ���Cf�SF�� The ability to distinguish

prompt � rays from delayed � rays via the Doppler correction was used to set limits

on the lifetime of the E� decay of the ���

�level in ���I� The experimental limit of ���

ns agrees well with the shell model prediction� The ability to observe levels at higher

spin was used to extend rotational bands in ���������������Mo� ���Ru� �����������Nd and

�����������Sm� The band crossing region occurring in ���Mo was observed to completion�

and a band crossing in the � band of this nucleus was also observed� The higher spin

states observed in ���Ru indicate that the triaxial behavior exhibited at lower spins

continues at higher excitation energy� The ground bands of �������Nd were extended

to spins of �� �h� These are the largest angular momenta observed to date in ssion

products of ���Cf�Sf��

The level diagrams for the even mass neutronrich Pd were extended and the

shape properties were inferred based on identi cation of the orbitals responsible for

the observed band crossings� The yrast bands in �����������Pd were extended to spins of

�� �h� A probable negative parity band in ���Pd and a second band crossing in ���Pd

were observed� Rotational structures also were newly identi ed in the odd mass

�������Pd� The ground band of ���Pd was identi ed to a spin of ����h and a rotational

band based on the lowlying �

�isomeric level was identi ed to a spin of ��

�� The

ground band of ���Pd was observed to a spin of ���and the rotational band based

the �

�isomeric level was identi ed to a spin of ��

��h� The band crossings occurring

in the even mass Pd are blocked in the neighboring odd� Pd indicating that the

���

aligning nucleons are a �h����� neutron pair� This is consistent with the behavior of

the band crossings occurring in the odd� even� �������Rh� where the odd proton

does not block the band crossing� Comparison to cranked shell model calculations

indicate that the shape of the even mass Pd remains prolate� at least through ���Pd�

The technique developed in this thesis of studying the neutronrich ssion products

from ���Cf�SF� by the collection of highstatistics� highfold � ray data in conjunc

tion with the detection of the recoiling ssion partners complements and extends the

thick source experimental technique� The level diagrams of many nuclei have been

developed previously using the thick source data� The majority of these nuclei are

eveneven or evenodd mass� and have been studied rst because of their simpler

decay schemes� With this new technique the decay schemes of these nuclei can be

extended to higher excitation energies� With the added selectivity of this new tech

nique� speci cally the ability to assign the � rays to either the heavy or light ssion

partner� the development of the decay schemes for the largely unexplored oddodd

nuclei will be an easier task�

The development of new detectors holds promise for future spectroscopic study of

ssion products� The next generation of � ray detector arrays� such as the proposed

� ray energy tracking array� GRETA ������ will have higher peak e�ciencies �������

and peaktototal ratios ������ and improved � ray position resolution of � �mm�

The latter will nearly eliminate the Dopplerbroadened line shapes ensuing from the

nite size of the � ray detectors in the present arrays� The sensitivity provided by

the high e�ciency and the selectivity provided by the higher � ray fold of these new

arrays will extend the observable region of neutronrich nuclei even further�

���

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��� S� J� Zhu� J� H� Hamilton� Q� H� Lu� A� V� Ramayya� M� G� Wang� B� R� S�

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J� Asztalos� S� Y� Chu� K� E� Gregorich� I� Y� Lee� A� O� Macchiavelli� R� W�

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R� Aryaeinejad� J� Rasmussen� M� A� Stoyer� S� Y� Chu� K� E� Gregorich� M� F�

Mohar� S� Prussin� G� M� TerAkopian� Yu� Ts� Oganessian� N� R� Johnson� I�

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��� D� Cline� NSRL Annual Report ���� ���

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����� C� Y� Wu� personal communication

����� R� J� Storm and M� W� Guidry� Nucl� Inst� and Meth� ��� ��� ������

����� F� Rosel� H� M� Fries� K� Adler and H� C� Pauli� At� And Nucl� Data Tables�

�� �����

����� I� Y� Lee� Proceedings of the Workshop on GRETA Physics� A Slide Report�

Ernest Orlando Lawrence Berkeley National Laboratory February �� ���� �

���

Appendix A

Lifetime Measurement of low�lying

levels in ���Ho

A�� Introduction

���Ho is a well deformed nucleus with an unpaired proton in the ������ Nilsson

orbital� ���Ho also has K���

�and K���

�

�levels which have been interpreted as �

vibrations� The con gurations of these � vibrational levels involve the coupling of a

K�� quadrupole phonon to the �

�ground state� These two collective levels indicate

that ���Ho exhibits a � degree of freedom� Because of this nuclei�s strong quadrupole

deformation the level diagram also exhibits collective rotational bands built on the

ground state and the two � vibrational states� These collective vibrational and ro

tational features make this nucleus a good candidate to test the validity of collective

models in strongly deformed oddA nuclei� For this purpose a study of this nucleus

had been initiated with the goal of measuring the complete set of electric and mag

netic matrix elements connecting the lowlying collective states by using Coulomb

excitation� Coulomb excitation preferentially populates the collective states of a nu

cleus making it the ideal probe for such an investigation� The motivation for the

present recoildistance method �RDM� lifetime measurement of the lowlying levels

of ���Ho was to con rm the results from Coulomb excitation experiments performed

by E� Vogt et al ��� ��

���

A���� The Coulomb Excitation Experiments

Several Coulomb excitation experiments of ���Ho were performed previously using

��O� ��Ni� and ���Pb beams ���� By measuring the excitation process using projectiles

with di�erent nuclear charge over a wide range of scattering angles� it is possible to

overdetermine the values of the electromagnetic matrix elements connecting the low

lying levels� In these experiments four rotational bands were observed� the negative

parity groundstate band� the negative parity K����

�and K��

�

�� vibrational bands�

and a positive parity K���

�band based on the � �

������ orbital� A diagram of levels

observed in these experiments is presented in Figure A��� The ground band was

observed to a spin of ���� the K���

�

�and K��

�

�bands were populated to spins of

��and ��

�� respectively� and the positive parity band was populated to a spin of ��

��

The matrix elements from the experimental � ray yields and scattering angles were

determined from a t to the data using the Coulomb excitation least squares search

code GOSIA ���� The complete error analysis for matrix elements and lifetimes from

these experiments has not been completed and the errors presented are preliminary

and may underestimate the true errors�

The electromagnetic matrix elements measured ���� via these Coulomb excitation

experiments indicate that the intrinsic quadrupole moment� eQ�� of the K����

�and

K���

�� vibrational bands are anomalously large� �� to �� percent larger than that

of the ground band� This result is surprising when interpreted within the framework

of the collective model� In this model the � bands are not expected to have a de

formation� or hence an intrinsic quadrupole moment� signi cantly di�erent than the

ground state� The signi cant di�erence in deformation of the � vibrational band

and groundstate band might be explained by a change in the underlying microscopic

con guration of the valence nucleons� This� however� is not supported by calcula

tions ����� The origin of the larger than expected quadrupole moments of the � bands

remains an unanswered question�

���

7/2− 0.009/2− 94.7011/2− 209.80 13/2− 344.9515/2− 499.2517/2− 672.80

19/2− 863.20

21/2− 1072.40

23/2− 1294.60

25/2− 1536.00

27/2− 1785.30

29/2− 2055.20

31/2− 2326.50

33/2− 2621.30

35/2− 2909.50

37/2− 3226.40

39/2− 3525.50

41/2− 3866.50

43/2− 4162.10

45/2− 4525.50

47/2− 4806.50

49/2− 5192.50

51/2− 5451.00

53/2− 5866.00

11/2− 688.60 13/2− 819.20 15/2− 968.70 17/2− 1136.20

19/2− 1321.00

21/2− 1522.20

23/2− 1739.30

25/2− 1970.40

27/2− 2216.00

29/2− 2471.90

31/2− 2739.00

33/2− 3015.00

35/2− 3300.00

37/2− 3600.00

3/2− 515.50 5/2− 566.80 7/2− 638.30 9/2− 730.30 1/2− 841.50 3/2− 973.10 5/2− 1122.10 7/2− 1292.50

3/2+ 361.70 5/2+ 419.50 7/2+ 491.00 9/2+ 601.30 11/2+ 733.00

19/2− 1476.60

21/2− 1685.00

165Ho

K=3/2−

K=11/2−

K=3/2−

K=3/2+

Figure A��� Level diagram for ���Ho� The matrix elements connecting the levels shownwere measured in the Coulomb excitation experiments ��� �� The level energies aregiven in KeV�

A���� Intrinsic Moments of Bands in ���Ho from InBandMa

trix Elements

The inband electric matrix elements of a rotational band give a direct measure

of its intrinsic quadrupole moment� eQ�� Assuming axial symmetry of the nucleus�

the intrinsic quadrupole moment is related to the inband reduced matrix elements

���

by the relation given in �����

� KI�jjM�E��jjKI� �� ��I� � ���

� � I�K��jI�K ���

���

� �

�

eQo �A���

For the simple collective model the intrinsic moment eQo also can be related to the

quadrupole deformation parameter � in a model dependent way by

Qo ��p��

Z����A

�

�

�� �A���

� � ���� � ���� �� � ����

���

�A���

where equation A�� gives the value of � assuming small deformations� The third

order expansion in equation A�� de nes the deformation parameter ��� which assumes

a spheroidal shape for the nucleus� even for larger deformations� and a sharp radial

cuto� for the nuclear charge distribution �����

The values for the intrinsic quadrupole moment extracted from the measured

static ��J��� and transitional ��J����� matrix elements from Vogt et al�� assuming

axial symmetry �Equation A���� are shown in Table A��� The intrinsic quadrupole

moments listed in the table are weighted averages of the measured matrix elements of

a particular �J for the given band� The �� are calculated only from the �J�� matrix

elements� since experimentally these are more accurately measured because of their

pure E� nature� The intrinsic quadrupole moments and deformations deduced from

the inband matrix elements for the K���

�and K���

�

�are signi cantly larger than

for the ground band� The K����

�band�s deformation of �� ��������� is unusually

large when compared to typical deformations in the rareearth region of � �����

A���� Motivation for the Lifetime Measurement Experiment

For a complex level spectrum� such as the level spectrum of oddA ���Ho� there

can be several hundred matrix elements which need to be t simultaneously� A di�

culty with the Coulomb excitation least squares search analysis� since the parameter

space is so large� is ensuring that the minimum found actually is a global minimum�

��

�J � � �J � � �J � � ����J � ���eb� �eb� �eb�

K��

�eQo � ��� ���� eQo � ��� ��� eQo � ���� ��� ���� ����

K����

�eQo � ��� ��� eQo � �� ���� eQo � ���� ��� ���� ����

K� ��

�eQo � �� ��� eQo � �� ��� eQo � ��� ���� ���� ����

Table A��� Quadrupole moments and deformations of the K��

�ground band and

the K����

�� ��

�� bands of ���Ho measured by Coulomb excitation�

Extracting matrix elements from a local rather than the global minimum would give

erroneous results not representative of the best t to the data� The surprising re

sult of larger than expected intrinsic quadrupole moments in the � bands from the

Coulomb excitation analysis suggest the need for additional experiments to provide

independent con rmation that the Coulomb excitation results are correct� and are

not an artifact of the analysis nding a nonglobal minimum�

In the present work� an additional experiment� a direct measure of the lifetimes of

the lowlying levels by the recoildistance method �RDM�� was performed to provide

an independent measurement of the properties of the lowlying levels of ���Ho� The

directly measured lifetimes and deduced matrix elements from the recoildistance

experiment can be compared to the lifetimes and matrix elements derived from the

Coulomb excitation work�

���

A�� The Recoil�Distance Lifetime Experiment

A���� Experimental Method

The mean lifetimes of lowlying levels of ���Ho are expected to be in the pico

second range� The measurement of the lifetimes was performed using the recoil

distance method �RDM�� which can measure lifetimes in the picosecond range� This

experiment is similar to previous lifetime measurements of ���Nd ����� ���Pd ����� and

�������W ����� A detailed description of the recoildistance method can be found in

references ���� ����

The experimental setup is shown in Figure A��� A beam of ��� MeV ��Ni ions�

accelerated by the Rochester MP Tandem Van de Graa�� was used to Coulomb excite

a �� �g�cm� ���Ho target� The target was prepared by sputtering ���Ho onto a ��

�g�cm� Ni foil� The foil was then stretched to form a �at� re�ective surface� The

backscattered ��Ni ions were detected in an annular parallel plate avalanche counter

�PPAC� ��� placed ��� cm upstream from the target� The PPAC covers a scattering

angular range of ��� to ��� corresponding to a calculated recoil for the ���Ho nuclei

into a forward cone extending from ���� to ������ The recoiling nuclei were slowed by

a movable �� mg�cm� stretched ��Ni foil �shifter foil� mounted between the target

and the � ray detector� The target foil and shifter foil were optically aligned to be

parallel within ������ corresponding to ���� �m variation in distance over the beam

spot diameter� The shifter foil reduces the velocity of the recoiling nuclei to a value

of ������ ������� measured by the Doppler e�ect� where is the fraction of

the speed of light �vc�� The initial recoil velocities of the nuclei were measured by

replacing the shifter foil with a foil ����� mg�cm� Ni� su�ciently thick to stop the

recoils� The Doppler shifted energy of � rays from the recoiling nuclei compared to the

unshifted � ray energy of the stopped nuclei yielded a measurement of the average

initial recoil velocity to be � ������������� introducing a di�erence in the Dopplershifted energy between � rays emitted before the shifter foil ��fast� � rays� and � rays

emitted after the shifter foil ��slow� � rays�� This di�erence in the Doppler shifted

energy allows the �fast� and �slow� peaks to be distinguished easily� For a ��� keV

���

Figure A��� Schematic of the RecoilDistance Lifetime Experiment

� ray the peaktopeak separation between the �fast� and �slow� peak is �� keV� The

� rays were detected by a Compton suppressed Ge detector� placed at �� with respect

to the beam axis� in coincidence with backscattered ��Ni ions�

An �Inchworm� transducer was used to adjust the separation distance between

the target and shifter foil� For distances less than ���m a capacitive measurement

was used to determine the separation to within � �m� Larger separations were

measured to an accuracy of � �m using a optical readout installed on the �Inch

worm� transducer� Gamma ray spectra were collected at �� separate distances from

�� �m to ���� �m� These separation distances between the target and shifter foils

correspond to �ight times for the recoiling ���Ho nuclei ranging from ���� ps to �����

ps�

A���� Lifetime analysis

The lifetimes are measured by comparing the intensities of the �fast� �If� and

�slow� �Is� component of a transition as a function of the separation distances �d�

between the target and shifter foil� For a constant recoil velocity v� the mean lifetime

� of a level is given to rst order by the exponential decay described by lnR � �d�v� �

���

R is the ratio de ned by

R �Is

Is � If�A���

in the case where both the �fast� and �slow� peak can be t� For cases where the

fast peak could not be t reliably due to contamination from other transitions� R was

calculated using

R �IsN

�A���

where N is the total number of recoil nickel ions detected in the PPAC and is pro

portional to total yield of a transition� If � Is�

To rst order� in a plot of lnR vs d� the slope of the data is ���v� � Since N is

proportional to the total yield of a given transition� the slope �and hence �� should

be the same using either Equation A�� or A��� For transitions in which both peaks

could be t� the lifetimes extracted using Equations A�� or A�� are in good agreement�

which validates the use of A��� Using Equation A��� however� results in larger errors

since the decay curve is no longer constrained to go through the point lnR � � at

d � �� There are levels for which the lifetimes could be measured by more than

one decay branch� For these levels� the quoted lifetime is a weighted average of the

lifetimes measured from each decay path�

There are several e�ects which cause deviations in the measured ratio R from

simple exponential decay behavior� These e�ects �nuclear deorientation� feeding

from higher states� solid angle e�ects� and di�erent � ray detection e�ciencies for

the �fast� and �slow� peaks due to their di�erent energies� were corrected using a

modi ed version of the computer code ORACLE ������ Additional modi cations ������

beyond those mentioned in Ref� ����� were made to the code ORACLE to include the

ability for the code to handle nonsequential decay patterns� such as for bands that

have both �J�� �cascade� and �J�� �crossover� transitions� Examples of the decay

curves� showing the raw data along with the data corrected for the above mentioned

e�ects and tted lifetimes� are shown in Figures A��� A��� and A���

In the present work� the lifetimes of the lowest �� levels in the K��

�ground band

and the lowest � levels in the K����

�band were measured� A total of �� observed

transitions were strong enough to yield lifetime information� �� of these were GSB

���

0 200 400 600 800Distance (μm)

0.01

0.10

1.00

R

11/2 GSB ΔJ=1

Corrected dataFit to corrected dataRaw data

τ=17.8+.8 ps

Figure A��� Lifetime of the ���GSB level measured from the ��

�GSB�

�GSB transition

transitions� and were K����

�transitions� Peak intensities of the �fast� and �slow�

component of the transitions were used where possible� For the ��� ��

��J���

��� ��

��J��� and the ��

�� ��

��J�� transitions in the K���

�

�band the fast

peak could not be t and the lifetimes were measured using the ratio R as de ned in

Equation A���

The measured lifetimes are shown in Tables A�� and A��� These lifetimes are

in good agreement with published values ���� and the results from the Coulomb

excitation work ����� That is the present recoil distance lifetime measurement provides

independent con rmation of the validity of the earlier Coulomb excitation results�

A�� Matrix elements derived from the lifetime mea�

surement

The determination of the electromagnetic transition matrix element from level

lifetimes� in principle� is straight forward if the decay branching ratios� transition

���

0 50 100 150 200Distance (μm)

0.10

1.00

R

11/2 K=11/2 to GSB ΔJ=1

Corrected dataFit to corrected dataRaw data

τ=8.66 + .90 ps

Figure A��� Lifetime of the ���K���

�level measured from the ��

�K���

��

�GSB

transition

0 50 100 150 200Distance (μm)

0.10

1.00

R

11/2 K=11/2 to GSB ΔJ=2

Raw dataFit to corrected dataCorrected data

τ=9.36 + .64 ps

Figure A��� Lifetime of the ���K���

�

�level measured from the ��

�K���

��

�GSB

transition

���

Ground Band Transitions

transition Recoil Distance Nucl� Datalevel type measured ��ps� average ��ps� Vogt �����ps� Sheets ���� �ps���

��J�� ���� ��� ���� ��� ���� ����

���

��J�� ���� ��� ���� ��� ���� ����J�� ���� ���

���

��J�� ��� ��� ��� �� ���� ����J�� ���� ���

���

��J�� ���� ��� ���� ��� ���� ��

��

��J�� ���� ��� �� ��� ���� ����J�� ���� ���

��

��J�� ���� ��� ���� ��� ��� ����J�� ���� ���

���

��J�� ���� �� ���� �� ��� ����J�� ��� ���

���

��J�� ����� ��� ����� ��� ��������

���

��J�� ���� �� ���� �� �������� ������

�

��J�� ���� ��� ���� ��� �������� ��������

Table A��� ���Ho Ground Band Lifetimes

K����

�Band Transitions

transition Recoil Distance Nucl� Datalevel type measured ��ps� average ��ps� Vogt �����ps� Sheets ���� �ps���

��J�� ���� �� ���� ��� ���� ����J�� ��� ���

��

��J�� ���� ��� ���� ���� ��� ���

���

��J�� ��� ��� ��� ��� ���� ���

�J�� to GSB ��� ������

��J�� to GSB ���� ��� ���� ��� �����

���

��J�� to GSB ��� ��� ������� ������� �������

���

��J�� to GSB ���� ���

Table A��� ���Ho K����Band Lifetimes

���

multipolarities� and mixing ratios for all the decay paths are known� In the RDM

experiment� the decay branching ratios can be reconstructed from the measured �

ray yields� but no measure of the E��M� mixing ratios for the �J�� transitions are

made� However� with a few reasonable assumptions� it is possible to set limits on the

electromagnetic matrix elements�

The quantities actually measured in this experiment are y����� the � ray yields

at ��� These � ray yields for the various decay paths deexciting a given level were

measured by adding the intensities of the slow and fast �Is � If� peaks in the �

spectrum summed over all distances� For the transitions where the fast peak could

not be t� the fast peak intensities were calculated by�

If � Is �I�

f

I �s�A���

where the I�

are intensities of clean decay branches originating from the same level�

These � ray intensities were then corrected for the energy e�ciency� �� of the � ray

detector at the energy of the observed � ray and for the angular distribution� W �����

of the � ray� The angular distribution correction factors were calculated with the

Coulomb excitation code GOSIA� The corrected � ray intensities are given by�

Ii �y����

�iW �����A���

A part of the decay for a given branch proceeds through internal conversion and

is unobserved by the � ray detectors in this experiment� Thus� the branching ratios

�BR� are given by

BRi �Ii � �� � �i�Pl Il � �� � �l�

�A��

where the �i are the internal conversion coe�cients as calculated in Ref� ������ The

electromagnetic part of the partial width for a speci c decay path now is given by

%iEM �BRi � �h

�� � �i� � �i �A���

For �J�� transitions� which have pure E� multipolarity� this partial decay width

is directly related to the transition probability B�E�� and� hence� also is related to

���

the square of the matrix element� For the �J�� mixed multipolarity transitions� the

electric and magnetic partial decay widths can be separated by

%EM � %E� � %M� � %E��� � ��� �A����

where is the E��M� mixing ratio of the transition� Since this experiment made no

measure of the mixing ratio� it is necessary to add an additional constraint to the

�J�� transitions in order to have enough information to set limits on the matrix

elements� For all inband transitions in both the K��

�and the K���

�

�band the

� J jjE�jjJ � � � matrix element was allowed to vary between � to � times the value

given by the rotor relation�

� J jjE�jjJ � � ��q� � �J � �� � � � �J � ��K��jJK �

s�

���eQ� �A����

with eQ������ eb ����� No constraints were placed on the E��M� mixing ratios for

the �J�� interband �K����

�band to K�

�

�band� transitions� These transitions

were allowed to vary in multipolarity from pure M� to pure E�� The limits on the

transition matrix elements were calculated with these constraints�

A���� Ground Band Matrix Elements

The derived electric and magnetic inband matrix elements for the ground band

from the RDM lifetime measurement experiment and from the Coulomb excitation

experiments are shown in Figures A�� and A��� respectively� The results from the two

experiments are in reasonable agreement� The measured electric and magnetic matrix

elements from both experiments show good agreement with the axially symmetric

rotor model with an intrinsic quadrupole moment of eQ������ eb and a di�erence in

gyromagnetic factors of �gK � gR� � ���� �����

A���� K���

�

�

InBand Matrix Elements

The matrix elements from the Coulomb excitation and RDM experiments for

the K����

�inband transitions are shown in Figures A� and A��� As mentioned

���

5.5 10.5 15.5 20.5Spin

1

3

5

7

9

11

<I||

E2|

|I−2>

(eb

)

Ground Band E2 ΔJ=2 Matrix Elements

Recoil−Distance Matrix ElementsCoulomb Excitation Matrix Elements

eQ0=7.67 eb

Figure A��� Ground Band E� matrix elements from the Coulomb excitation work andfrom the RecoilDistance lifetime measurement�

5.5 10.5 15.5 20.5Spin

0

2

4

6

8

10

<I||

M1

||I−

1> (

μ N)

Ground Band M1 ΔJ=1 Matrix Elements

Recoil−Distance ResultsCoulomb Excitation Results

gK−gR = 0.93(1)

Figure A��� Ground Band M� matrix elements from Coulomb excitation work andRecoilDistance lifetime measurement

��

7.5 9.5 11.5 13.5 15.5 17.5Spin

0

5

10

15

20

<I||

E2|

|I−2>

(eb

)

K=11/2 Band Inband E2 ΔJ=2 Matrix Elements

Recoil−Distance ResultsCoulomb Excitation Results

eQ=7.67 eb

eQ=10.4 eb

Figure A�� E� matrix elements for K����� from �J�� inband transitions

previously� the error analysis for the Coulomb excitation work has not been completed

and the errors presented for the matrix elements are still preliminary� Hence� a

quantitative comparison between the two data sets is not possible� The inband

�J�� matrix elements for the K����

�band from the RDM experiment show good

agreement with the Coulomb excitation results� and are consistent with this band

having a quadrupole moment eQ��������� eb� The di�erence in the gyromagneticfactors for this band is gk�gR � ��������� suggesting the same microscopic structureas the ground band�

A���� K���

�

�

Band to Ground Band Matrix Elements

The E��J��� E��J��� and M� matrix elements for the K����

�to K�

�

�ground

band transitions are shown in Figures A���� A���� A���� The RDM E��J�� and M�

matrix elements from the K����

�band to the ground band show good agreement with

the Coulomb excitation results� The derived limits for these matrix elements cover a

fairly large range since no restrictions were placed on the E��M� mixing ratio� Thus�

���

5.5 10.5 15.5Spin

0

5

10

15

<I

|| M

1 ||

I−1

> (

μ N)

M1 K=11/2 In−band Matrix Elements

Recoil−Distance ResultsCoulomb Excitaion Results

gK−gR = 0.90(10)

Figure A��� K����M� inband matrix elements

these do not present as sensitive a comparison with the Coulomb excitation results�

The �J�� K����

�to ground band matrix elements show only marginal agreement

with the Coulomb excitation results�

A�� Summary

The recoildistance method was used to measure the lifetimes of the �� lowest

levels �up to spin ��� of the ground band and the � lowest levels �up to spin �

�� of the

K����

�band� The measured lifetimes from the recoildistance experiment are in good

agreement with the lifetimes derived from the Coulomb excitation experiments� Lim

its on the transition matrix elements were extracted from the lifetimes and measured

� ray yields� These matrix elements show reasonable agreement with the results from

previous Coulomb excitation experiments performed by Vogt et al� �����The results

from the recoildistance lifetime measurement are consistent with the � vibration

K����

�band having an intrinsic quadrupole moment eQ������ ��� eb� correspond

���

5.5 6.5 7.5 8.5 9.5Spin

0.2

0.3

0.4

0.5

0.6

0.7

0.8

<I

K=

11/2

|| E

2 ||I

−2

K=

7/2>

(eb

)

E2 ΔJ=2 K=11/2 to GSB

Recoil−Distance ResultsCoulomb Excitation Results

Figure A���� E� �J�� matrix elements connecting the K����band to the ground

band

5.5 6.5 7.5 8.5 9.5Spin

−2

−1

0

1

2

<I,

K=

11/2

|| E

2 ||I

−1,

K=

7/2>

(eb

)

K=11/2 Band to GSB E2 ΔJ=1 Matrix Elements

Coulomb Excitation ResultsRecoil−Distance Results

Figure A���� E� �J�� matrix elements connecting the K����band to the ground

band

���

5.5 6.5 7.5 8.5 9.5Spin

−0.2

0

0.2

0.4

0.6

0.8

<I,

K=

11/2

|| M

1 ||

I−1,

K=

7/2>

(μ Ν

)

K=11/2 Band to GSB M1 Matrix Elements

Coulomb Excitation ResultsRecoil−Distance Results

Figure A���� M� matrix elements connecting the K����band to the ground band

ing to an unusually large quadrupole deformation of �������� which is ��� larger

that the ground state band deformation� The similarity of the di�erence of the gyro

magnetic factors gK�gR between the ground band and the K����

�band suggests that

these two bands have the same microscopic structure� The agreement between the

results from the RDM experiment and Coulomb excitation experiments con rms that

the surprising result of larger than expected quadrupole deformations in the � bands

is a real e�ect and not an artifact of the Coulomb excitation analysis� Further in

vestigation is required to understand the origin of the anomalously large deformation

observed in the � vibrational bands of ���Ho�

���

Appendix B

Gammasphere Calibration

The method for calibrating the energy and relative e�ciency of the Ge the energy

of BGO elements of the GAMMASPHERE array are described in this appendix�

B�� Energy and E�ciency Calibration

The energy spectra of the individual Ge detectors were calibrated using ���Ta

and ���Eu sources� A sample calibration curve is shown in Figure B��� The intrinsic

energy resolution of the GAMMASPHERE array was obtained from the measured

fullwidthhalfmaximum of the peaks in the summed energy spectra� and these were

t to the formula given in ���� The result is shown in Figure B��� The relative energy

e�ciency of GAMMASPHERE was measured from the intensities of the � ray peaks

in the summed calibration data� and is shown in Figure B��� The relative e�ciency

measurement was performed with ����� mm Cu and �����mm Ta absorber over Ge

detectors�

The energy spectra of the BGO detectors were calibrated using a ��Y source� The

resultant summed spectra of all the BGO elements is shown in Figure B��� The energy

resolution of the BGOs is ���

���

0 1000 2000 3000Channel (compressed by 2)

0

500

1000

1500

Ene

rgy

Energy Calibration152

Eu and 182

Ta Sources

Real EnergyFit Fnergies

E=a*chan+ba=0.6667(3)b=−0.1(4)

Figure B��� Energy Calibration curve for GAMMASPHERE�

0 500 1000 1500 2000E (keV)

0

1

2

3

4

FW

HM

(ke

V)

Calibration γ−ray ResolutionFWHM=(A1

2+A2

2(E

1/2)

2)

1/2

FWHM fitCalibration DataA1=1.66 (Noise)A2=0.0651 (counting)

Figure B��� Intrinsic � ray energy resolution for GAMMASPHERE

���

10 100 1000 10000Gamma Energy

0.01

0.10

1.00

10.00

Rel

ativ

e ef

fici

ency

Relative Efficiency of GAMMASPHEREWith 0.005 in. Cu and Ta absorbers

152Eu

182Ta

Figure B��� Relative e�ciency curve for GAMMASPHERE�

0 1000 2000 3000Energy (keV)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

1e+05

88Y BGO Calibration Spectum

Figure B��� BGO calibration spectra� The spectrum shown is the sum of all the BGOelements of the GAMMASPHERE array�