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UMI

Spectroscopy of 215Ac and (p,t) Studies of the

Stable Palladium Isotopes

A Dissertation Presented to the Faculty of the Graduate School

of Yale University

in Candidacy for the Degree of Doctor of Philosophy

by Ryan Winkler

Dissertation Director: Andreas Heinz

December 2009

UMI Number: 3395981

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Contents

List of Figures v

List of Tables ix

Acknowledgements xi

Preface 1

I Spectroscopy of 215Ac 3

1 Introduction 4

1.1 The nuclear shell model 4

1.2 The pairing interaction in nuclei 7

1.3 Single particle shell structure in heavy nuclei 9

1.4 Experimental verification of mean field predictions 14

2 Experimental Techniques 18

2.1 Spectroscopic studies of fusion-evaporation residues 18

2.1.1 Gas-filled separators 19

2.2 SASSYER 22

2.2.1 YRASTball 23

2.2.2 SASSYER focal plane apparatus 23

iii

2.2.3 Recoil tagging of prompt gamma rays 28

2.2.4 Recoil-Decay tagging of prompt gamma rays 32

2.2.5 Signal processing and electronics 32

2.3 Experimental determination of gamma ray characteristics 36

3 Experimental Results 39

3.1 Experimental parameters 39

3.2 Delayed gamma ray emission 40

3.3 Alpha decay and implant identification 40

3.4 Recoil-decay tagging of prompt gamma emission 46

3.4.1 MACY energy loss measurements 49

3.5 Recoil tagged prompt gamma analysis 50

3.6 Alpha-gamma coincidences 55

4 Discussion 59

4.1 Observation of low-lying states in 215Ac 61

4.2 High-spin states of 215Ac 66

II High-resolution (p,t) Studies of the Stable Palladium Isotopes 71

5 Introduction 72

5.1 The Interacting Boson Model 74

5.2 Quantum phase transitions in nuclei 77

5.3 Excitation of nuclear states via transfer reactions 78

5.3.1 The Distorted-wave Born approximation 78

6 Experimental Techniques 82

6.1 Experimental apparatus 82

IV

7 Experimental Results 89

7.1 Population of excited states of I04,u)6,i08pd 8 9

8 Discussion 100

8.1 Systematics of low-lying states of the Palladium isotopes 100

8.2 The search for enhanced level density of excited 0+ states 102

8.3 Collective model description of the two-nucleon transfer strengths to excited

0+ states 106

8.4 Excited 0+ populations strengths in the sd-IBM framework 108

III Conclusions and Outlook 117

Appendix 120

References 124

v

List of Figures

1 Nuclear landscape 2

1.1 Modified harmonic oscillator level energies 6

1.2 Schematic depiction of pair scattering 8

1.3 Self-consistent mean field prediction of single particle spectra in 208Pb . . . 11

1.4 Self-consistent mean field prediction of single particle spectra in f§f 114 . . . 12

1.5 Two-proton separation energies for the iV = 126 isotones 15

1.6 Decay paths of an excited compound nucleus 17

2.1 Trajectory of ions through a gas-filled magnetic region 21

2.2 YRAST ball Germanium detector array 24

2.3 SASSYER focal plane assembly 25

2.4 Photograph of the mounted wire grids that comprise MACY 26

2.5 Exploded view of MACY 26

2.6 Schematic of the delay lines in the position-sensitive wire grids of MACY . 27

2.7 Schematic of the geometry of SASSYER and its detector systems 28

2.8 Photograph of the pair of DSSDs mounted in the focal plane chamber . . . 30

2.9 Design schematic of the DSSD cooling assembly 31

2.10 Digital schematic and output signals of the MUX-16 module 33

2.11 DSSD signal path to the ADC/Trigger input 34

2.12 Trigger logic for SASSYER focal plane detectors 35

2.13 Orientation for linear polarization measurements 38

v i

3.1 Previously observed excited states of 215Ac 41

3.2 Delayed gamma spectrum observed at the focal plane of SASSYER in coin­

cidence with a MACY anode event 42

3.3 Delayed gamma rays coincident with the 175 keV transition of 215Ac . . . . 42

3.4 The energy spectrum for each (front side) strip of the beam left DSSD . . . 43

3.5 Energy spectrum of the first-generation alpha decay observed in the DSSDs 43

3.6 Energies of the position-correlated first- and second-generation alpha decays 44

3.7 Second-generation alpha decay of 2 : iFr 45

3.8 Second-generation alpha decay of 209Fr 46

3.9 First-generation alpha decay of residues 47

3.10 Natural logarithm of the decay time for the ground state alpha decay of 215Ac 48

3.11 Recoil-decay tagged spectrum of prompt gamma rays of 215Ac 48

3.12 Recoil-decay tagged spectrum of prompt gamma rays of 213Ac 51

3.13 Cathode energy loss measurement of ions traveling through MACY 51

3.14 Time-of-flight of ions between MACY and the DSSDs 52

3.15 Cathode energy loss measurement gated on the recoil time-of-fiight peak . . 52

3.16 Recoil-tagged prompt gamma rays coincident with the 296 keV transition of

215Ac. The prominent K-shell x-rays and gamma rays are labeled accordingly. 53

3.17 Recoil-tagged prompt gamma rays coincident with the 999 keV transition of

215Ac. The energies of prominent gamma rays are labeled 53

3.18 Delayed gamma emission coincident with the 296 keV prompt transition of

215Ac 54

3.19 Time-of-flight dependence of the correction factors for the intensities of the

delayed gamma rays 55

3.20 Alpha-gamma coincidence spectrum 56

4.1 Comparison of previously available spectroscopic data of 215Ac with large-

scale shell model calculations 60

vii

4.2 Prompt gamma events coincident with isomeric gamma decay 62

4.3 Prompt gamma rays coincident with the 304 keV transition of 215Ac 63

4.4 Prompt gamma events coincident with 859 keV peak 64

4.5 Systematics of the energies of the low-lying states in the N = 126 isotones . 65

4.6 States below the 29/2+ isomer in 215Ac 68

4.7 Comparison of excited state energies of 213Fr and 215Ac with shell model

calculations 69

4.8 Experimental level scheme of 215Ac 70

5.1 Region of nuclear chart spanned by recent (p,t) studies 73

5.2 Symmetry triangle of the IBM 76

5.3 Depiction of the coupled channel mechanism for a transfer reaction 79

5.4 Triton angular distributions for a variety of ground state wavefunctions for

a two-neutron transfer reaction 80

6.1 Schematic of the MLL Q3D spectrograph 83

6.2 Photograph and schematic of position-sensitive cathode strip detector . . . 84

6.3 Shape of angular distribution for L = 0, 2, 4 transfer 85

6.4 Triton position spectrum for three excitation energy windows 86

6.5 The excitation energy dependence of the position of the scattered tritons . . 87

7.1 Particle energy loss in the cathode strip detector 90

7.2 Particle kinetic energy and energy loss in the cathode strip detector . . . . 90

7.3 Triton position spectra for the production of 108Pd 91

7.4 Angular distribution for the population of the 2145 keV state in 108Pd . . . 93

7.5 Angular distributions of selected 108Pd states 95

7.6 Angular distribution for the population of the 2014 keV state in 108Pd . . . 97

7.7 Angular distribution for the population of the 1624 keV state in 108Pd . . . 97

8.1 Evolution of the low-lying structure of the Palladium isotopes 101

viii

8.2 Evolution of 2f energies and R4/2 values of the Pd isotopes 102

8.3 Evolution of R4/2 and population strength of 0+ for Gd isotopes 103

8.4 IBM description of the energy of excited 0+ states as a function of 77 . . . . 104

8.5 Number of excited 0+ states and IBM fits for rare earth isotopes 105

8.6 Excited 0+ state energies of the Pd isotopes and IBM comparison 106

8.7 Two-neutron transfer population strengths of 0+ states in i°2,i06,ro8pd 108

8.8 Relative s boson transfer cross sections to 0^ for U(5)-SU(3) 110

8.9 Relative s boson transfer cross sections to 0+ax for U(5)-0(6) 112

8.10 Calculated s boson transfer cross sections for contours of <5R4/2, C = -V7/2 113

8.11 Calculated s boson transfer strengths to excited 0+ states for multiple tra­

jectories through the symmetry triangle 114

8.12 Cross sections for the population of the first excited 0+ state and corre­

sponding <5R4/2 values for Mo(t,p) reactions 115

13 Horizontal position spectrum for a single DSSD exposed to an alpha cali­

bration source 120

14 DSSD hit pattern generated after exposure to an alpha calibration source. . 121

15 Front strip energy spectra for PuCm source 122

16 Combined PuCmAm source energy spectrum of front strips for beam left

DSSD 123

17 Energy difference between front and rear strips of the beam right DSSD. . . 123

IX

List of Tables

3.1 SASSYER experimental settings for the transmission of 215Ac 40

3.2 Ground state alpha decay energies and lifetimes of selected Francium, Radon,

Radium, and Actinium isotopes 49

3.3 Energies and Intensities for the recoil-decay tagged prompt gamma rays for

215 Ac and 213Ac 50

3.4 Recoil tagged prompt gamma-gamma coincidences 57

3.5 Energies and intensities for the gamma ray decay of 215Ac and 213Ac . . . . 58

7.1 Energies and cross sections for observed 0+ states in 108Pd 94

7.2 Energies and cross sections for observed 0+ states in 102>106pd gg

7.3 Energies and maximum cross sections of 2+ states of I02,i06,i08p^ gg

7.4 Energies and maximum cross sections of 4+ states of io2.106.108p(i 99

8.1 Number of observed excited 0+ states of the Palladium isotopes 107

8.2 Parameter values for the calculation of two-nucleon IBM transfer strengths

along the U(5)-SU(3) leg of the symmetry triangle 116

3 Alpha decay energies of PuAmCu source used for energy calibration of DSSDs.122

x

Acknowledgements

The completion of this work would not have been possible without the group of family

and friends that have offered me their unwavering support during my time as a graduate

student and throughout the rest of my life.

Andreas Heinz, thank you for being a great adviser through all the ups and downs of

my graduate student career. Thank you for your guidance and support that began with

my first summer at WNSL, persevered through a difficult project, and ultimately led to

the completion of this thesis.

I am grateful to Rick Casten, Volker Werner, Con Beausang, and Andreas Heinz for your

boundless enthusiasm and advice. You, along with the former graduate students of WNSL:

Libby McCutchan, Deseree Meyer, John Ai, and Giilhan Giirdal, laid the foundation for

my love of Physics. I came to Yale not knowing exactly which direction my studies would

take me and, because of you, I do not regret the path I have chosen.

Thank you to all the members of my dissertation committee: Andreas Heinz, Rick

Casten, Yoram Alhassid, Peter Parker, Michael Zeller, and my outside reader Paddy Regan.

I greatly appreciate the time you have spent selflessly as members of my committee.

To all of the staff at WNSL: Karen DeFelice, Paula Farnsworth, Mary Anne Shultz,

Kelli Kathman, Jeff Ashenfelter, Walter Garnett, Sam Ezeokoli, Sal DePrancesco, Craig

Miller, John Baris, Tom Barker, and Dick Wagner, thank you for making life at the lab

possible. You were always there to help solve the many problems I encountered as a student

at WNSL.

xi

I am indebted to all the past and present scientists at WNSL: Robert Casperson, Nick

Thompson, Adam Garnsworthy, Russ Terry, Liz Williams, Jing Qian, Gregoire Henning,

Axel Schmidt, Daniel Prank, Christopher Lambie-Hanson, not only for your intellectual

contributions to this work but for making the lab an exceptional place to work.

Mom, Dad, and Kevin, I am where I am today because of you. None of this work would

have been possible without your unconditional love and encouragement.

Anne, words cannot express how lucky I am to have you in my life. Thank you for your

limitless patience, love, and support.

This work was supported by the US Department of Energy, under grant numbers DE-

AC02-06CH11357 and DE-FG02-91ER-40609, and by Yale University.

XII

Abstract

Spectroscopy of 215Ac and (p,t) Studies of the Stable

Palladium Isotopes

Ryan Winkler

2009

The study of both the microscopic and macroscopic structural evolution of the atomic

nucleus is presented in this work. The excited states of the N = 126 isotone 215Ac were

investigated at WNSL using the gas-filled recoil separator SASSYER. Recoil-decay tagging

of the gamma rays corresponding to the decay of 215Ac after production via a fusion-

evaporation reaction was made possible by using the redesigned SASSYER focal plane

apparatus, including the addition of a pair of DSSDs and the multi-wire avalanche counter

MACY. A number of transitions feeding the 29/2+ isomeric state corresponding to the

(7r/ig ,2)®(7ri13//2) configuration were observed and tentatively assigned as decays from the

high-spin 35/2+, 39/2+, and 41/2+ states. Additionally, the decay from the low-lying

13/2+ state, corresponding to a 7ri13/2 quasiparticle excitation, was observed at 859 keV.

This excitation energy is consistent with the systematics of the lighter N = 126 isotones

suggesting a decrease in the energy gap between the 7r/i9/2 and 7ri13/2 orbitals.

High-resolution (p,t) spectroscopy of the stable, even-even Palladium isotopes was per­

formed in the search for signatures of quantum phase transitional behavior. A total of

54 previously unidentified 0+ , 2+ , and 4 + states below an excitation energy of 3.5 MeV

were discovered in this experiment. No enhancement of the 0+ level density, a signature

of first-order phase transitions in nuclei, was observed in the studied isotopes. A theoret­

ical description of the population strengths of excited 0+ states in two-nucleon transfer

reactions was investigated within the framework of the IBM. These studies reveal that an

enhanced population strength is not exclusive to regions of shape-coexistence but rather

is a measure of the magnitude of the "change of structure" from the initial to residual

nucleus.

Preface

From the moment the existence of the atomic nucleus was confirmed by Rutherford in

1911 [1], great effort has been dedicated to the experimental and theoretical study of its

structure. Subsequent experiments revealed that the nucleus is composed of two strongly

interacting constituents, the proton and neutron. The complex interactions of these two

nucleons dictate the properties of the nuclear quantum many-body system. Further inves­

tigation of the nuclear landscape, depicted in Figure 1, exposed regions of similar structure

and systematic trends centered around specific numbers of protons and neutrons. These

observations lead to the adoption of the shell structure paradigm of atomic physics for

the description of nuclei. It was also observed that the spherical shape of the nuclei near

these closed shells gives way to a variety of deformations as the number of valence nucleons

increases.

The study of this quantum many-body system continues today after nearly a century

of steadfast commitment. The present work addresses two current, seemingly unrelated

topics of nuclear structure: the microscopic variation of the energies of single particle

states and the macroscopic transition between nuclear shapes. However, both of these

ideas represent the common and pervasive theme of the structural evolution of the atomic

nucleus as a function of the number and type of nucleons it possesses. As the development

of novel experimental techniques continues the extension and exploration of the boundary

of known isotopes, particularly in the regions of very neutron-rich or super-heavy nuclei

(Z > 102), the interpretation of these nuclei requires microscopic, macroscopic, or even a

1

Stable nuclei

Terra incognita

Neutrons

Figure 1: Nuclear landscape adopted from Ref. [2]. The yellow region represents all known nuclear isotopes. Stable isotopes are indicated in black. The region labeled "Terra incog­nita" contains isotopes yet to be discovered. The locations of the "magic numbers" are depicted with red lines.

combination of these two approaches.

The first part of this dissertation focuses on the microscopic description of the nucleus,

namely the evolution of the energies of proton single particle states in the N = 126 isotones

beyond Lead and the effect of the details of this evolution on the stability of super-heavy

elements. The second part of this work involves the investigation of excited 0 + states in

even-even collective nuclei and the properties of these excited states that provide signatures

of rapid shape transitions along isotopic chains.

2

Par t I

215 Spectroscopy of Z i 0Ac

3

Chapter 1

Introduction

1.1 The nuclear shell model

Perhaps the most utilized description of the atomic nucleus is the nuclear shell model

[3, 4]. The foundation of the shell model begins with the assumption that the complex

many-body interactions between constituents in nuclei can be, to first order, described as

independent single particle motion in a mean field. The assumption that all the nucleons

move independently in a mean field potential, a potential that is itself composed of the

sum of all nucleon-nucleon interactions within the nuclear system, drastically simplifies the

physical description of the nuclear many-body problem. The Hamiltonian describing an

A-nucleon system in can be written as

A A

i= l i,j=l

where Tj describes the kinetic energy of nucleon i and Vij describes the the two-body

interaction between nucleon % and j . Assuming the nucleons are bound in a mean field

4

potential, the above equation yields

A A A

H = ^[Ti + U(ri)] + {±1£iVij-YiU(ri)) i= l i j = l *=1

== tl0 -+- tlrea

A = ^h0[%) + HTea. (1-2)

i=i

Here H0 describes the motion of A non-interacting nucleons in a mean field. The second

term of the Hamiltonian represents residual interactions, small perturbations on the inde­

pendent A-nucleon system. The description of the nucleus is achieved by solving for U(r;),

the mean field potential experienced by all constituents in the nuclear system.

Properties of the atomic nucleus, such as an increase in nucleon separation energies for

specific numbers of nucleons [5], suggest a shell structure similar to that of electrons orbiting

the nucleus. The so-called magic numbers, the number of nucleons experimentally observed

to result in enhanced stabilization, can be reproduced by applying a few modifications,

described below, to the well-known simple harmonic oscillator potential. The states of the

simple harmonic oscillator are designated by the quantum numbers (n, j , I) corresponding

to the major oscillator shell, the total angular momentum (the vector sum of the intrinsic

spin and the orbital angular momentum), and the orbital angular momentum of the state.

In a spherical potential, the orientation of the orbital angular momentum, associated with

the quantum number m has no effect on the energy of the state. Hence, an orbit of angular

momentum I has (21 + 1) degenerate magnetic substates. The addition of a centrifugal I2

term breaks the orbital angular momentum degeneracy while the addition of a spin-orbit

interaction is the dominant ingredient in the reproduction of the magic numbers. The

characteristic single-particle energies for the simple harmonic oscillator and the effect of

each modification to the potential and the resulting breaking of degenerate states of the

simple model are conveyed in Figure 1.1.

The residual interaction, H res, of Equation (1.2) is a two-body interaction that is typi­

cally, for realistic descriptions, derived from bare nucleon-nucleon scattering data [7]. How-

5

N-6

aw V

^JLAQJ •••'Jcifi

3? -*<• - h

N = 4 3s : .2di„ -r = — — - - - — a ~L ^ ^ _ 3li,

^ ~ ~ _ . * Z "^*l/n

^ X F r - N - , - ' ' ""*"- Ifyfl (3£> ig ^ ^ cm M^ *%2

N = 3 2p 2n " sr — — f - - - — ^ ^ *• IP

2tf> u " ^ - C2Hy Ir'^ 7/2

N = 2 2 s _ _ - - 1 d w "™ *"" - * »-, .. -*" - / ^

id - i d g

^-^ CD N = l ^P - - - ~ l p i Q

,f"

N = 0 Is

SJH.O + I2 + hs -Is

1311/2

Figure 1.1: The energies of single particle states in the simple harmonic potential (SHO). The effect of the addition of a spin-orbit and centrifugal interaction is displayed. The major oscillator shell is denoted by N. This figure is adopted from Ref. [6].

ever, the extraction of the two-body matrix elements from the bare nucleon-nucleon po­

tential is quite difficult. The "bare" two-body matrix elements must be renormalized to

account for a finite model space and nuclear medium effects to produce an effective interac­

tion [3]. The residual interactions are responsible for configuration mixing, the scattering

6

of nucleons from one orbit to another. It is the primary physical ingredient for the evo­

lution of the structure of nuclei across the nuclear landscape. The effect on the nuclear

Hamiltonian and the energies of multi-particle configurations are described below. The

energy shift of a two-particle configuration can be written as [6]:

AEU1J2J) = < JihJM\V12\jij2JM >= - = L = < J132JWV12WJ1J2J >, (1-3) y/2J + 1

where identical particles in state \j1j2J > are coupled to a total angular momentum J

and magnetic substate M. In the absence of this interaction all J states of a two-particle

configuration would be degenerate.

The shell structure described above provides a simplified framework for the physical

description of the atomic nucleus. Protons and neutrons occupying states in the filled shells

of their respective potentials can be excluded in the shell model Hamiltonian describing the

nuclear system. The nucleons in these filled shells are typically not involved in the low-lying

excitation structure of a nucleus and can thus be treated as an inert core. However, bulk

properties of the nucleus, for example the binding energy, are dependent on the nucleons

"excluded" from the shell model Hamiltonian.

1.2 The pairing interaction in nuclei

The description of the residual interaction is not complete without the inclusion of a vital

additional ingredient, the pairing interaction. The pairing force is the strong, attractive,

and short-range interaction between two identical nucleons coupled to a J = 0 configura­

tion. In the absence of the pairing interaction, nucleons fill their respective orbits up to the

sharp Fermi level; all states above this energy are unoccupied while states below are fully

occupied. The short-range force of the pairing interaction scatters pairs of identical nucle­

ons across the Fermi level creating a smoother probability distribution for the occupation

of single-particle states. The idea of a discrete number of particles occupying each state

7

shifts to a partial filling of levels near the Fermi energy with the introduction of the pairing

interaction. The configuration of excited states also shifts from a particle-hole description

to that of the creation of two or more quasi-particles. A schematic of the distribution of

nucleons and the effect of pair scattering is presented in Figure 1.2.

Fermi Level

Particle Quasi part ic le

Figure 1.2: A schematic depiction of pair scattering. The red circles represent particles filling orbits. In the quasiparticle picture, the pairing interaction results in the partial occupancy of each state.

The pairing interaction introduces a short-ranged, attractive component to the nuclear

Hamiltonian that can be written as [61

< jl32J\VVair\hjiJ' >= -G{jl + - ) 2 ( J 3 + ^ 2 5nj26J3J4SJoSj>0 (1.4)

where G is the strength of the pairing force. In the absence of pairing, the excitation energy

required to excite a nucleon beyond the Fermi energy A is simply (e, - A), where e; is a

single-particle energy. This single-particle excitation energy is modified to a quasi-particle

8

excitation energy Ei with the introduction of pairing. Ei can be written as

Ei = V(ei - A)2 + A2 (1.5)

where A is the pairing gap parameter [6].

The main consequence of the introduction of the pairing force in even-even nuclei is

the depression of the 0+ ground state as a result of mixing with higher-lying 0+ states.

For this reason the ground state of nearly all even-even nuclei is a 0+ state. However, in

odd nuclei the pairing interaction leads to a compression of quasi-particle excited states

above the ground state. The excitation energy E^.i required to replace the quasi-particle

corresponding to the ground state with that of a different level is written as

E°xi = Ei-E0 = y/{ei - A)2 + A2 - ^(e0 - A)2 + A2. (1.6)

For quasi-particle configurations near the Fermi level, ej - A < < A. Therefore, the resultant

excitation energy Exi decreases in the presence of the pairing interaction for odd mass

nuclei.

1.3 Single particle shell structure in heavy nuclei

The extrapolation of proton and neutron shell structure towards super-heavy nuclei is a

vital ingredient for the prediction of the existence and location of the next spherical dou­

bly magic super-heavy nucleus. The description of heavy nuclei, where the shell model

problem becomes intractable due to the size of the model space and the limits of mod­

ern computer capabilities, is typically provided by alternate methods; the most popular

being the macroscopic-microscopic model introduced by Strutinsky [8]. In the macroscopic-

microscopic model, the energy of the nuclear system is divided into two parts: a macro­

scopic term in which bulk properties of the nucleus are described, and a microscopic term

that includes the effects of proton and neutron shell structure. The liquid drop model [9],

9

in which the nucleus is described as a charged, incompressible fluid with a well-defined

surface, is often used for the macroscopic description. It is the competition between the

macroscopic and microscopic components of this model that dictates not only the stability,

but the very existence of super-heavy nuclei. Qualitatively, the fission barrier of the nu­

clear system described by the liquid drop model becomes negligible due to the dominance

of the long-range Coulomb repulsion over the short-range nucleon-nucleon interaction in

a system with many protons. As a result, bound state stability is derived directly from

the proton and neutron shell structure, offsetting the repulsive Coulomb forces. Therefore,

the accurate extrapolation of proton and neutron shell structure to the super-heavy mass

regions is of paramount importance for the successful prediction of the location of relatively

long-lived, super-heavy mass regions where half-lives are expected to increase [10, 11, 12].

In addition to the macroscopic-microscopic model, there are a variety of other theo­

retical approaches used to predict nucleon single-particle states in super-heavy systems.

The extrapolation of proton and neutron shell structure is model-dependent and heavily

influenced by the parameters used for each calculation. Relatively recent parametrizations

of macroscopic-microscopic models suggest ^||114 to be the next doubly magic nucleus

i.e. predicted proton and neutron shell closures at Z = 114 and N = 184, respectively

[13, 14, 15]. However, these predictions are hindered by the required knowledge of level

density and nuclear potential that is limited at the extremes of nuclear stability [16]. Al­

ternatively, self-consistent mean field methods can be used for the extrapolation of both

proton and neutron single particle shell structure to super-heavy nuclei. The Skyrme-

Hartree-Fock (SHF) approach [17] and relativistic mean field model (RMF) [18, 19, 20] are

two successful techniques that have been used to predict single particle spectra for heavy

isotopes.

A large number of parametrizations are available for both the Skyrme interaction [21,

22], an effective two-body force, used in the SHF approach and scalar or vector field

strengths used for RMF calculations. These parametrizations vary in the description of

the nucleon effective mass, average level density, and spin-orbit strength but generally

10

produce similar results for stable nuclei. Only when these parametrizations are used to

predict the shell structure of super-heavy nuclei discrepancies arise. Figure 1.3 shows the

+1 > « C L ,t a , ' P < , - ' - < ' * r r t e ' 5 N C " » ! ^

ii to m

Figure 1.3: Self-consistent and relativistic mean field predictions of proton (top) and neu­

tron (bottom) single particle spectra in 208Pb. The dependence of the orbital energies as

a function of the parameter set used is displayed. Parameter sets designated with the Sk-

prefix correspond to Skyrme force parameterizations. RMF parameter sets are designated

by the NL- prefix. Energy spacings at Z = 82 and N = 126 are evident for each parameter

set. A significant energy gap between the 7rlh9/2 and ^2/7/2 orbitals is suggested by RMF

calculations. The self-consistent mean field predictions are compared with those of the

folded-Yukawa model (FY) [23]. This figure is adopted from Ref. [16].

11

single particle spectra for protons and neutrons of Pb derived from various Skyrme

force (Sk- prefix) and RMF (NL- prefix) parameter sets. Gaps in the single particle spectra

at Z — 82 and N = 126 are obvious but the SHF method has difficulty reproducing level

orders consistent with experimental observations. The results of the RMF approach are

generally in good overall agreement with experiment. It is interesting to note that the

RMF parameterizations, displayed in Figure 1.3, suggest a significant energy gap between

the nlhg/2 and ^2/7/2 orbitals.

Figure 1.4: Self-consistent and relativistic mean field predictions of proton (top) and neu­

tron (bottom) single particle spectra in f | | l l 4 . See text for details. This figure is adopted

from Ref. [16].

12

The parametrizations used in Figure 1.3 can be applied to predict single particle

spectra of j | | l l 4 , the next spherical doubly-magic nucleus according to the macroscopic-

microscopic model. The resulting single particle spectra are shown in Figure 1.4. Only for

the Skyrme functional SkI4, the interaction with the largest amplitude spin-orbit splitting,

are the proton single particle spectra consistent with a shell closure at Z = 114. In other

cases, there is a significant energy gap at Z = 120. Figure 1.4 also shows the predicted

neutron single particle spectra of J | | l l 4 . Again, there is significant variation in the predic­

tion of neutron shell structure with both the model and parametrization used though the

prediction of a neutron shell closure at N = 184 is consistent for all parameter sets.

Experimental verification of the self-consistent mean field model predictions of nucleon

shell structure for super-heavy systems is currently extremely difficult. The lack of available

experimental data due to the difficulty of producing and obtaining spectroscopic informa­

tion of super-heavy isotopes near the predicted magic numbers inhibits any comparison

to model predictions. Current data of experimentally accessible nuclei suggests, based on

measured alpha decay Q-values and half lives, that the majority of the known super-heavy

nuclei possess significant ground state deformation. This is consistent with the observation

of rotational bands in 254No [24]. The observation of high-K isomers [25, 26], long-lived

excited states of deformed shapes where K is the quantum number defined by the pro­

jection of the nuclear spin J onto the symmetry axis of the nucleus, provides additional

evidence of deformation in this mass region. Presently, the detailed verification of the sets

of parameters used in the self-consistent mean field models must be carried out by using

observables of lighter nuclei. The structure of the Actinides, particularly the AT = 126

isotones beyond 208Pb, can be used to benchmark the variety of parametrizations of these

models. More specifically, it is now possible to begin to experimentally investigate the

Z = 92 subshell closure the RMF parametrizations suggests.

Obtaining spectroscopic data for the N = 126 isotones near the Z = 92 is at the

current limit of experimental techniques. The results of exceedingly difficult experiments,

such as the study of isomeric states in 216Th by Hauschild et al. [27] begin to provide

13

evidence contrary to the existence of a subshell gap at Z = 92. In fact, results of this

experiment imply the 7r/ig/2 and 7r/7/2 orbitals are nearly degenerate. Recent large-scale

shell model calculations of the N = 126 isotones by Caurier et al. [28] provide additional

insight into the evolution of proton shell structure. The results of these calculations can

be used as a tool to compare current spectroscopic data with the benchmarks of the mean

field predictions.

1.4 Experimental verification of mean field predictions

As mentioned above, obtaining spectroscopic information for the N = 126 isotones becomes

exceedingly difficult with increasing proton number. The difficulty is the consequence of

rapidly decreasing production cross sections with proton number Z combined with a large

fission probability. Additionally, experimental single particle energies can not be directly

compared to mean field predictions. Pairing, quadrupole, and octupole correlations that

are present in measured single particle energies are often not accounted for in mean field

models [29] increasing the difficulty for the comparison of experimentally extracted single

particle energies to the structure predicted by mean field models. Spectroscopic data

obtained in this mass region is at the current experimental limit but recent large-scale

shell model calculations of the N = 126 isotones [28] provide the advantage of the ability

to examine the expected structure of the N = 126 isotones near Z = 92 using realistic

interactions while being able to directly compare predicted spectroscopic observables to

those of lighter isotopes.

Shell model calculations using a modified Kuo-Herling interaction [30, 31] and the

full proton Z = 82 — 126 model space have been used to search for any indication of a

subshell gap at Z = 92. Figure 1.5 shows predicted two-proton separation energies of the

N = 126 isotones beyond 208Pb and their comparison with experiment [28]. The existence

of a significant energy gap between the 7rl/i9/2 and 7r2,/V/2 orbitals would result in an

enhancement of the two-proton separation energy at Z = 92. However, the presented shell

14

model calculations show no indication of any peak structure. The proton occupations of

the Oft.g/2) I/7/2) a n d 0*13/2 orbitals, the states that dominate the yrast structure of the

N = 126 isotones, also show no indication of a subshell closure at Z = 92.

100 k rr-. ST I !

H c. m rT Vi

>

>

0

1.00

8 6

4

2h

82 84 86 88 90 92 Z

Figure 1.5: Comparison of shell model two-proton separation energies with experiment (top) and the separation energy differences for the Ar = 126 isotones (bottom) adopted from Ref. [28]. The predicted values of the two-proton separation energies agree well with experiment. No peak structure is observed in the separation energy differences, &2p: at Z = 92.

Verification of these shell model results along with their comparison to predictions of

a variety of mean field parametrization can be accomplished using known spectroscopic

information in this mass region. For the even-even N = 126 isotones beyond 208Pb there

is a fairly large data set up to 216Th. While calculated energies and transition strengths

agree well with existing data for these isotopes, the lack of data for the odd isotopes beyond

213Fr inhibits further comparison of single particle energies.

As previously mentioned, in-beam gamma ray spectroscopy of the Actinide isotopes is

very difficult for a variety of reasons. The proton-rich Actinides are typically produced via

fusion-evaporation reactions for which production cross sections decrease drastically with

proton number. In a fusion-evaporation reaction, a compound nucleus can be formed in

an excited state after the fusion of two lighter nuclei. By definition, the excitation energy

15

of the compound nucleus is equilibriated with respect to all internal degrees of freedom.

De-excitation of the compound nucleus is a "step-by-step" process that that depends on

both the excitation energy and angular momentum which limits the available phase space

of the different de-excitation channels.

At each "step" of the de-excitation process there are three are possible outcomes: fission,

light particle emission, or gamma ray emission. Fission is by far the dominant de-excitation

channel for heavy compound nuclei and the high probability of this particular channel at

each de-excitation step is one primary reason for the low-production cross sections of heavy

nuclei produced in fusion-evaporation reactions. For excitation energies below the fission

barrier, light particle emission, predominantly neutron decay due to the extra proton bind­

ing energy provided by the Coulomb barrier, becomes the favored mode of de-excitation.

The emission of a neutron decreases the excitation energy of the compound nucleus by the

sum of the binding energy of the emitted neutron and its kinetic energy. The decrease in

the angular momentum of the compound nucleus after neutron emission is typically small

due to the comparatively small mass of the ejected particle. As the excitation energy of

the compound nucleus approaches the separation energy of the remaining neutrons in the

system, gamma ray emission becomes the only available mode of decay. At this point, the

nucleus emits a cascade of gamma rays that removes the remaining excitation energy and

angular momentum of the evaporation residue while populating states near the yrast line.

A schematic of the possible decay modes and their dependence on the excitation energy

and angular momentum can be found in Figure 1.6.

16

Figure 1.6: A schematic depiction of available decay paths of an excited compound nucleus as a function of the excitation energy and total angular momentum is shown. Excitation energy is initially released via the ejection of light particles. As the excitation energy decreases, gamma ray emission becomes the only available decay mode.

17

Chapter 2

Experimental Techniques

2.1 Spectroscopic studies of fusion-evaporation residues

For the study of heavy nuclei, the extraction of nuclear structure information from sub­

sequent decays of a fusion-evaporation product can be achieved by a variety of methods.

Techniques such as delayed gamma spectroscopy and alpha-gamma coincidences have been

used successfully in the study of the structure of 215Ac [32, 33]. For delayed gamma spec­

troscopy, a pulsed beam is used and gamma de-excitations are only observed in anticoinci­

dence with beam incident on the target material. This method provides good background

reduction but is only sensitive to the decay of isomeric states. However, prompt transitions,

that occur no longer than a few picoseconds after population of the initial state, will not

be observed.

Recoil tagging and recoil-decay tagging (RDT) are two common methods used to study

prompt gamma ray emission of isotopes produced in fusion-evaporation reactions with low

production cross sections [34, 35]. Both the suppression of background, achieved using

both methods, and channel selection, provided by RDT, are vital for the extraction of

the decay events associated with the isotope of interest. The majority of background

suppression is achieved by using separation techniques based on magnetic or a combination

of electric and magnetic fields. Fusion products are separated from the scattered beam and

18

fission fragments in order to reduce the overwhelming background of gamma ray decay

associated with these events. RDT provides the additional capability of channel selection

by the correlation of prompt gamma decays to subsequent alpha (or beta) decay of a

particular fusion product. These two techniques are described in greater detail following

the introduction of the experimental apparatus used in this work.

2.1.1 Gas-filled separators

Recoil separators are widely used to isolate heavy ions produced in fusion evaporation re­

actions from non-reacted beam or fission fragment contaminants. Separators that use a

combination of electric and magnetic components, such as the Fragment Mass Analyzer

(FMA) [36] and the Oak Ridge Recoil Mass Separator (RMS) [37], and are capable of

A/q selection, where the mass and atomic charge state of a recoil are defined as A and

q, respectively. While the recoil separation and background suppression are superb (The

resolving power of the FMA is typically AAA « 250), separators of this type are limited

in transmission efficiency for fusion products. The transmission efficiency is constrained

by the charge state distribution of the recoils exiting the target material. Residues pro­

duced in a typical fusion evaporation reaction exit the target material with a distribution

of charge states and, as a result, a distribution of magnetic rigidities. Electromagnetic

separation of these residues in vacuum results in a series of discrete trajectories. For recoil

separators similar in design to the FMA or RMS, it is only possible to direct two or three

of the most abundant charge states to the focal plane apparatus due to the acceptance of

the spectrograph. This relatively low transmission hinders spectroscopic studies of fusion

products produced at low cross sections and/or in weak reaction channels.

A significant increase of the transmission efficiency of a magnetic recoil separator is

achieved with the addition of low pressure gas in the separation region. Residues traveling

through the gas undergo collisions with the gaseous atoms or molecules. During these

collisions, electrons are exchanged between the residues and gas particles and the mean

19

free path between these collisions, A, can be described as

A = — , (2.1) nat

where n is the atom or molecule density and at is the total charge-changing cross section

that is strongly dependent on the charge state of the residue, its velocity, and the com­

position of the gas [38]. If the mean free path between the charge-exchanging collisions

is sufficiently short, the original charge state distribution is focused to a so-called average

or equilibrium charge state; the result of the equilibrium of charge transfer between the

heavy residues and gas particles. This mechanism is depicted schematically in Figure 2.1.

The desired consequence of the collapse of the initial charge state distribution is that the

final average charge state depends largely on the atomic number of the residue and its

velocity. In other words, a significant increase in transmission of residues to the focal plane

apparatus, regardless of initial charge state, can be achieved if the average charge state is

known. Additionally, the gas pressure in the separation region must be kept sufficiently

low in order to minimize the broadening of the profile of the transmitted recoils caused by

small-angle scattering and energy loss straggling.

The trajectory of a charged particle traveling through a gas-filled magnetic field region

is described with the relatively simple equation

Bp = ?. (2.2)

Recoils of linear momentum p and average charge state q traveling through a magnetic field

region of strength B follow a trajectory with a radius of curvature p. The adjustment of

the strength of the magnetic fields of a recoil separator can be performed if the charge state

and momentum of the recoil of interest is known. Assuming complete linear momentum

transfer, the momentum of the recoil immediately following formation is equal to that

of the incident beam ions. The theoretical description of the behavior of the charge state

20

Figure 2.1: Illustration of the trajectory of ions traveling through a magnetic field region in the absence (top) or presence (bottom) of a low-pressure gas. Ions traveling through the region in vacuum follow a set of discrete trajectories. Collisions with gas atoms or molecules results in the collapse of the initial charge state distribution to an average value. Adopted from Ref. [38].

distribution of heavy ions traveling through a gaseous volume is limited. However, a number

of expressions for the average charge state of a recoil have been determined empirically for a

variety of velocity regimes and operating conditions [39, 40, 41]. Two expressions, derived

from results of magnetic separation of heavy ions in 1 Torr of Helium gas, that have

been successfully implemented using the gas-filled separator SASSYER (this separator is

introduced in the following section) are [39]

{1.8 • K r t Z 1 / 3 + 1.65, for vZllz < 2 • 107

(2.3) 3.3 • lCT^Z 1 / 3 - 1.18, for vZl>z > 2 • 107.

The magnetic rigidity Bp is a measure of the momentum per unit charge (mv/q) and the

21

average charge state is proportional to the velocity of the recoil. Consequently, the average

magnetic rigidity is nearly independent of the initial velocity distribution of the ions exiting

the target material. The velocity and proton number of the unreacted beam ions differ

significantly from those of reaction products. As a result, unreacted beam contaminants are

magnetically separated from the residues produced in the fusion reaction. One disadvantage

of magnetic separation of heavy ions in gas is the lack of intrinsic isotopic identification

after separation from scattered beam or fission fragment contaminants. Techniques used

for recoil identification following separation are discussed following the description of the

apparatus.

2.2 SASSYER

The A.W. Wright Nuclear Structure Laboratory currently utilizes a gas-filled separator for

nuclear structure studies of medium and heavy mass nuclei [42]. This recoil spectrome­

ter, originally SASSY II of Lawrence Berkeley National Laboratory, was constructed in

1988 for high-efficiency transmission of products from heavy-ion induced reactions with

cross sections in the picobarn range [43]. The spectrometer was then transported to

Yale University in 2000 where it was re-commissioned as the recoil separator SASSYER

(Small Angle Separator System at Yale for Evaporation Residues). SASSYER consists

of two vertically-focusing magnetic dipoles separated by a horizontally-focusing magnetic

quadrupole singlet. Vertical focusing is achieved at each dipole by the design of the pole

tips which provide a strong vertically-focusing gradient. To minimize transmission losses

due to scattering during each charge-exchange collision, the total path length through the

spectrometer is only 2.5 m. The system is designed to have an angular acceptance for

reaction products of ± 50 milliradians in each plane [43].

Under typical operating conditions, SASSYER is filled with 1 Torr ultra high-purity

Helium gas. A ~50/Ug/cm2 carbon window is used to separate the high-vacuum beam line

volume from the gas-filled volume. Helium gas is introduced into the separation volume

22

at the exit of the second magnetic dipole, regulated using the MKS Type 250 module,

and removed 1 m upstream from the target position by a dry vacuum roughing pump.

Continuous gas flow minimizes contamination and impurities present in the gas in the

separation volume. Impurities in the gas-filled separation volume can have a drastic effect

on both the energy loss and the average charge state of the recoils traveling through the

separator resulting in severe transmission losses.

2.2.1 Y R A S T ball

Gamma rays emitted at the target position of SASSYER were detected by the array of

Germanium detectors that comprised YRAST Ball [44]. In the present work, this detector

array consists of two rings of Compton-suppressed HPGe clover detectors. Each clover

detector was enclosed in a high gamma efficiency BGO shield in order to veto events in

which the gamma ray imparts only a fraction of its total energy in the Germanium crystal

before escaping. Four clover detectors were placed in the backward ring at 138.5° relative

to the beam axis. The remaining five clover detectors were oriented at right angles to the

beam axis in the plane of the target. A schematic of the target position surrounded by the

YRAST ball geometry is presented in Figure 2.2.

2.2.2 S A S S Y E R focal plane apparatus

Detection and identification of recoils exiting the separator is accomplished by using the

combination of a parallel-grid avalanche counter and a pair of highly-segmented silicon

detectors; a schematic of the configuration of these detectors is shown in Figure 2.3 followed

by a description of each instrument.

MACY

The Multi-wire Avalanche Counter at Yale (MACY) is positioned 48 cm downstream from

the exit of the second magnetic dipole of SASSYER. The design of this detector is largely

based on a similar apparatus at Argonne National Laboratory [45, 46]. This instrument

23

Figure 2.2: Schematic of the YRAST ball array geometry. In this figure, the target position is surrounded by two rings of HPGe clover detectors. Eight detectors are positioned in the ring perpendicular to the beam axis and four are placed in the backward ring at 138.5°.

consists of a chamber, 5.1 cm in length, filled with 3 Torr isobutane counting gas contained

by 7.0 /ig/cm2 Mylar (CioHgC^) windows. Mounted in the chamber is a series of compact,

Gold-plated Tungsten [47] wire grids. The grids are composed of 20 ^m diameter wire at

a millimeter spacing. The mounted wire grids are depicted in Figure 2.4 and an exploded

view of this detector is shown in Figure 2.5.

MACY is composed of 4 planes of wire grids separated by 2 mm PCB spacers: an

anode, cathode, and two position-sensitive planes. The operating bias of the anode and

cathode are +450V and -300V, respectively. As a recoil travels through the MACY volume,

collisions with counting gas molecules produce electron-ion pairs which will then drift in the

applied electric field toward their respective collecting electrodes. During the drift time,

these charges are accelerated by the applied fields to energies greater than the ionization

24

Figure 2.3: Schematic of the SASSYER focal plane assembly. Residues exiting SASSYER travel through MACY (from the right side of the page) and are then implanted in the Silicon detectors (DSSDs). A small array of Germanium detectors surrounds the focal plane chamber.

energy of the neutral gas molecules. Collisions between the accelerated, free charges with

the gas molecules produce secondary ionization which is then re-accelerated to produce

additional ion pairs. This process, resulting in a charge-producing cascade, is known as

the Townsend avalanche [48]. The voltage applied to the anode and cathode of MACY is

required for sufficiently large charge multiplication as a recoil travels through the counting

gas to produce a reasonable signal size in the unbiased wire grids used to measure the

horizontal and vertical position of the recoils.

A number of simultaneous measurements are made as a recoil passes through the MACY

volume. The number of positive ions collected at the cathode is proportional to the energy

loss of the recoil traveling through the gas of the detector. This energy loss is proportional

to the charge of the particle and inversely proportional to its velocity as described by the

Bethe-Bloch formula [49, 50]. Therefore, slow-moving, light scattered beam contaminants

25

Figure 2.4: Photograph of the open chamber of MACY displaying the mounted wire grids. The set of LEMO vacuum feedthroughs for the signal cables is visible at the top of the chamber.

can be distinguished from the slow, highly-charged recoils of interest. The anode signal is

used for trigger and timing purposes and is discussed in detail below.

The horizontal and vertical position of each event in MACY is derived from the grids

upstream and downstream from the cathode wire plane. A front-view schematic of the

horizontal and vertical position-sensitive wire grid assembly is shown in Figure 2.6 for

reference.

x-position

y-position Cathode

Spacer Boards

Figure 2.5: Exploded view of the wire grids that comprise MACY. Residues exiting SASSYER pass through the sequence of MACY wire grids (from right to left in the above schematic).

26

TDC TDC

3IMI SOUt'C

center

Delay line

Figure 2.6: Schematic of the delay lines in the position-sensitive wire grids of MACY. The vertical blue bars represent wires in the grid plane. From the residue position (labeled as signal source), the signal is split to opposite sides of the wire grid. The time difference {IA ~ ts) is proportional to the distance of the resid\ie from the center of the grid. This figure is adopted from Ref. [51].

Each wire plane has two signal outputs. These outputs correspond to the left and

right side for the wire grid sensitive to the horizontal position and the top and bottom

of the vertically-sensitive grid. A portion of the cloud of drifting electrons/ions traveling

to cathode and anode is incident on the unbiased wires of the position-sensitive grids.

This incident charge travels to the signal outputs on either side of the wire grid, displayed

schematically in Figure 2.6. As the charge travels to the signal output, it is delayed by a

series of 10 ns delay integrated circuits (ICs). The total delay applied to the signal of a

horizontal or vertical output is proportional to the distance from the position of the original

ion cloud to the side of the output; the signal must pass through an increasing number of

delay ICs as its path length increases. Consequently, any deviation of the position of the

ion cloud from the center of the wire grid results in a difference in signal travel time to

the opposing signal outputs. The anode signal of MACY is used as a time reference for

each position signal. The time difference between the "start" anode signal and each "stop"

27

position signal is converted to a digital representation by a series of time-to-digital converter

(TDC) channels. The horizontal and vertical position of the recoil event in MACY can then

be deduced from corresponding the TDC output as the the time difference of the left and

right (top and bottom) outputs are proportional to the horizontal (vertical) position of the

recoil traveling through MACY. In addition to providing a time reference for the MACY

position signals, the anode signal also serves as a master trigger for the data acquisition

system and as a time reference for recoil time-of-flight measurements from MACY to the

DSSDs and from the target position to MACY.

2.2.3 Recoil tagging of prompt gamma rays

For the following description of recoil tagging and recoil-decay tagging, please refer to Fig­

ure 2.7 as a guide to the experimental geometry. The primary goal of recoil tagging is

YRAST Bal

YRAST Bal 7

MACY

Double-Sided m 2 Strip Detectors

SASSYER (Small Angle Separator System atYale for Evaporation Residues)

Figure 2.7: Schematic of the gas-filled separator SASSYER (taken from Ref. [51]) and the relative geometry of the associated electronics. The target position of SASSYER is surrounded by detectors in the YRAST ball array. Upon exiting the second magnetic dipole of the separator, residues pass through MACY and are implanted into a pair of Double-Sided Silicon Strip Detectors (DSSDs).

the correlation of gamma rays observed at the target position of a recoil separator to the

coincident production of the desired recoils. After production, the recoil exits the target

28

material and travels into the separator. Prompt decays or transitions originating from

very short-lived isomeric states are observed by detectors surrounding the target position.

The observation time for prompt gamma rays is constrained by the requirement of line-

of-sight by the target position detectors to the evaporation residue and is typically not

more than 10 ns for heavy-ion fusion reactions. It is dependent on the reaction kinematics.

The observed gamma rays, along with gamma rays from all other contaminant reaction

channels, are detected by the YRAST ball array of Germanium detectors surrounding the

target chamber (see Section 2.2.1). Gamma rays emitted from the nuclei of interest are

"tagged" by requiring coincidence of any gamma ray detected at the target position with

an event in MACY at the exit of the recoil separator. This tagging eliminates the majority

of contamination of the prompt gamma spectrum by Coulomb excitation of nuclei in both

the beam and target as well as fission fragment decays. Scattered beam events are not

completely eliminated by the recoil separator but the prompt gamma decays associated

with these contaminants, which travel through MACY, can be suppressed by energy loss

and time-of-fiight requirements. The cocktail of nuclei produced in fusion-evaporation re­

actions arrives at the focal plane of the separator with no significant difference in measured

energy loss and position in MACY. Therefore, the sole means of correlating any previously

unobserved gamma transition to a specific isotope is by the requirement of a coincidence

with a known gamma decay. This is exceedingly difficult for isotopes for which there is

limited spectroscopic data or that are produced in very weak fusion channels.

The disadvantage of the lack of isotopic selection during separation is remedied by

the observation of subsequent decay at the focal plane of the separator. This recoil-decay

tagging technique is identical to the recoil tagging method but requires the additional

observation of a time- and position-correlated alpha decay subsequent to a recoil implanted

in a highly-segmented silicon detector at the focal plane of the recoil separator. Before

presenting a detailed description of the RDT technique, it is helpful to provide additional

geometric and operational details of the Double-Sided Silicon Strip Detectors (DSSDs)

commonly used for this application and instrumental in the detection systems present at

29

the focal plane of SASSYER.

Double-Sided Silicon Strip Detectors

The pair of DSSDs mounted at the SASSYER focal plane, depicted in Figure 2.8, consist

of a 60x40 mm, 300 /zm active thickness Silicon geometry that is mounted in the opening of

a 7-layer printed circuit board (PCB). The Silicon crystal used in the DSSDs was produced

and mounted on the WNSL-designed PCB [52] by Canberra. The front (rear) side of the

DSSD is segmented into vertical (horizontal) strips of 1 mm pitch; each DSSD is segmented

into 60 front (vertical) and 40 rear (horizontal) strips. Under normal operating conditions,

a potential of +40 V is applied to the n-type front layer while the rear p-type layer is

grounded to ensure adequate charge collection.

Figure 2.8: Photograph of the pair of DSSDs mounted in the focal plane chamber of SASSYER.

The minimization of leakage current during operation is required to avoid reduction of

signal resolution. Several steps are taken to ensure adequate suppression of the leakage

current in the DSSDs mounted at the focal plane of SASSYER. The three adjacent the

30

outermost strips (from the center of the beam axis) share a common trace on the PCB

in order to mitigate the surface leakage current at the edge of the Silicon crystal. For

the same reason, a single rear strip is used as a guard ring. As a result, there are 57(39)

front(rear) strips available for experimental use. An additional reduction of the leakage

current is achieved by maintaining the temperature of the Aluminum mount to which

the DSSD PCB is attached at approximately -5 C° using a temperature-regulated alcohol

cooler. An approximate 1:1 mixture of ethanol and distilled water is used as the cooling

medium. The design schematic depicting the DSSD mount and cooling configuration is

shown in Figure 2.9.

Figure 2.9: Design schematic of the DSSD cooling assembly. A 5 C° ethanol-water mixture is circulated through the cooling block which is in thermal contact with the cold plate and cooling mount in the focal plane chamber. The DB-25 feedtlirough panel is visible on the right side of the schematic.

The geometric overlap of the vertical and horizontal strips provides an effective pixel,

31

in essence an individual detector with an area of approximately 1 mm2. This segmentation

is the crucial tool required for the RDT technique.

2.2.4 Recoi l -Decay tagging of prompt gamma rays

For each implantation event in a DSSD, an event is recorded for both the rear and front

side of the detector. Each implantation event is identified by the coincidence of a signal

from the anode of MACY and a signal from both sides of the DSSD. Such an implantation

event of a recoil can be, within the gamma detection efficiency, coincident with prompt

gamma decays observed at the target position. After implantation, this particular pixel is

tracked for subsequent decays. Decay events are identified with an event in the implant

pixel and the absence of a MACY anode signal. High segmentation is required to avoid

an additional implant event in the tracked pixel prior to the decay of the recoil. If the

lifetime and energy of the subsequent decay are consistent with known decays of a specific

isotope produced at the target position, the prompt gamma decays coincident with the

implant event correlated to the decay can be extracted. The additional requirement for

the observation of the implanted recoil decay further reduces background in the prompt

gamma spectrum and provides channel selection after transmission through a gas-filled

separator. It must be mentioned that while the RDT method is particularly suited for the

study of heavy nuclei that decay with the emission of an alpha particle of a discrete energy,

it has also been successfully applied nuclei for which beta decay is dominant [53].

2.2.5 Signal processing and electronics

The signal from each strip of the previously described DSSDs must be processed sepa­

rately in order the extract energy and time information for each recorded event. Signal

multiplexing is used to minimize the number of peak-sensing analog-to-digital converter

(ADC) channels required to process each event. Multiplexing is achieved by using a series

of Mesytec MUX-16 units. Each board, depicted in Figure 2.10, contains 16 channels of

charge-sensitive preamplifier inputs. A simplified schematic of the modules can also be

32

found in Figure 2.10. The output of each preamplifier is split to a leading-edge discrim­

inator and a shaping amplifier. The fast leading edge discriminator signals are sent to a

decoder where the multiplexing process occurs. The hit decoder selects up to two channels

in which the hits occur within 50 ns and the slower shaping amplifier signals of the corre­

sponding channels are fed to the output buffers. Simultaneous to the output of the energy

signals, two 7-bit output DACS process the channel identification. An analog signal, its

peak height proportional to channel number, is coincident with each energy output for

strip identification.

-input* bias filter

15 inputs,.

HV'S1h5haperJ-"v^ switch matrix

I le- | dis 4 | discr.

15 further channels

-difL^ hit decoder

V I - "iMCf

gain/poJ/ >) [ A Si thrpot

E RG

-»buf>

Y

El

E2

3E .Jmc\—Jb$>—E«I »

enable

=t

nigger / RC

itoNlMl

|j£C.an^g)i,ED _pulser_

_bia& HV -6\'

Energy Signal

Position Signal

Figure 2.10: Digital schematic of the Mesytec MUX-16 module adopted from Ref. [54]. Typical energy and position output signals of the MUX-16 are displayed below the schematic. See text for details.

The front and rear strips of each DSSD must be multiplexed separately to produce the

appropriate trigger logic. The path of the signal of an event in a single DSSD is shown

schematically is Figure 2.11. After each implant or decay event in a DSSD, a signal is

33

observed in both a rear horizontal strip and front vertical strip. Signals for each strip travel

from the DSSD PCB via 100-pin connector to a conversion board that splits the 100-pin

cable into a series of DB-25 connectors. The DB-25 connectors provide a signal feedthrough

from the high-vacuum of the detection chamber to the outside atmosphere where 25-pin

cables are then input to the MUX-16 modules. Four (three) MUX-16 modules are used

for a vertical (horizontal) strip bus (providing one multiplexed output for all input signals)

consisting of 57 (39) strip signals. The MUX-16 modules combined to form a single bus

are attached via a 20 pole flat wire cable that is then input in a driver PCB. The primary

purpose of the driver PCB is to provide an amplification by a factor of 3.3 to interface with

8V peak-sensing ADC channels. Using this setup, only eight ADC channels are required

for the processing of both the energy and position signals of the 192 strips of the pair of

DSSDs.

Figure 2.11: DSSD signal path to the ADC/Trigger input. Details can be found in the text.

Trigger logic

A schematic of the trigger logic of the focal plane apparatus for a recoil-decay tagging

experiment using SASSYER is depicted in Figure 2.12. The primary purpose of the dis-

34

played trigger logic is to distinguish implant and decay events based on coincidence or

anti-coincidence between events observed at the DSSDs and in MACY. In typical opera­

tion mode, the master trigger is provided by the logic OR of the anode of MACY and both

the front and rear strips of each DSSD. It is important to note that this figure does not

contain any information from detectors present at the target position of the separator. Sig­

nals from detectors at the target position must be delayed by an appropriate time interval

to arrive at the appropriate ADC/TDC channel within its respective trigger window.

Anode CFD

BLRear Triggcr

BLFrsni Trigger

Le Cray 465 CclncUnit

P/S 794 G+D Gen.

d - 8 5 0 ns P/S 794 G+D Gen.

w= 150 ns TDCO] Cenunen (slap)

P/S 757 fin/fitllt

P/S 794 G+D Gen.

Le Cray 465 Ceinc.Unit

OrTec416A G+D Gen.

Implant

Trigger

P/S 794 G+D Gen.

AH Strip OR

P/S 757 fta/feut

P/S 757 fin/but

LeCrey622 Quad Co we

BRFroxt Trigger

P/S 757 fix/lout

F Strip OR

Le Cray 622 QuadCoine

BR Rear Trigger

P/S 757 fin/taut

MACY-DSSD TAC Start -Anaae Step - F Strips

Le Cray 622 QiianCeinc

P/S 794 G+D Gen.

' 1 Start: Y4 r-

P/S794 G+D Gen.

-gam TAC

-| Start: Q2 r-ganTAC |

LeCray622 QuaiCeinc

P/S 794 | < - 7 5 0 » s | P/S 794 | | P/S 7571 |OrTee4l6A G+D Gen. G+D Gen. fin/but G+D Gen.

Master

Trigger

Decay

Trigger

[ Start: Y2r-eamTAC|

Figure 2.12: Trigger logic for the detection systems at the focal plane of SASSYER.

A 10 MHz clock is used to time stamp observed implant and decay events and the timing

information is readout with each trigger. The data acquisition software SpecTcl [55],

developed by the National Superconducting Cyclotron Laboratory (NSCL) at Michigan

State university was used for online sorting. This software package allowed the online

inspection of two-dimension spectra that was vital for the troubleshooting involved in the

commissioning the the new focal plane detection apparatus at SASSYER. Data obtained in

35

the present experiment was converted to a format compatible with CERN's ROOT package

[56]. The majority of the offline data analysis was performed using the tools provide in the

ROOT package [57]. In some cases, namely the analysis of gamma-gamma coincidences,

the WNSL developed sorting code CSCAN [58] was used. Histograms produced using

CSC AN were analyzed with the interactive graphical analysis package RADWARE [59].

2.3 Experimental determination of gamma ray characteris­

tics

The alignment of the detectors in the YRAST array relative to the beam direction provides

a tool for the extraction of various properties of the emitted radiation. Properties of

the angular distribution of a particular transition give insight to the multipolarity of an

emitted gamma ray. In a fusion-evaporation reaction, a nucleus is produced in such a way

that the angular momentum of the excited states is aligned in a specific direction. To a

good approximation, the nuclear angular momentum is perpendicular to the incident beam

direction [60]. The gamma ray intensity W{9) as a function of emission angle 9 relative to

the beam direction is [61, 62]

W{6) = Y,AkPk{cosB) (2.4)

k

where Ak are the angular distribution coefficients and Pk{cos6) are the Legendre Poly­

nomials, and the index k encompasses the even integers less than or equal to twice the

angular momentum of the photon. Therefore, for dipole transitions (L = 1) the expansion

is carried out to k = 2 while the Picos{0) term is included for quadrupole transitions. For

detector rings or the YRAST array at 9 = 90° and 135° and with the assumption that the

observed gamma rays correspond to pure dipole or quadrupole transitions, Equation 2.4

can be used to determine the multipolarity of the emitted photons. One would expect a

transition of dipole character to be more intense at the 90° detector ring and the intensity

36

of transitions quadrupole in nature increased at 138.5°.

Properties of internal conversion, where excitation energy is removed from the nucleus

through the interaction and ejection of a bound electron rather than the emission of a

gamma ray, can also be used to determine the multipolarity of a transition. The ejection of

a conversion electron is often accompanied by the emission of x-rays corresponding to the

filling of the hole created by the removal of the electron. The probability of the emission

of a electron to gamma ray is the internal conversion coefficient a where

Itotal = h + h- = Ij(l + a) (2.5)

in which Itotal is the total intensity and 77(/e-) is the gamma ray (conversion electron)

intensity. The internal conversion coefficient increases with decreased gamma energy and

increases rapidly with proton number [9]. Therefore, internal conversion becomes a signif­

icant decay path for the de-excitation of heavy high-Z nuclei, particularly for low-energy

transitions.

A more direct measure of the electric and magnetic nature of a transition is accom­

plished using Linear Polarization techniques [63]. The technique is based on the mea­

surement of the direction of Compton scattered gamma rays in segmented Germanium

detectors, effectively Compton polarimeters, where the scattering direction is dependent of

the magnetic or electric nature of the photon [64, 65]. The angular momentum vector of an

electric transition is polarized perpendicular to the beam axis while a magnetic transition

is polarized parallel to the beam axis. With these proprieties in mind, the polarization

asymmetry is defined as [64]

A = -± - 1 (2.6 iVx + iVy v '

where A j_ (iV|[) is the number of Compton scattering events in a direction perpendicular

(parallel) to the beam axis. Therefore, the measurement of the asymmetry of a decay

results in a negative value for those of magnetic nature and a positive value for electric

37

Figure 2.13: A schematic diagram of the orientation of clover crystals with respect to the beam axis. The Compton scattering of electric transitions emitted by the residue will be favored in the direction perpendicular to the beam axis. Figure is adopted from Ref. [66]

transition. Figure 2.13 is included as a reference to the scattering geometry described

above.

38

Chapter 3

Experimental Results

3.1 Experimental parameters

Spectroscopy of 215Ac was conducted at the A.W. Wright Nuclear Structure Laboratory at

Yale University. A 26Mg beam at 123 MeV (121 MeV center-of-target) was provided by the

ESTU tandem ion accelerator and was incident on a self-supporting 220 /xg/cm2 natural

Iridium target (62.7% 193Ir, 37.3% 191Ir). 215Ac recoils were produced via the 193Ir(26Mg,

4n)215Ac fusion-evaporation channel. For production at the center of the target, the kinetic

energy of the recoiling 215Ac nuclei was 14.2 MeV; 13.7 MeV at the exit of the target after

energy loss [67]. At this energy, the tinie-of-flight from the target position to the exit of

the separator SASSYER is approximately 750 ns with a velocity of 0.0117c where c is the

speed of light. As per Equation (2.3), the average charge state of the 215Ac recoils traveling

through 1 Torr Helium gas was calculated to be 4.32 prior to energy loss of the recoil

while traveling through the low-pressure gas. The average charge state and corresponding

magnetic rigidity of a 215Ac residue at the center of each element of SASSYER is displayed

in Table 3.1. Also included in this figure are magnetic field strengths used for maximum

transmission of the recoils to the focal plane apparatus.

39

M l

Q M2

Setting (T-m)

0.389 0.303 0.375

for Bp = 0.814 q of 215Ac at element [39]

4.320 4.266 4.205

center of Setting used during ex­periment (T-m)

0.850 0.658 0.807

Table 3.1: SASSYER experimental settings for the transmission of 21oAc

3.2 Delayed gamma ray emission

The pair of DSSDs at the focal plane of SASSYER were surrounded by three coaxial Ger­

manium detectors in the geometry depicted in Figure 2.3. Events observed by these three

detectors were recorded up to 19 /zs following any implant or decay event. The delayed

gamma ray emission observed in coincidence with a MACY anode event is displayed in

Figure 3.2. The most obvious features of Figure 3.2 are the presence of four transitions at

175.27(3), 303.98(2), 641.62(5), and 1316.7(1) keV and the observation of peaks associated

with Ac x-ray emission. The energies of the four delayed gamma transitions are consistent

with the previously observed isomeric decays of 215Ac [32] shown in Figure 3.1. The rela­

tively long duration of the time window for which delayed gamma events are accepted is

attributed to noticeable contamination from room background sources. The most promi­

nent line is located at 1460 keV corresponding to the presence of 41K. Delayed gamma

coincidences indicate that the four transitions, observed consistent with the isomeric decay

of 215Ac, are indeed mutually coincident. The 304, 641, and 1316 keV delayed gamma rays

which are coincident with the peak at 175 keV are shown in Figure 3.3.

3.3 Alpha decay and implant identification

The observation of alpha decay events in the DSSDs is required for both the isotopic

identification of the implanted recoil and their subsequent correlation to prompt gamma

events. The energy spectrum for each DSSD strip (front side) of the accumulated decay

events is depicted in Figure 3.4. A projection of this figure onto the energy axis yields

the alpha decay spectrum of Figure 3.5. One must emphasize that the events displayed in

40

(29/2+)-

(23/2").

21/2--

17/2~-

13/2"-

9/2"

642

175

T 304

131"

•2438+x 335(10) ns

•1796+x

•1796 185(30) ns

•1621 30(10) ns

•1317

Figure 3.1: Previously observed excited states of 2 1 oAc in using delayed gamma spec­troscopy techniques [32]. Decays from the (23/2~) state were not directly observed. It is inferred by extrapolating the energy of the corresponding state in 2 1 3Fr that the energy of the (23/2- ) -> 21/2™- transition is 50±50 keV.

Figure 3.4 and 3.5 are of the first-generation decay events following an implant event in a

corresponding pixel.

The different isotopes produced by the fusion-evaporation reaction were identified using

the alpha decay energy spectrum of Figure 3.5. The dominant alpha decay branches of a

number of proton-rich pre-actinides and actinides are listed in Table 3.2. Using the energies

of these decays as reference, the prominent peaks of Figure 3.5 were identified. The peak

at 7.55(10) MeV is consistent with the value measured by Hefiberger et al. [68] for the

ground state alpha decay energy of 2 1 5Ac. A total of 77700(280) counts, attributed to the

alpha decay of 2 1 5Ac, were observed throughout the experiment.

Subsequent to the first-generation alpha decay in a given pixel, the second-generation

41

in

o

\ / y

f*si 10

^H**J W " * ^ ^ * * * * ^ . . ! * ^ ^ ^ - , ^ . ; . - . ..-— ,i . . 120Q 1800

Channel Number

o ID

+s

Figure 3.2: Delayed gamma spectrum observed at the focal plane of SASSYER in coinci­dence with a MACY anode event. Four transitions at energies consistent with the decay from isomeric states in 2I5Ac were observed [32]. The three peaks at 91, 88, and 103 keV correspond to the KQl, KQ2, and K^ Actinium x-rays, respectively.

o m

2ff UKtoT _ 1900 . U 1

Channel

Figure 3.3: Background subtracted delayed gamma ray spectrum coincident with the 175 keV transition of 215Ac. The four transitions correspond to the decav from isomeric states of 215A c were observed to be mutually coincident.

alpha decay energy was recorded. This information was used to verify the isotopic assign­

ments of the peaks present in Figure 3.5 particularly in regions in which resolving adjacent

peaks is difficult. The correlation of the energies of the first- and second-generation decay

events following an implant event is presented in Figure 3.6. For the decay chain beginning

with the ground state alpha decay of 213Ac, one would expect to observe the subsequent

time- and position-correlated alpha decay at an energy of 6.65 MeV from the decay of the

daughter nucleus 209Fr [69]. The region marked as 1 in Figure 3.6 corresponds to the alpha

decay chain 215Ac —» 211Fr —> 207At. The projection of the events with a first-generation

42

.a- so i -

% 1 50 Q

40

30

20

10

>t"i >

"

I I

I 1

I I

• " -

_ . .. 1

•. * sa r i - :• 1

• • •V: . . r ' o f e : * -'. .'•

'S'.f-'./iV , *

. i . , \ t ; n ;. .j

, ,.-• • . , -^vv • • .• , ^ . j * ; f -

•,'.'.•• ' • • ' ' ' ^ ; i - . i ' ' - .? v. • • ' „,V. '.'*;•( •:• <•/

• • • > • • ' . - l r > ! >

. . , I «- J.V. I . . . i

' - V s .

: $ • • • •

i S i ' i

K..\ ,41 ' >'

is Of.-' •' •

; 1h ' '' .IT? '

: i < « ?

Ml'ii'Vvih"

' . ' : A !•';-: .••'! ,' ! ' ' i i ' i "

) ' ,

','"V'' <t ,••' ' ! ' ' 1

10*

10

10 12 14 16 MeV

Figure 3.4: The energy spectrum for each (front side) strip of the beam left DSSD. See

Figure 3.5 for the isotopic assignment of the presented events.

Figure 3.5: Energy spectrum of the first-generation alpha decay observed in the DSSDs;

projection of Figure 3.4 onto the energy axis.

alpha decay energy between 7.45 and 7.6 MeV (the first-generation decay energy range

of Region 1) onto the second-generation decay energy axis is presented in Figure 3.7. The

6.53(12) MeV centroid of displayed fit of the prominent peak agrees within error with

43

the dominant alpha decay energy of 211Pr measured by Hefiberger et a/. [68]. Similarly,

the spectrum displayed in Figure 3.8 is the projection of the events of Figure 3.6 of the

first-generation alpha decay energies defined by Region 2.

6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 First Decay Energy (MeV)

Figure 3.6: Energies of the position-correlated first- and second-generation alpha decays.

The events included in Region 1 correspond to the alpha decay chain 21oAc —> 211Fr —»•

207At. See text for details.

Region 2 corresponds to the alpha decay energies of the 213Ac —> 209Fr —> 205At chain

while the energies in Region 3 are consistent with those of the 214Ac —> 210Fr —> 206At

decay chain. The energies of events in Regions 4-6 of Figure 3.6 are not consistent with

any expected decay chain. The presence of these events is most likely due to unobserved

implant and/or decay events which then result in the erroneous generation assignment for

the decay chain. For example, the events in Region 4 are consistent with a first-generation

215Ac alpha decay and a second-generation alpha decay energy of similar energy. The

44

most likely origin of these events is an unobserved 215Ac implant event following the first-

generation decay for a specific pixel. This scenario would result in both the first- and

second-generation alpha decay energies consistent with those of 215Ac. Long-lived activity

of neutron-deficient Francium and Radon isotopes, the decay products of implanted fusion-

evaporation residues, could also cause an incorrect assignments for the generation of an

alpha decay cascade. These contaminants most likely contribute to the background events

of Figure 3.6.

580 600 620 640 660 680 700 720 740 760 780 2nd decay (10 keV/channel)

Figure 3.7: Second-generation alpha decay of 211Fr. This spectrum contains the position-correlated events subsequent to the alpha decay of 215Ac.

The measured lifetime of alpha decay following an implant event is an additional mea­

sured quantity used to verify the isotopic assignments in Figure 3.5. The time difference

between an implant event and the subsequent decay is plotted for the first-generation decay

energy of each event in Figure 3.9. Figure 3.10 displays the projection of events in Region

A onto the time axis and the resulting fit. The measured lifetime 172.2(6) ms of the events

in Region A is consistent with values reported by Browne et al. [70] for the lifetime of

ground state alpha decay of 215Ac. Regions B and C, as in Figure 3.6, correspond to the

decay of 213Ac and 214Ac with lifetimes of 0.793(8) s and 8.14(8) s, respectively. The dom­

inant component of the events included in Region D is the alpha decay of 209Fr. Regions

E and F are attributed to the alpha decay of 215Ra and 216Ac. Lifetimes in this work were

45

600 620 640 660 680 700 720 2nd decay (10 keV/channel)

Figure 3.8: Second-generation alpha decay of 209Fr. This spectrum contains the position-correlated events subsequent to the alpha decay of 213Ac.

extracted using the correlation time formalism of Schmidt et al. [71]. Further discussion

of this technique can be found in References [71] and [51].

Due to the reasonable separation in both energy and time of the isotopic constituents

present in Figure 3.9, these regions are used to tag the prompt gamma events coincident

with the corresponding time- and position-correlated implant events. The application of

software gates denned by each of these regions to the gamma spectrum observed at the

target position of SASSYER extract the gamma events corresponding to a single isotope

of interest. This process will be discussed in further detail in the following section.

3.4 Recoil-decay tagging of prompt gamma emission

The prompt gamma ray spectrum obtained by recoil-decay tagging associated with an

implant event followed by the subsequent alpha decay of 215Ac is displayed in Figure 3.11.

A total of 17 recoil-decay tagged transitions correlated to the ground state alpha decay

of 215Ac were observed in the present work. The energies of the transitions presented in

Table 3.3 were determined by Gaussian fits of the peaks in Figure 3.11. Measured intensities

were corrected for absolute efficiencies and normalized to the strongest transition at 999

46

22 F

^ mfm^MM •••••'. •• '• :

114 plwlf^Pw,.1 Ml I; laiLJ. .0" Vjl „>, ' " ''-'i .••WM'.l A 1 2 ^

10

8

J>", Hi

I

1 • • I ' • I I I I I I I I I I

tow _LJ_

102

550 600 650 700 750 800 850 900 950 1st decay energy (10 keV/channel)

Figure 3.9: First-generation alpha decay of residues. The ordinate is the measured decay time, in units of 100 ns, on logarithmic scale. The events in Region A correspond to the ground state alpha decay of 215Ac with a measured 172.2(6) ma lifetime.

keV.

The prompt gamma rays correlated to the decay of 213Ac are presented in Figure 3.12.

A total of five transitions corresponding to 213Ac excited states were observed. These

results are also included in Table 3.3. The only previous observation of excited states

in 213Ac was performed following the population of these states via 217Pa alpha decay

[78], Three mutually coincident gamma rays were reported in that work at 450, 612, and

820 keV. These three transitions were observed in the present work in addition to new

transitions at 445, 702, and 1116 keV.

Due to the similarity in decay energy and lifetime of 213Ac and 215Ac, as evidenced

by the proximity of the events corresponding to the decay of these two isotopes in Fig­

ure 3.9, cross-contamination in the RDT spectra was investigated. The most prominent

transitions of either 213Ac or 215Ac were not observed in their isotopic neighbors' RDT

spectra. Therefore, isotopic contamination is assumed to be negligible in the presented

RDT spectra.

47

5000

4000

3000

2000

1000

8 10 12 14 16 18 ln(t-(100 ns))

Figure 3.10: Natural logarithm, of the decay time for the ground state alpha decay of 215Ac. The counts included in this spectrum are the events of Region A of projected on the time axis of Figure 3.9. The lifetime of 21oAc was measured to be 172.2(6) ms.

Figure 3.11: Recoil-decay tagged prompt gamma rays position- and time- correlated to the ground state alpha decay of 215Ac. Prominent peaks are labeled accordingly.

The spectra presented in Figure 3.12 and 3.11 provide an excellent tool for the iden­

tification of gamma rays for a specific isotope produced in the present work as they are

relatively free of background and isotopic contaminant events. Unfortunately, the number

of events present in these spectra is not sufficient for adequate 7-7 coincidence analysis

of either isotope. This disadvantage can be overcome through the study of recoil-tagged

prompt gamma events; the gamma events detected at the target position of SASSYER

coincident with recoil events observed at the exit of the separator in MACY. The loss of

statistics using the RDT method due to transmission losses between MACY and the DSSDs

and the alpha decay detection efficiency are overcome using the recoil-tagging technique.

48

Isotope Lifetime Energy (MeV) Intensity Ref.

• Ac 0.440(16) ms 9.064(10) 90 [72j 215Ac

214Ac

2l3Ac 215Ra 214Ra 213Ra 212Ra

2 i 2 F r

•in F r

2 i o F r

209 F r

2 1 0 R n

2 0 8 R n

170(10) ms

8.2(2) s

0.80(5) s 155(7) ms 2.46(3) s 2.1(1) ms 13.0(2) s

20.6 m

3.10(2) m 3.18(6) m 50.5(7) s 2.4(1) h

24.35(14) rn

7.604(5) 7.082(5) 7.214(5) 7.364(8) 8.700(5) 7.137(3) 8.466(5) 6.899(2) 6.262(2) 6.342(3) 6.383(2) 6.534(5) 6.545(5) 6.646(5) 6.041(3) 6.140(2)

99.1 41 48 100 95.9 99.74 0.69 85

16.3 13.2 10.3 80 71 89 96 62

[70] [73]

[74] [70] [73] [74] [75] [75]

[76] [77] [69] [77] [77]

Table 3.2: Ground state alpha decay energies and lifetimes of selected Francium, Radon, Radium, and Actinium isotopes.

3.4.1 MACY energy loss measurements

A brief aside is required for a description of the required conditions for the recoil tagged

prompt gamma events used in the 7-7 coincidence analysis. Contaminants in the prompt

gamma spectrum, such as those originating from scattered beam events, can be minimized

with appropriate constraints placed on the MACY energy loss measurements. The energy

loss of the species traveling through MACY is displayed in Figure 3.13.

One would expect, according to the Bethe-Bloch equation [49, 50], that the peak at

a larger energy loss would correspond to the slow-moving, large-Z recoils. However, this

is not the case: Figure 3.14 represents the time-of-flight between MACY and the DSSDs.

The peaks at lower channel number correspond to shorter flight times and faster particles.

The broad peak at larger channel numbers represents the time-of-flight of the relatively

slow-moving evaporation residues. The events that correspond to the time-of-flight peak

of the residues in the MACY energy loss measurements are presented in Figure 3.15. The

gate on the longer time-of-flight events results in the elimination of the larger energy loss

49

2 1 5 A c 2 1 3 A c

Energy (keV) Intensity Energy (keV) Intensity

i64(r 220(1; 296(i; 304(1, 601(1; 606(1N

612(1; 701(1 718(1, 843(1, 860(1' 999(1

9(3) 15(4) 75(8) 25(4) 38(8) 25(7) 32(8) 52(11) 9(6) 23(6) 43(8)

100(13)

445(1) 450(1) 612(1) 702(1) 820(1) 1116(1)

36(7) 57(8)

100(11) 19(6) 60(9) 13(7)

1317(1) 51(9)

Table 3.3: Energies and Intensities (normalized to the strongest transition after correction for detection efficiency) for the recoil-decay tagged prompt gamma rays correlated to the alpha decay of 215Ac and 213Ac.

peak i.e. the recoil events of interest were measured to have a lower energy loss through

MACY than contaminant events. The peak that corresponds to a larger energy loss in

Figure 3.13 is most likely due to backscattered target material; slow-moving isotopes near

Z = 77 ejected from the back of the target into the separator.

This observation was confirmed by the study of prompt gamma events coincident with

the larger energy loss peak shown in Figure 3.13. The energies of the prompt gamma peaks

coincident with the larger energy loss events in MACY were consistent with those expected

for the Coulomb excitation of 193Ir and 191Ir [79, 80].

3.5 Recoil tagged prompt gamma analysis

The transitions that were observed and correlated to the decay of specific isotopes using the

recoil-decay tagging technique were used as reference for the analysis of the recoil tagged

spectrum. Using the observed energies corresponding to the decay of 213Ac and 215Ac, the

gamma events coincident with the peaks of Table 3.3 were correlated to the appropriate

Actinium isotope. Gamma rays coincident with the prominent 215Ac peak at 296 keV are

50

?r,

m m$B^mimdmkmAk^u Channel

Figure 3.12: Recoil-decay tagged prompt gamma rays position- and time- correlated to the ground state alpha decay of 213Ac. Prominent peaks are labeled accordingly.

A

/ \

o u a

V/ g s

JL IS

u

Channel

Figure 3.13: Cathode energy loss measurement of ions traveling through MACY. Sec text for details.

shown in Figure 3.16. Transitions of 164, 178, 626, 701, 718, and 999 keV were found to be

coincident with this peak. With the exception of the 626 keV transition, these decays are

also observed in the 215Ac RDT spectrum. Transitions coincident with a second prominent

215Ac peak at 999 keV are displayed in Figure 3.17. This transition was found to be

coincident with gamma lines at 164, 178, 296, and 701 keV, again, all previously observed

in the 215Ac RDT spectrum. Table 3.4 contains the coincident transitions for each peak

present in the 7-7 matrix and the corresponding isotopic assignment.

The relation between the four transitions from isomeric states observed at the focal

plane of SASSYER, shown in Figure 3.2, and the prompt gamma transitions of 215Ac

51

Recoils

220C 2600

Channel

Figure 8.14: Time-of-flight of ions between MACY and the DSSDs. The slow-moving recoil peak is indicated.

A

Channel

Figure 3.15: Cathode energy loss measurement gated on the recoil time-of-flight peak.

was investigated using a similar coincidence analysis. The gamma rays detected at the

focal plane of SASSYER coincident with the prompt peak at 296 keV are displayed in

Figure 3.18.

It is evident that all four delayed transitions, previously attributed to the decay of

215Ac [32], are coincident with the prompt peak at 296 keV. A similar analysis of the 999

keV prompt transition reveals that it is also coincident with all four 215Ac delayed gamma

rays. This indicates that the relatively intense 296 and 999 keV transitions observed at

the target position of SASSYER originate from states at greater excitation energy than

the isomeric 29/2+ state of 215Ac. These two transitions and, in fact, the majority of the

52

Figure 3.16: Recoil-tagged prompt gamma rays coincident with the 296 keV transition of 215Ac. The prominent K-shell x-rays and gamma rays are labeled accordingly.

annel

Figure 3.17: Recoil-tagged prompt gamma rays coincident with the 999 keV transition of 21oAc. The energies of prominent gamma rays are labeled.

decays observed at the target position were attributed to decays from states that feed the

previously observed isomeric states.

The short lifetime of the known isomeric states of 215Ac relative to the time-of-flight

through the separator provides an additional challenge to the correction of the measured

gamma ray intensities at both the target position and focal plane. The 17/2 - , 23/2~, and

29/2+ states of 215Ac have lifetimes of 30, 185, and 340 ns, respectively [32]. Assuming the

transitions originating from the isomeric states of 215Ac form a cascade where the general

decay chain can be written as

Ni - » N2 - • N3 (3.1)

where Ni designates the number of nuclei in each state i. This time-dependent solutions

of the set of coupled, differential equations that describe this system are

53

I . ill

f N

** lO

ill! :,MI i i! i i i .

r» t H

m

II' : 1 i l l

7.00 •

3.0D

,

Figure 3.18: Delayed gamma emission coincident with the 296 keV prompt transition of 215Ac.

Ni(t) = aue-Xlt

N2{t) = a2ie-Xlt + a22e-X2t

N3{t) = a 3 ie-A l t + a32e-A24 + a33e-A3i

(3.2)

where Ni represents the number of nuclei at each step in the decay chain, t is the time-

of-fiight of recoil, Aj is the decay constant for step i, and the coefficients a fc are given by

the recursive relation

o-k,i ^k-i

-C-k-1,1 (3.3) Afc — Aj

with the initial condition a n = N\(t = 0) [9]. Using the halflives of the isomeric states

of 215Ac, the dependence of the fraction of remaining nuclei at each step in the decay chain

on the time-of-flight through the separator was determined. This dependence, depicted in

Figure 3.19, represents the correction factor for the intensity of each transition observed at

the focal plane of SASSYER as a function of the time-of-flight of the evaporation residue.

The intensities of all transitions correlated to the decay of 213Ac and 215Ac after correction

for in-flight decays and detection efficiencies are presented in Table 3.5.

54

100

8 0 '

5 z

« H

40-

20-

Population of 29/2

Population of 23/2

Population of 17/2

I i | i J i | i | i | i |

200 400 600 800 I (XX) 1200 1400

Lifetime (ns)

Figure 3.19: Time-of-flight dependence of the correction factors for the intensities of the delayed gamma rays.

3.6 Alpha-gamma coincidences

For the alpha decay of a nucleus, the population of excited states of the daughter nuclei,

though typically of little strength, is possible. For the case of the alpha decay of 214Ac, the

branching ratio of the alpha decay populating the 139 keV 210Fr excited state is 44 % [73].

After population of this excited state, it will immediately decay and one will observe a

139 keV transition coincident with the alpha decay event. Figure 3.20 depicts gamma rays

observed at the focal plane of SASSYER that are coincident with an alpha decay event.

The three peaks at 83.6, 86,6, and 97.8 keV are at energies consistent with K-shell x-rays

of Francium. Also apparent in the spectrum is the peak at 139 keV corresponding to the

decay to the ground state of the (5,6,7)+ state populated by the alpha decay of 214Ac.

A conversion factor a = 4.6(5) was determined for the 139 keV transition assuming that

the x-ray events observed correspond to the internal conversion of the 139 keV photon.

The internal conversion coefficient for a 139 keV Ml transition in a Z = 87 nucleus is

55

5.6(1) [81], comparable to the measured value. The measured conversion coefficient is also

consistent with the previously measured multipolarity of the (5,6,7)+ state to 6+ ground

state of 210Pr [73].

jyJir

<7>

+j m^Kmu v %

i ^M

Channel

70 £

Figure 3.20: Alpha-gamma coincidence spectrum. The ground state alpha decay of 214Ac populates the 139 keV excited state in 210Fr. The subsequent decay from this state was observed in coincidence with the parent alpha decay.

56

164

2 1 5 A c 2 1 3 A c

Energy (keV) Coincidence Energy (keV) Coincidence

174 450 178 .,_ 612

445 296 701 (612) 820 701 445 999 ,„ 612 164 4o0 701 178 820 296 440 999 445

701 164 612 (174) (820) 296 440 701 445 718 612 999 701 304 1116 612

174

178

220

278

(1317) (296) 636 164 178 626 701 718 999

304 220

296

595

601

626

636

701

296 999 296 999 296 999 278 298 164 178 296 999 178

718 296 999 164 178 296 601 626 701

999

Table 3.4: Recoil tagged prompt gamma-gamma coincidences

Cn

00

arc o

H ts

os

5'

CD

•r

i.

r+ u

^+

fD

co

>-i

rro

0)

co

c-t

-

93

CO

c-h

ion of

a>

03

t^

w

CO

O

o

X) n

&

CO

Cn

H ^ CD

ao

a>

CO

0 n,

p fD

CO

<T>

CO

>-b

'. >

<r-t- gam rs

tf *- 05

P-

o n JO

o >-n

> fD

CO

fD

CO

00

IO

o o

CO

OS

o s "—'

to

Co

> o

CC

I—

i

to

^ to

>—>

o o

1—'

H^

*>.

tt-

CO

OS

to

Cn

C

O

'to -—' #>

• •f

c-

cn

i^

CO

CO

C

^i

^3

'—'

it

CO

h-l

j—1

/—

•.

5<

^—

•'

CO

'666 1 CO

•00

-J

'to "—' 0

0 C

n

00 cn

O

i *

to

to

••

—'

00

tfs- CO

o

h-'

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-J

t—'

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h->

to

1—»

O

H-»

" '

-3

O

H-i

1—

l

»—*

CO

to

'-3

OJ *- H-1

rf*.

S

—'

1^.

00

'co

-—

-

Oi

CO

O

S

^ t—»

CO

to

'-3

CD

C

O

to

o

H^

1—1

SI s

Is2

Cn

> fD

OD

to

O

D

00 rf^

on

(—>

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l—

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to

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1—1

;i6)

CD

o

CD

OS

i—"

to

cn

'oo

"—' O

D

CD

1

l

CO

1 l

CO

•S

I

'oo

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CO

j^

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i

00 to

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*•

—'

to

co

CD

CD

'to

CD

O

D

I—1

"—' to

-

J •S

I

bo

1—»

t—-1

Cn

to

CD

to

to

o

CO

t—1

cn

.3(7)

1—»

-

J 0

0 o

1—1

Cn

o

CO

1—»

sr

Cn

rf^ to

to

to

00

I—*

C5 *"

rf^

1—>

I—1

to

•SI

OD

H-<

CO

Q

ct

- o

fD M

1-i

aq

'<

;keV) I 0 fD

03.

r+*

^

Chapter 4

Discussion

Prior to this work, the spectroscopy of 215Ac had been limited to delayed-gamma or alpha-

gamma coincidence techniques. Figure 4.1 compares the most recent experimental data

with results from large-scale shell model calculations. The data is comprised of the results of

a delayed-gamma spectroscopy experiment in which four isomeric transitions were observed

[32]. These transitions have been attributed to decays from excited states that have been

interpreted as maximally-aligned configurations of protons occupying the 0h9/2, If7/2, and

01x3/2 orbitals. Decays originating from the 23/2~ state, corresponding to a f7/2hg ,2 proton

configuration have not been directly observed but the existence and energy of this state

have been inferred [32].

Insight into the evolution of proton shell structure beyond Z = 82 is obtained through

the study of the structure of the N = 126 isotones. The structure of the low-lying states of

these isotones is dominated by valence proton configurations occupying the 7r/i9/2, i^ji/i-,

and 7ri13/2 orbitals. Previous studies of the Z = 89 isotone 215Ac, a system comprised

of seven valence protons, were limited to delayed-gamma or alpha-gamma coincidence

techniques due to the low-production cross section reactions resulting in the production

of this isotope. Figure 4.1 compares the most recent experimental data with results from

large-scale shell model calculations by Caurier et al. [28]. The data consist of the results of a

delayed-gamma spectroscopy experiment in which four transitions from isomeric states were

59

4000 H

30QQ-

2000-

1000-

• 17/2"

13/2

EX •9/2

-41/2"" -39/2 j •35/21 • 37/2

-33/2"1

• 33/2"

•31/2

- 29/2"* - ( 2 9 / 2 + r

17/2

13/2"

• 13/2"*

•7/2

SM -9/2

Figure 4.1: Comparison of previously available spectroscopic data of 215Ac with large-scale shell model calculations. Figure adopted from Ref. [28].

observed [32]. The 9/2~ ground state is consistent with a single quasi-particle occupation

of the hg/2 orbital. The 13/2 - , 17/2 - , and 21 /2 - multiplet is formed by the breaking of a

spin-coupled proton pair occupying the /19/2 orbital, a seniority v = 3 configuration where

v is the number of unpaired valence nucleons. The 23/2~ and the 29/2+ states are also v

= 3 configurations of two unpaired quasi-particles occupying the /ig/2 orbital coupled to a

7r/7/2 and 7rz13/2 quasi-particle excitation, respectively. Decays originating from the 23/2~

state, corresponding to a /7/2^9/2 proton configuration were not directly observed but the

existence and energy of this state were inferred [32].

The present work has significantly expanded the experimental data available for com-

60

parison to existing shell model calculations. The following section is the interpretation of

the new results and discussion in the framework of the nuclear shell model. In the interest

of clarity, the results presented in Section 3.1 are separated into two categories: Transi­

tions observed to be feeding the known isomeric structure in 215Ac and transitions that

were determined not to be coincident with the decays from isomeric states.

4.1 Observat ion of low-lying s tates in 215Ac

The majority of the transitions presented in Table 3.5 are in delayed coincidence with the

decays from isomeric states in 215Ac. However, this is not the case for all the gamma rays

detected at the target position which are correlated to the decay of 215Ac. Figure 4.2 depicts

the prompt gamma spectrum for two separate conditions. The blue spectrum represents

the 215Ac RDT gamma rays while the red spectrum consists of the gamma rays detected

at the target position of SASSYER that were coincident with any delayed gamma event

observed at the focal plane. Upon the overlay of these two spectra, it is apparent that the

two gamma lines at 631 and 859 keV of the RDT spectrum are not coincident with any

215Ac isomeric gamma event expected to be observed well within the 19 /xs window for

the detection of delayed gamma rays. Therefore, these two decays originate from states

disconnected from and most likely with significant structural differences from the known

levels of 215Ac which are fed by the decay of isomeric states.

Particularly interesting was the observation of decays at 304 and 1317 keV (correlated

to 215Ac decay) at the target position of SASSYER. The levels from which these transitions

originate are known to be fed by decays from isomeric states [32] presented in Figure 3.1.

Therefore, the presence of these transitions at the target position of SASSYER suggests the

existence of decays that bypass the 23/2~ and 29/2+ longer lived isomeric states of 215Ac.

Prompt gamma events coincident with the 304 keV transition are presented in Figure 4.3.

The lone decay coincident with the 304 keV 17/2 - —> 13/2~ transition was observed at

220 keV. The 1317 keV 13/2" -> 9 /2 - 215Ac transition was most likely not observed in

61

• ; l

if r**ti.iir-

Channel

*'. V i.V.>

Figure 4.2: Prompt gamma events coincident with isomeric gamma decay. The blue spec­trum represents recoil-decay tagged gamma rays corresponding to the ground state alpha decay of 215Ac. The red spectrum corresponds to prompt gamma rays that are coincident to any delayed gamma event detected at the focal plane of SASSYER. The 631 and 859 keV lines were found to not be coincident with any isomeric gamma decay of 21oAc.

the coincidence gate with the 304 keV peak due to low statistics.

Additional evidence for the existence of prompt transitions that bypass the known

isomeric states of 215Ac is provided by the relative intensities of the 1317 keV and 304

keV peaks at both the target position and the focal plane. The ratio of the intensities

(corrected for detection efficiency and in-flight decays) of the 304 keV to the 1317 keV

transition /304/A317 at the focal plane was determined to be 1.04(6). At the target position

this ratio decreases to 0.47(8), indicating a loss of half the transition strength of the 304

keV relative to that of the 1317 keV peak. This lost intensity is most likely accompanied

by additional prompt transitions feeding the 13/2" state.

Inspection of the coincident gamma events with the 631 keV peak yields only the

peaks at 88, 91, and 103 keV. These decay energies are consistent with the energies of the

Ka2,Kai, K^i Actinium x-rays [82] indicating that the 631 keV transition is coincident with

a completely converted transition(s). The detection of a 215Ac gamma ray at this energy

is very unlikely. A 104 keV Ml decay of a Z = 89 transition is highly converted (a = 3.07

[81]), resulting in the emission of the a 84.3 keV L-shell x-ray that is not observed in this

work. A similar analysis of the events coincident with the 859 keV peak events reveals an

62

200 400 ftOC

Channel Figure 4.3: Prompt gamma rays coincident with the 304 keV transition of 215Ac.

equivalent behavior, displayed in Figure 4.4, where the coincident transitions are observed

to be completely converted.

The 859 keV transition is most likely a decay directly to the ground state of 215Ac as

it was not observed to be in coincidence with the 304 or 1317 keV decays. Linear polar­

ization measurements of this transition yield a value of-0.23(5), suggesting the transition

is of magnetic nature. Additionally, the anisotropy of the transition, a value of -0.11(7),

indicates that it is most likely a L > 2 transfer. These characteristics are expected of

photons in a stretched M2 transition from the 13/2+ state to the 9/2~ state. Therefore,

the 859 keV transition is tentatively assigned as the decay from the 13/2+ state of 215Ac.

As a proof of principle, the anisotropy of the 304 keV transition was determined to be

-0.12(7) with a linear polarization of 0.11(7). Both these values are consistent with the

interpretation of this decay as the stretched E2 transition between the 17/2" and 13/2^

7r/igy2 multiplet states. Figure 4.5 depicts the evolution of the energies of the 13/2+ states

in the N = 126 isotones. Upon inspection, the placement of the 13/2+ state of 215Ac at 859

keV is consistent with the trend of decreasing excitation energy of this state with proton

number for the N = 126 isotones. A summary of the transitions observed below the 29/2+

63

Channel

Figure 4.4: Prompt gamma events coincident with 859 keV peak. The Actinium K-shell x-rays were the only transitions observed to be in coincidence with the 859 keV peak indicating a coincident transition that is completely converted.

state of 215Ac is presented in the level scheme of Figure 4.6.

With regard to the evolution of single particle states, the energy of the 13/2+ state

of 215Ac can be used to track the energy of the 7ri13/2 single particle state. Following the

simple pairing description of Equation 1.5, where the single particle energies are mainly

determined by A since A2 <C A2 and A = 12/y/A, the excitation energy of the 13/2+ level

gives insight into the relative energies of the /i9/2 and i13/2 single particle states. This

analysis is dependent on the extraction of the ?i3/2 quasi-particle energy from the energies

of the high spin v = 3 states and works under the assumption that the residual interaction

between the active particles is constant [83]. With these assumptions, the excitation energy

of the 7ri13/2 and 7r/7/2 quasi-particles were determined to be 0.8 and 0.2 MeV, respectively

[32]. This value of the expected excitation energy of the 13/2+ state of 215Ac is comparable

to the quasi-particle energy of the tentatively assigned 13/2+ state. It is unfortunate that

the decay from the 7/2~ quasi-particle state of 215Ac was not directly observed. However,

the consistency of the energies for the i13/2 state in this work and the work of Decman et

al. [32] gives credence to their conclusion that there is no indication of the formation of a Z

64

13/2--

Figure 4.5: Systematics of the energies of the low-lying states in the N = 126 isotones. The decrease of the excitation energy of the 13/2+ state across the N = 126 isotones is consistent with the observed 859 keV transition in 2l0Ac corresponding to the decay of a. 7r*i3/2 quasiparticle state.

= 92 subshell due to a significant energy difference between the 7rh9/2 and 7ri13/2 orbitals.

These observations are also consistent with the conclusion the the /i9/2 and / 7 / 2 states

of 216Th are nearly degenerate based on the measurement of the energy of the 7r/i9/2/7/2

isomeric state [27].

There is a significant discrepancy between the observed excitation energy of the ten­

tatively assigned 13/2+ state in 215Ac with predictions of recent large-scale shell model

calculations of Caurier et al. [28]. While the predicted energies of the 13/2+ state in the

lighter odd-A N = 126 isotones agree well with experiment, the shell model predictions

of this state do not account for the magnitude of the decrease in excitation energy of the

13/2+ state in 213Fr to 215Ac. The agreement of the shell model prediction with the ob-

65

served energies can be improved with a monopole correction of 100 keV for levels involving

the i13/2 orbital, which has been previously suggested [31]. There are two explanations for

the apparent need for this correction. The probable strong coupling of the ^3/2 state to

the L = 3 phonon [27, 84], not accounted for by the single particle energy extracted from

209Bi, is one possible explanation. Another possible origin of these discrepancies is the

general deficiency of the Kuo-Herling interaction, as discussed in the works of Warburton

et al. and Bergstrom et al. [31, 85],

4.2 High-spin s ta tes of 215Ac

The most prominent transitions feeding the 29/2+ isomeric state, consisting of quasi-

particle excitations in the 7r/ig/2 and niiz/2 orbitals, are the mutually coincident peaks

observed at 296 and 999 keV. These transitions are comparable to the 33/2+ and 37+ lev­

els feeding the 29/2+ state of 213Pr, shown in Figure 4.7. Identification of the 999 keV peak

as the 33/2+ -> 29/2+ transition and the 296 keV peak as the 37/2+ - • 33/2+ transition

reveals fairly good agreement between the observed excitation energies of these states with

shell model predictions [28]. This comparison is also depicted in Figure 4.7. In addition,

the 164, 174, and 178 keV mutually coincident transitions are tentatively identified as de­

cays from the high-spin 35/2+ , 39/2+ , and 41/2+ states, consisting of a (7r/i9/2)4 ® (7^13/2)

configuration, where the order of these low energy transitions is based on the observed

gamma ray intensities presented in Table 3.5.

The remaining spin assignments of the states for which decays were observed in the

present work proved exceedingly difficult. This difficulty was due to the combination of the

lack of systematic data of the lighter N = 126 isotones, particularly information regarding

high-spin states, and the relatively low statistics of the present work. Therefore, the place­

ment of the remaining transitions presented in Table 3.5 relative to the states previously

discussed was performed based entirely on gamma-gamma coincidence and intensity mea­

surements. The level scheme of 215Ac containing all information acquired in the current

66

experiment and the data of Decman et al. [32] is compiled in the level scheme presented

in Figure 4.8.

67

(29/2+) 2483 335(10) ns

215

1948

1841

1796

1621

185(30) us

30(10) ns

1317

859

Ac Figure 4.6: States below the 29/2+ isomer in 215Ac. The spin-parity of the 859 keV state is tentatively assigned as 13/2+ . The relative intensity of the 304 and 1317 keV transition indicate additional level feeding the 13/2" state. Although the coincidence of the 631 keV decay with the peaks at, 304 and 1317 keV was not directly observed, the latter possibly due to lack of statistics. The tentative placement this transition is not inconsistent with the measured intensities of these transitions. The 220 keV peak was observed to be in coincidence the the 304 keV transition and is interpreted as the decay from the 23/2" state.

68

(41/2*)-

37/2+-

Exp 2X3

37/2*-

33/2*.

SM

Fr

(39/2*) >|< 4137

(35/2*) "I" 3959

(37/2*) + 3785

(33/2*) -

Exp 2 1 5

41/2* 4013 39/2* 3941

35/2* 3850 37/2* 3778

-2483 29/2+-

AC SM

Figure 4.7: Comparison of energies of the excited states above the 29/2+ isomeric state in 213Fr and 215Ac with the results from large-scale shell model calculations of Caurier et al. [28].

69

(29/2+)

1403

4125

2483 335(10) as

1948

1S41

1796

1621

185(30) as

30(10) as

1317

859

215 Ac

Figure 4.8: Experimental level scheme of °Ac

70

Part II

High-resolution (p,t) Studies of

the Stable Palladium Isotopes

71

Chapter 5

Introduction

While the shell model provides a successful description of atomic nuclei near closed shells,

this approach becomes unreliable due to computational constraints as the number of valence

nucleons is increased. Nuclei far from closed shells are typically described using geomet­

ric or algebraic models such as the Interacting Boson Model [86] which is introduced in

the following sections. These approaches define a macroscopic shape for the nucleus and

excitations are characterized as rotations or vibration of the collective nuclear body. The

shapes of the nucleus vary from vibrating, spherical nuclei, to axially symmetric rigid or

"soft" rotors.

As depicted in Figure 5.1 for even-even (even numbers of protons and neutrons) rare

earth nuclei, the shape of the nucleus undergoes a transition with the addition or removal

of nucleons. In some cases, the transition from a spherical to a deformed nuclear system

occurs very rapidly. These rapid shape changes have been linked to the study of quantum

phase transitions in many-body systems [2, 87, 88] which, in many ways, behave similarly

to phase transitions of infinite, thermodynamic systems. The topic of finite-system shape-

phase transitions will be discussed in the following sections.

The idea of quantum phase transitions and the search for experimental signatures

of this phenomenon led to a survey of low-lying excited 0+ states in even-even nuclei

throughout the rare earth region [89]. The rare earth isotopes, schematically depicted in

72

Figure 5.1, were chosen for the variety of structure exhibited by nuclei in that region.

One extraordinary result of this survey was the discovery of a large number of previously

unobserved excited 0 + states. The density of these states was found to increase significantly

near regions of rapid shape transitions [89]. This increased density of excited 0+ states was

interpreted as a signature of phase transitional behavior, the mechanism of which will be

described below.

Figure 5.1: Regions of the nuclear chart studied in the survey of low-lying 0+ in even-even nuclei. Isotopes studied by Meyer et al. [89] are denoted with red circles while nuclei studied in this work are labeled in red.

Depicted in Figure 5.1 is the region of interest for the present work, the continuation

of the systematic search for excited 0+ states. Even-even isotopes in the transitional

region below the Z = 50 and beyond the N = 50 shell closures were investigated using

two-nucleon transfer reactions. Specifically, the stable Palladium isotopes were candidates

in the search for further signatures of phase transitions in finite nuclear systems. The

remainder of this chapter includes an introduction of the models typically used to describe

phase transitional behavior in nuclei. Experimental evidence of such behavior is discussed

as well as the experimental techniques used in the present work.

73

5.1 The Interacting Boson Model

The interacting Boson Model (IBM) [90, 91, 92, 93, 94] has become one of the primary-

models, along with the Geometric Collective Model (GCM) [95], used to describe the col­

lective behavior of nuclei. The success of this particular model is hinged on its intrinsic

simplicity while keeping the ability to describe collective behavior spanning from vibra­

tional to rotational nuclei. The foundation of this algebraic model is the truncation of

the fermionic shell model space of a nuclear system by the assumption that the valence

nucleons exist in correlated pairs, forming bosons with specific spins. In the simplest de­

scriptions, nucleons are allowed to form bosons of total spin J = 0, 2, typically referred to

as s and d bosons, respectively. All low-lying collective structures of a nucleus can then

be described as the interaction of the s and d bosons with the appropriate Hamiltonian

consisting of bilinear operators that conserve boson number, defined as half of the total

number of valence nucleons.

In its simplest form, the Hamiltonian of the sd-IBM is composed of bilinear terms of

boson creation and annihilation operators s, s\ d, d). The combination of the operators

form a Lie algebra and span the 6-dimensional space U(6). The underlying beauty of this

model is that the U(6) space can be decomposed into three rotationally invariant subgroups:

U(5), 0(6), and SU(3), and each of these dynamical symmetries corresponds to a different

geometric analogue. The U(5) subgroup corresponds to a spherical vibrator nucleus and

the 0(6) and SU(3) subgroups correspond to 7-soft vibrator and deformed rotor nuclei,

respectively.

The simplest and intuitive form of the Hamiltonian employs the consistent Q formalism

(CQF) [96]. Using the CQF, the Hamiltonian can be written as

H = KQ-Q-K'L-L (5.1)

74

where the quadrupole operator Q is defined as

Q = (sfd + Ss) + xi.d]d){2). (5.2)

and the L operator is defined as y/lO[d^d]^\ The parameter % is allowed to vary from 0

to -y/7/2.

The CQF Hamiltonian allows for the evolution of nuclear structure from 7-soft behavior

to that of deformed rotational nuclei. However, an additional term is needed for the

description of spherical vibrator nuclei. This is accomplished in the extended CQF (ECQF)

[97] where the Hamiltonian is given by

H = end + KQ-Q-K'L-L (5.3)

where n^ is the number operator for d bosons, (d^d)°. The orbital angular momentum

term L • L is not required for the discussion of the evolution of structure between the

dynamical symmetries and therefore is omitted. The dynamical symmetries of the U(5),

0(6), and SU(3) correspond to the the three parameters of the Hamiltonian: e, K, and %. A

helpful visual aid to understand the evolution between these symmetries is provided by the

introduction of the symmetry triangle [98]. In this parametrization, the U(5) limit is given

by K = 0 and any % value, the SU(3) limit is given by e = 0 and x = -V7/2, and the 0(6)

limit is given by e — 0 and x — 0- These limits and their associated geometric analogues

and low-lying level schemes are shown at the vertices of the symmetry triangle, displayed

in Figure 5.2. All points within the triangle can be described by the ratio n/e and X- The

ratio e/« can be construed as the deformation-driving parameter of the Hamiltonian.

The number of parameters in the Hamiltonian presented in Equation (5.3) can be even

further reduced with the introduction of a new parameter (. ( is defined as

^ (e/K + 4NB)'

75

(5.4)

0(6)

U(5) 1st order SU(3)

Figure 5.2: The symmetry triangle of the IBM (adopted from Ref. [2]). Each vertex of the triangle corresponds to a dynamical symmetry with an analogous geometric interpretation as described in the text. Schematics of the low-lying states for each dynamical symmetry are presented at each vertex. The trajectory within the triangle is described by the parameters £ (the distance from the U(5) limit) and % (the angle from the U(5)-SU(3) leg). As described in Section 5.2, the first-order phase transition exists for any trajectory within the triangle (X ± 0) for C « 0.5.

where NB is equal to the total number of bosons in the nucleus. Substitution of ( into

Equation (5.3) leads to the following result [99, 100, 101]

H(0 = c[(l-Qnd--^-QX-Q- (5.5)

where c is a scaling factor. With the introduction of (, all aspects of collective nuclear

structure within the symmetry triangle can be described with the variation of the param­

eters ( and x- The limits of the dynamical symmetries are now ( = 0 and any x for U(5),

C = 1 and x = -\/7/2 for SU(3), and C = 1 and x = 0 for 0(6).

76

5.2 Quantum phase transitions in nuclei

Though not identical, the thermodynamic description of a phase transition in an infinite,

macroscopic system and the idea of quantum phase transitions between equilibrium shapes

in nuclei have many analogues. Both describe the evolution of a system as a function

of an order parameter: temperature or pressure for a thermodynamic system or simply

the number of valence nucleons in the nuclear system. Both descriptions adhere to the

basic properties of phase transitions established by Landau [102, 103]. For a first-order

phase transition, the first derivative of the order parameter is discontinuous. The critical

point of a first-order phase transition is characterized by the coexistence of two phases.

In nuclei, this corresponds to the coexistence of spherical and deformed shapes and in the

thermodynamic picture this results in the simultaneous existence of two phases of matter.

A second-order phase transition is designated by the discontinuity of the second derivative

of the order parameter. Under this condition there is no phase coexistence at the critical

point.

The study of quantum phase transitions in nuclei is facilitated using the framework of

the IBM. The Hamiltonian of the IBM can be extended to include the geometric shape

parameters /3 and 7 using the coherent state formalism [104, 105] where j3 is defined as the

quadrupole deformation of the nucleus while 7 is a measure of the axial asymmetry. Inspec­

tion of the resulting Hamiltonian has revealed that rapid transitions between equilibrium

shapes of nuclei occur with the variation of the IBM parameter £ [106, 107]. The order

of the phase transition is dependent on the value of x- A second-order phase transition

occurs for x = 0 corresponding to the transition from a spherical vibrator to a 7-soft rotor.

For all other values of x, the transition from a spherical to a deformed nuclear shape is a

first-order transition. Any trajectory through the symmetry triangle (see Figure 5.2) from

a spherical to a deformed shape must pass through either a first- or second-order phase

transition. Experimental signatures of phase transitional behavior have been established

in regions of nuclei in which rapid change in the ground state deformation is observed,

77

namely the enhancement of the level density of low-lying 0+ states [89]. A discussion of

these signatures is included in Section 8.2.

5.3 Excitation of nuclear states via transfer reactions

There are a number of experimental techniques used to populate excited states of nuclei.

In a fusion-evaporation reaction, the mechanism of which is discussed in section 1.4, the

population of states with high-spin and large excitation energies is preferred. From the

Yrast line, these states will then decay via gamma ray emission (see Figure 1.6). Unfor­

tunately, low-spin states of up to a few MeV excitation energy can be bypassed during

this de-excitation cascade. Alternative methods of nuclear excitation include /?-decay and

direct reactions, the transfer of one or more nucleons between a projectile and target nu­

cleus. In contrast with fusion-evaporation reactions where the populated excited states are

in close proximity to the Yrast line, these methods are specifically biased towards the pop­

ulation of all states with low-spin and/or energy. Therefore, a direct reaction, specifically

a two-neutron transfer reaction that is particularly sensitive to the population of 0+ states

due to pairing correlations, is utilized in the survey of excited 0+ states in collective nuclei.

5.3.1 The Distorted-wave Born approximation

In a direct reaction, the transfer of nucleons between the projectile and target nucleus

occurs without the formation of an intermediate state. As the name implies, a direct

reaction proceeds directly from the initial to the final state. A simple description often

used to compute differential cross sections for elastic scattering is the Born Approximation

[108]. If there is no interaction between the projectile and target, the incoming particle

can be approximately described as a plane wave. However, in nuclear direct reactions this

approximation is no longer valid when determining transition amplitudes of the available

channels of the reaction. In this case, the Distorted-Wave Born Approximation (DWBA)

[109] sufficiently describes the incoming and outgoing channels of the direct reaction. Dis-

78

torted waves of the entrance (exit) channels are asymptotically described as plane waves

plus and incoming (outgoing) spherical waves [109]. The so-called optical model potential

[110, 111, 112] is used for the description of the interaction between the entrance and exit

channels. In the corresponding optical model, the nucleus is assumed to have the same

properties as an optical material [113]: an absorption component and a diffraction com­

ponent. The absorption component corresponds to inelastic collisions while the diffraction

term describes elastic scattering. The optical model potential used in this work is de­

scribed with three components: a spatial distribution term of a Woods-Saxon shape, a

spin-orbit interaction, and a Coulomb potential for a spherical uniform charge distribu­

tion. The strength of these terms is dependent on the identity of the constituents in the

entrance and exit channel and have been phenomenologically determined by comparison

to the experimental data [114].

The DWBA formalism presented above is adept at describing a transfer reaction that

occurs in a single-step. It is also possible for more than one interaction to occur between

the incident particle and target nucleus during the direct reaction. A schematic of this

mechanism is presented in Figure 5.3. In the scenario presented, the particle is initially

transferred to the target and an excited state of the residual nucleus is formed. The second

step of the reaction is the decay of the residual nucleus to the ground state.

Figure 5.3: Depiction of potential interactions during a two-step coupled channel mech­anism for a direct reaction. The schematic corresponds to the inelastic excitation and rearrangement processes during the A(a,a')A*(a',b)B or A(a,a')B*(a',b)B reaction.

These indirect, two-step coupled channel mechanisms become particularly important in

79

two-nucleon transfer reactions [115] and their effects are specifically prevalent for transitions

populating low-lying 2 + states in even-even transitional or deformed nuclei [116, 117].

As the reaction chosen in this work involves the transfer of two neutrons to transitional

nuclei, these mechanisms and their potential effects on the results of the experiment must

be understood. The most dominant component of a two-step reaction is the inelastic

excitation of the first 2 + state in either the target or projectile nucleus. These amplitudes

may interfere constructively or destructively with the first order amplitude and modify

the magnitude and shape of the angular distribution. In general, the angular distribution

of the population of a 0+ state is only significantly affected at larger angles by the most

dominant coupled channel component and its characteristic shape can be used for spin-

parity identification. The coupled channels code CHUCK3 [118] is used to calculate the

reaction cross sections which are then compared to the experimentally determined cross

sections for the (p,t) reactions presented in this work.

1E-3-;

IR-4-

^ „ ' \

V

2155 kcV

\ \

8,,,

-

6l;Ji (degrees) e „ (degrees)

Figure 5.4: Triton angular distributions for a variety of ground state wavefunctions for the n 0Pd(p,t)1 0 8Pd reaction. The left figure is the angular distribution for the population of a 0+ state at 2155 keV while the right depicts the angular distribution for the population of the 2219 keV 2+ state. There are slight differences is the location and depth of the minima in both figures but the overall shape for each neutron occupation is consistent.

In addition to coupled channel effects, the shape of the angular distribution is dependent

on the description of the wave function of the target nucleus. The orbitals occupied by the

valence nucleons involved in the transfer reaction are a vital ingredient in the calculation of

the interaction matrix elements. The effect of the ground state composition on the shape

80

of the angular distribution of the outgoing tritons in a (p,t) reaction was investigated by

varying the neutron occupation of single particle states of a n o P d target nucleus. The

resulting angular distributions for the population of excited 0+ and 2 + states in the 108Pd

residual nucleus are displayed in Figure 5.4. The calculations show a slight difference in the

location and depth of the first minimum of the angular distribution but the overall shapes

are fairly consistent. Therefore, even in the absence of detailed spectroscopic information

regarding the ground state of the target nucleus, the overall shape of the measured angular

distribution should provide a reliable tool in the spin-parity assignment of states populated

in the (p,t) reaction.

81

Chapter 6

Experimental Techniques

6.1 Experimental apparatus

The (p,t) study of the stable even-even Palladium isotopes was performed at the MLL

(Maier-Leibnitz Laboratory of LMU and TU Munich) MP tandem accelerator laboratory.

A Q3D [119] spectrograph, comprised of a focusing magnetic quadrupole element followed

by a series of three magnetic dipoles (see Figure 6.1) separated the scattering tritons

according to their momentum-to-charge ratio. As a result of this separation, the triton

distance from the optical axis in the bending direction of the spectrograph was dependent

on its kinetic energy. The kinetic energy of an outgoing triton will simply be the sum of the

beam energy with the Q-value of the particular (p,t) reaction less any excitation energy of

the residual nucleus. The spectrograph and associated detector systems are mounted on a

rail system such that the system can be physically rotated about an axis through the target

chamber and relative to the fixed direction of the incident beam. This system aided in the

measurement of the triton angular distributions where the intensity of the population of

various excited states in a residual nucleus must be measured at multiple angles. The energy

resolution of the spectrograph is approximately A E/E = 10~4 with a flight path distance

of ~5 m. A position-sensitive cathode strip detector is located at the focal plane of the Q3D

[120, 121, 122]. This 1 m long detector is fixed in a horizontal position at the exit of the

82

Dipole 2

Track

Dipole l£% Dipole 3

Quadrupole,

, Target Chamber

Beam

Focal Plane Chamber

Figure 6.1: Schematic of the MLL Q3D spectrograph. The spectrograph consists of a focusing magnetic quadrupole element followed by a series of three magnetic dipoles. The entire experimental apparatus is mounted on a movable platform that can be rotated about target chamber.

third dipole and is sensitive to the horizontal displacement of ions exiting the spectrograph.

A photograph and a schematic of this detector are presented in Figure 6.2. The detector

is filled with continuously flowing isobutane at atmospheric pressure that is used as a

counting gas. As an ion passes the anode of the detector, an electron cloud is created.

This in turn creates a mirror charge distribution on the few cathode strips in proximity.

The position of the implanted ions is deduced offline on an event-by-event basis by fitting

the shape of the mirror charge distribution with a 75% Gaussian, 25% hyperbolic secant

function. The position of the ion events is determined within 0.1 mm using this fitting

technique. After passing through the gas-filled region, ions are implanted in a scintillation

detector where the intensity of the output signal is proportional to the kinetic energy of the

implant. The combination of the resulting rest-energy measurement and the energy-loss

measurement of the ion passing through the counting gas is used for particle identification.

Excellent triton position (energy) resolution of transfer reaction products and very low

83

/ avalanche region incident particle

Figure 6.2: Photograph and schematic of position-sensitive cathode strip detector at focal plane of Q3D. The region containing the cathode and anode of the detector is filled with isobutane at atmospheric pressure. The histogram depicts a typical image charge distri­bution measured at cathode strips of the detector. This distribution weighted average of this distribution is used to the determine the position of incident particles during online analysis. This figure is adopted and modified from Ref. [122]

background contamination is achieved with the combination of the Q3D spectrograph and

the continued development of the focal plane detector [120, 121]. For 15-20 MeV tritons,

a 4-6 keV FWHM resolution is obtained. Cross section measurements of states populated

in the residual nuclei are possible down to a few /xb/sr. These operational characteristics

make this experimental setup ideal for the measurements of cross sections for any weakly

populated state in transfer reactions. The ability to the measure cross sections to ~ 0.1%

of the ground state population strength provides confidence that a nearly complete set of

0+ states is observed in the excitation energy regions studied.

For the study of the Palladium isotopes in this experiment, a 25 MeV unpolarized

proton beam was incident upon isotopically enriched Palladium targets (> 95% by mass

for the target of each isotope studied). The results from the 110Pd target were analyzed

at WNSL while the 108-106Pd target data sets were analyzed by collaborators [123]. The

number of outgoing tritons were measured at angles of 5°, 12.5°, 20°, 30°, 40°, and 50° with

84

respect to the incident beam axis. These angles are chosen to emphasize the sensitivity

for the identification of populated 0+ states. The larger angle positions of the Q3D are

included in order to distinguish the angular distributions corresponding to the populations

of 2+ and 4 + states.

The spin and parity assignments of the excited states of the residual nuclei populated in

a two-neutron pickup (p,t) reaction are deduced from the shape of the angular distribution

of the outgoing tritons. Characteristic shapes of the angular distributions corresponding

to the population of L = 0, 2, 4 transfer are displayed in Figure 6.3. Coupled channel

effects that may influence the differential cross section of each state populated in a residual

nucleus, particularly at larger scattering angles, were not considered in this work. For each

10 20 30 40

Angle (degrees) 50 60

Figure 6.3: Typical shapes of the angular distribution of the outgoing tritons following a (p,t) reaction for L = 0, 2, 4 transfer. The L = 0 transfer is characterized by a large scattering amplitude at forward angles. The cross section for a L = 2, 4 transfers are typically peaked at approximately 15° and 30°, respectively.

angular distribution shown, the maximum differential cross section is dependent on the

transferred orbital angular momentum. The maximum of the L = 0 transfer distribution

is found at 0° and the first minimum at ~ 15-20°. In general, for a L = 0 transfer, the

distribution is peaked at forward angles and falls off dramatically as the angle is increased;

at times with a reduction in strength greater than an order of magnitude. The unique shape

85

of the L = 0 angular distribution facilitates the identification of populated 0+ states, one of

the primary goals of this experiment. As the transferred angular momentum is increased,

the maximum intensity of the angular distributions is found at more backward angles. The

strength of the angular distributions of L = 2, 4 transfers are typically peaked at 15° and

30°, respectively. States with excitation energies up to 3.5 MeV were populated in this

200-

150-

100-

50 -1

0 - *

2.2 - 3.5 MeV

JL.IJLAJ. lL rJLi^ , i fJ $hjl\iA iJL . JL

c 3 O U

c

200-

100-

0 - M

1 . 2 - ;

<Jy>. I .

500 1000 1500

L7 MeV

L.ix..\ A .l.iit, i , 1 ,

2000

i

2500

^ 4 - , 0

10000

1000-j

100-g

10

500

0 - 1.5 MeV

1000 1500 2000 2500

: i n nil III t\ 11,III l i i ii 1,1 ill11.1 r

500 1000 1500

Channel Number

LIU 1,11 I

2000 2500

Figure 6.4: Typical triton position spectra for each excitation energy window. The range of each excitation energy window is approximately 1.5 MeV. The data for the spectra were obtained at the 5° setting of the Q3D for a proton beam incident on a 110Pd target.

work. Due to constraints of the acceptance of the Q3D, data was taken in three energy

windows, each spanning an excitation energy range of approximately 1.5 MeV. An example

of the particle spectra of each excitation energy window is displayed in Figure 6.4. The

energy windows overlap slightly in order to ensure the consistency of results of measured

cross sections of populated states present in multiple windows. A quadratic relationship

between the channel number and excitation energy, a result of curvature of the optical focal

plane, was extracted from the positions of known excited states of the residual nucleus.

An example of the dependence of excitation energy on channel number is presented in

Figure 6.5. Excitation energies of the previously unobserved states were then interpolated

86

using the calibration information from each energy window. The graphical analysis software

package RAD WARE [59] and spectrum analysis program GASPAN [124] were used in the

analysis of the presented spectra. Differential cross sections were determined from the areas

i i i i i i i i i i i 0 500 1000 1500 2000 2500

Channel Number

Figure 6.5: The excitation energy dependence of the position of the scattered tritons for the u 0Pd(p,t)1 0 8Pd reaction. This dependence is slightly quadratic due to the slight curvature of the optical focal plane of the Q3D. The presented data points were obtained at the 5° setting of the Q3D in the energy window centered at 500 keV.

of the peak corresponding to the population of a particular state in the residual nucleus

using the code Intens4 [125]. This code corrects for detector and data acquisition dead

time, spectrograph acceptance, and provides a normalization factor for the conversion of

peak areas to the final differential cross section result. Areas were determined by fitting

the observed particle spectra peak with left-tailed Gaussian functions using the GASPAN

package where the tails of the position peaks were caused by the range of energy loss of

the tritons traveling through the target material. Scattered tritons from reactions that

occur near the front of the target will exit the material at a lower kinetic energy than those

produced at the rear of the target. The strength of the tail parameter was determined by a

least-squares minimization fit of a prominent peak for a specific energy range and then held

constant for the remainder of the fits for that particular spectrum. In order to reduce the

uncertainty in the final areas, the width of the Gaussian was assumed to be proportional

87

to the excitation energy.

88

Chapter 7

Experimental Results

7.1 Popula t ion of excited s ta tes of I04,i06,i08pd

A number of previously unobserved low-spin states of 104>106,i°8P(i w ere identified in the

analysis of this experiment. In total, 54 new 0+ , 2+ , and 4 + were identified with the

majority of the new states assigned to 108Pd. Before a discussion of the observation and

spin-parity assignments of these states, it is helpful to introduce the method used to gener­

ate triton energy spectra that are virtually free from background contamination. Deuteron

contaminant events were identified and removed from the triton position spectra used in

the identification of excited states of the Palladium isotopes. Figures 7.1 and 7.2 [123] are

examples of spectra used to isolate the triton events from the lighter particle contaminant

events using measured values of the energy loss and rest energy at the focal plane detector

of the Q3D on an event-by-event basis. In Figure 7.1, the energy loss at each cathode wire

grid is used to determine a measure of the successive energy loss of each particle traveling

through the counting gas of the detector. The displayed particle spectrum was recorded

during the (p,t) study of 102Pd at a 5° Q3D setting. The events corresponding to the

transmission of tritons are well separated from the deuteron events. This is also the case

in Figure 7.2 where the rest energy of a particle implanted in the scintillator of the focal

plane detector is plotted relative to the corresponding energy loss in the counting gas. The

89

Figure 7.1: Energy loss at the first and second cathode measured at the cathode strip detector at the focal plane of the Q3D. The regions corresponding to triton and deuteron events are labeled accordingly. The data was taken during the study of 102Pd at the 5° setting of the Q3D centered at an excitation energy of 1800 keV. This figure is adopted and modified from Ref. [123].

Kinetic energy (channel)

Figure 7.2: Energy loss and kinetic energy measured at the cathode strip detector at the focal plane of the Q3D. The regions corresponding to triton and deuteron events are labeled accordingly. The data was taken during the study of 102Pd at the 5° setting of the Q3D centered at an excitation energy of 1800 keV. This figure is adopted and modified from Ref. [123].

spectrum displayed was obtained at Q3D settings identical to those used for Figure 7.1.

Here, again, the deuteron events are well separated from the observed triton events and

appropriate cuts on these spectra generate triton energy spectra that are almost completely

free of background events.

The spin-parity assignments were based on the shape of the measured angular distribu­

tion of each populated state and its comparison with the DWBA. A detailed discussion of

the spin-parity assignments is included in the present section. Spectra obtained at the 5°

setting of the spectrograph are presented in Figure 7.3. Low-lying excited states of 108Pd

90

Cou

nts

600-]

550 -

500-

450 -

400 -

350 -

300-

250 -

200-

150-

100-

5 0 -

0 -

>

1441

I

J_

(N CO

a

500 I

1000 1500

Channel Number

2000

- Q3D at 12.5

Q3D at 20°

o >"

2500

Figure 7.3: Triton position spectra for the production of 108Pd for the excitation energy window centered at 500 keV. The spectra obtained at two different Q3D angular settings are shown to emphasize the scattering angle dependence on the observed intensity. The energy and spin-parity assignments of the populated 108Pd states are labeled accordingly.

were studied in two separate instances using the two-neutron pickup reaction. Differential

cross section measurements were made with the Q3D spectrograph at the 5°, 12.5°, and

30° settings in March of 2006. During September of 2006, additional measurements were

made, obtaining data using an identical method but with the addition of the 40° and 50°

angular settings of the spectrograph. In order to remove any systematic differences in the

measurements taken at separate times, cross sections of states populated during both the

March and September instances were compared. The most likely sources of inconsistencies

between the two sets of data is the uncertainty in the measurement of the magnitude of

the intensity of the proton beam. The cross sections obtained during the September ex­

periment were normalized to be consistent with those of the original March run. For the

excitation energy window centered at 500 keV, the September cross section were found to

be consistent with the March values after multiplication with a 0.73 normalization factor.

91

The normalization factor for the 1800 and 2900 keV energy windows were found to be 0.84

and 0.8, respectively.

The energies and differential cross sections at each scattering angle of all 0+ 108Pd

states populated in the experiment are displayed in Table 7.1. The value R(5/20) is the

ratio of the cross section observed at 5° to that at 20°. Due to the dramatic decrease

in population strength between these two angles for an L = 0 transfer, this ratio is a

helpful indicator for spin-parity identification. For reference, the R(5/20) value for the

population of the 0 + ground state of 108Pd and its first excited 0 + state are 28 and 4.6,

respectively. This value is in contrast to R(5/20) for the population of higher spin states.

For example, R(5/20) of the ground and gamma band 2+ states were found to be 0.823(2)

and 0.346(1). The excited state at 2145 keV was identified with a tentative 0+ spin-parity

assignment in earlier (p,t) studies [126]. The angular distribution of this state in this

work (see Figure 7.4) confirms the assignment as a 0 + state. The larger uncertainty values

for the states observed at higher excitation energies are attributed to uncertainties in the

energy calibration. The combination of high level density in the triton particle spectra

for the Ex = 2900 keV setting and the lack of knowledge of low-spin states in this energy

region contributes significantly to the increased uncertainty of the extrapolated excitation

energy. The angular distribution of the outgoing tritons after population of the two lowest

energy 0+ , 2 + , 4 + excited states of 108Pd are presented in Figures 7.5. Each of the angular

distributions displayed also includes the DWBA calculations with the CHUCK3 code (see

section 5.3.1). The absolute values of each theoretical angular distribution is normalized to

the largest experimental value for each observed state. Quantitative measurements of the

composition of the ground state wavefunction, particularly the occupation of the valence

neutrons picked up in the transfer reaction, of the U 0 P d target nucleus were not performed

in this experiment. However, knowledge of the ground state wavefunction is not required

for an adequate comparison of the shape of the angular distributions with those of the

present experiment. A variety of neutron orbitals for the target nucleus were used in the

CHUCK3 description of all observed excited states of 108Pd. The angular distribution

92

0.01 -J

1E-3H

•8

Id.,

IE-4

Figure 7.4: Triton angular distribution for the population of the excited state at 2145 keV in 108Pd. The observed cross sections (indicated by the black points) are compared to DWBA predictions for a variety of 110Pd ground state wave function orbitals. The DWBA cross sections are normalized to the 5° experimental cross sections.

calculations were performed under the assumption that the pair of transferred neutrons

occupied various available states, specifically in the I57/2, l< 5/2> a n d 0/in/2 orbitals. As

shown in Figure 7.5, the assumed occupation orbital of neutrons does not have a large

effect on the shape of the angular distribution after normalization to the experimental

cross sections. The analysis of 102Pd and 106Pd using the (p,t) reaction was performed by

collaborators [123]. The observed 0+ states in each of these isotopes populated via two-

neutron transfer are presented in Table 7.2. Of the states presented, three new 0+ states

were observed in 102Pd at excitation energies 2120, 3166, and 3323 keV. Two new 0+ states

were attributed to 106Pd at 3162, and 3572 keV. The 0+ states of 106Pd at 2878 and 3321

keV, both previously studied using 106Rh /?"" decay [127, 128] were not observed in this

experiment. Additionally, two 0 + states at 1340 and 1877 keV of 106Pd identified in this

work were determined to originate from 110Pd isotopic contamination in the enriched 108Pd

target. The difference in the Q-value for the (p,t) reaction using a 110Pd or 108Pd target is

93

Energy (keV) Differential Cross Section (/ib/sr)

5 degrees 12.5 degrees 20 degrees 30 degrees R(5/20)

0.0 1052.6(3)a

1314.1(2)a

2145.4(1)6

2152.8(2) 2432.3(1) 2682.6(1) 2872(1) 2877(2) 3136(5) 3180(5) 3257(7) 3286(7) 3347(8) 3460(9) 3508(12) 3537(13)

3540(30) 51.3(1) 4.9(3) 9.1(4) 6.4(4) 18.5(6) 4.9(7) 30.3(9) 11.7(7) 18.6(6) 14.6(7) 10.6(4) 12.9(5) 11.1(6) 10.3(5) 18.5(7) 19.5(7)

1237(7) 24.8(8) 1.7(2) 2.8(2) 2.4(2) 6.0(3) 1.5(4) 8-1(1) 1.4(9) 4.5(3) 4.0(0 2.2(3) 5.0(4) 5.1(5) 2.6(3) 4.7(4) 5.4(4)

137(2) 11.1(4) 0.43(9) 0.6(1) 0.24(6) 0.25(6) 1.1(3) 2.7(6) 0.6(4) 1.3(2) 6(4)

2.7(2) 1.9(2) 4.4(7) 2.1(2) 0.9(2) 1.5(2)

389(3) 6.9(2)

0.14(4) 0.39(5) 0.70(7) 1.9(1) 0.8(3) 4.6(9)

3.2(2) 2.4(4) 2.2(2) 1.9(2) 1.6(4) 1.6(2) 2.2(2) 3.0(3)

25.8 4.6 11.4 15.2 26.7 11.0 4.5 11.0 18.3 13.8 2.3 4.0 6.8 2.5 5.0 19.7 12.7

Table 7.1: Energies and differential cross sections of the low-lying 0+ states in 108Pd populated in the two-neutron pickup reaction.

"Previously known excited 0 + state

'Previous tentative spin assignment

808 keV. In the analysis of the excited 0 + states in 106Pd, one would expect any 110Pd target

contamination to result in the observation of 108Pd states at an excitation energy of (E . pd

- 808) keV in the triton position spectra. The 108Pd 0+ states at 2145 and 2685 keV are

indeed observed at 2145 and 2685 keV in the triton position spectra corresponding to the

population of excited states in 106Pd. These excitations have been subsequently corrected

in the results of the 106Pd analysis. The measurement of differential cross sections at larger

scattering angles allowed for the identification of states populated via L = 2 and L = 4

transfer. Twenty previously unobserved 2 + states of 108Pd were identified in the present

work. The majority of these states are in the excitation energy range from 2.5 to 3.5 MeV.

The observation of such a large number of states in this energy range is consistent with the

expected increased level density above the pairing gap. Table 7.3 contains the excitation

energy and maximum differential cross section of each 108Pd 2+ state populated in the (p,t)

94

0.010-

o.uw -

o.«w -

11.1)07 -

aoo6-

«.«»• 0.004-

0.(10* -

O.U02 •

O.UOI -

^ \ . ' \J;

if \ l 9 5 8 keV

w vv vr:

3

- i . 1 . ' " 1

1990 keV

6,^ (degrees)

- 1 • r—

6 ^ (degrees)

Figure 7.5: Triton angular distributions for the population the first and second excited 0+ , 2+ , and 4 + states in 108Pd. The observed cross sections (indicated by the black points) are compared to DWBA predictions for a variety of 110Pd ground state wave function orbitals. The DWBA cross sections are normalized to the largest measured experimental differential cross sections.

reaction. The spin-parity assignment of each level tabulated was made on the basis of the

shape of the angular distribution and its comparison with the DWBA description. These

angular distributions were typically weak at very forward angles and of greatest intensity

between 15° and 20°. The measured cross section decreases rapidly at larger angles for an

L = 2 transfer.

The excited state of 108Pd at 2014 keV was first observed using a (t,p) reaction however

the spin and parity were left unassigned [126]. The angular distribution of this state is

presented in Figure 7.6. It is clear that the triton angular distribution following population

95

102p d 106p d

E (keV)

0.0 1592.9(6)° 1658.6(6)a

2120.3(6) 2432.3(6)6

2545.8(3)6

3039.6(l)b

3165.6(2) 3322.6(6)

da (lib \

4475(20) 85(1)1 3.5(3) 5.4(3) 14.3(4) 31.3(6) 36.7(6) 11.5(3) 3.4(2)

6 d„ (degrees) d0.m.av.

5 5 5 5 5 5 5 5 5

E (keV)

0.0 1133.9(l)a

1704.4(2)a

2001.5(1)° 2277.0(2)a

2624.3(6)a

2828.1(2)a

3081.7(4)a

3161.8(3) 3219.6(2)a

3571.8(6)

da r txb \ dClmax *• sr >

2216(8) 62(1)

18.9(4) 27.6(5) 0.8(1) 5.7(3) 5.2(3) 13.6(4) 7.6(3)

45.9(8) 4.4(3)

9 d<r (degrees) dtlrnnT.

5 5 5 5 5 5 5 5 5 5 5

Table 7.2: Energies and maximum differential cross sections of low-lying 0+ states in I02,i06pcl populated in the two-neutron pickup reaction.

"Previously known excited 0+ state

^Previous tentative spin assignment

of this state corresponds to a L = 2 transfer. The levels at 1540 and 2098 keV, previously

tentatively assigned as either 1 + or 2 + states [129, 130], were not observed in the present

experiment. As the population of 1 + states is forbidden in the (p,t) reaction, the exper­

imental results suggest the spin-parity of these states is indeed 1 + . Also included in

Table 7.3 are the results of the analysis of the population of 2 + states in 102Pd and 106Pd

[123]. A total of five previously unobserved 2+ states were observed in 102Pd at excitation

energies from 2.4 to 3 MeV. Additionally, six states for which the spin and parity were ten­

tatively assigned as 2 + , were observed at excitation energies of 3.2 to 3.5 MeV. The level

at 2391 keV was tentatively identified as either a 1+ or 2+ state [131]. The 2 + spin-parity

assignment of this level is confirmed in this work. However, states at 2610 and 2716 keV

thought to be of either 1 + or 2 + character [132] were not observed in this experiment.

The identification of 4 + states of 102>106>108pd populated during the experiment, though

more difficult due to lower population strengths, was also possible in the present experi­

ment. A total of 18 previously unobserved 4 + 108Pd states were found between the exci­

tation energies of 2 and 3.5 MeV. These states, and the 4 + states of 102Pd and 106Pd, are

96

IJ 20 30

Ba (degrees)

Figure 7.6: Angular distribution for the population of the 2014 keV state in 108Pd. The shape of the angular distribution corresponds to a L = 2 transfer. Calculated DWBA cross sections are normalized to the 12.5° experimental cross section.

displayed in Table 7.4. The tentatively assigned 4 + state at 1624 keV [133], a probable

7-band state was observed in this work. The angular distribution of this state is presented

in Figure 7.7. The maximum differential cross section was observed at the 30° setting of

the Q3D. The comparison of the overall shape of the angular distribution to the DWBA

predictions confirm the previous 4 + spin-parity assignment.

e i * (degrees)

Figure 7.7: Angular distribution for the population of the 1624 keV state in 108Pd. The shape of the angular distribution corresponds to a L = 4 transfer and confirms the previous tentative spin assignment [133]. Calculated DWBA cross sections are normalized to the 30° experimental cross section.

97

102p d I 0 6 p d 108p d

E (keV)

556.4(6)° 1534.9(6)" 1944.3(6)° 2248.8(6)° 2391.2(6)6

2490.2(6)° 2574.2(1)° 2696.2(3)° 2773.8(1) 2792.1(2) 2866.2(1) 2940.5(2) 3123.2(2)° 3293.0(3) 3360.8(4) 3390.7(4) 3416.1(6) 3466.7(4) 3503.2(3)

da i fib \

18.0(4) 10.0(2) 1.2(1) 4.6(2) 14.2(4) 22.5(4) 8.7(3) 1.3(1) 17.6(4) 8.7(3) 10.4(3) 3.4(2) 3.1(2) 1.2(1) 0.7(1)

0.52(7) 0.56(8) 0.54(7) 0.90(9)

E (keV)

511.8(1)° 1127.7(9)° 1558.9(2)° 1908.9(3)° 2084.7(4) 2242.7(3)° 2308.2(4)° 2438.6(3)° 2484.4(3)° 2499.5(1)° 2784.1(3)° 2821.4(6)° 2849.9(3)6

2917.8(3)° 2935.0(3)° 2969.3(9) 3066.5(4)° 3109.8(2) 3126.6(7) 3172.9(2)° 3214.1(2) 3249.2(1)° 3272.7(3) 3329.2(4) 3373.7(1)6

3404.8(3) 3449.3(3) 3482.8(4) 3492.0(3)° 3510.1(6) 3585.6(5) 3621.6(4) 3639.2(6) 3691.2(3)

da / ftb \ dilmn-,: ^ ST >

48(1) 6.4(5) 5.9(2) 1.8(2)

34.2(4) 3.8(2) 1.5(1) 3.5(2) 2.2(2) 56.1(7) 18.6(4) 2.7(2)

0.38(6) 13.2(3) 0.9(1) 8.4(3) 3.1(2) 1.41(9) 0.5(1) 2.7(2) 1.2(2)

14.2(3) 1.14(9) 1.0(2) 5.9(2) 1.8(2) 1.0(2) 1.6(2) 2.8(3) 0.7(2) 0.6(2) 1.0(2) 0.7(2) 1.9(2)

E (keV)

431(1)° 931.6(6)° 1441.3(3)° 2014.3(5)° 2219.0(1)°

2228(2) 2404.6(1) 2538.6(3) 2592.5(2) 2667.2(2) 2736.9(5) 2846(1) 2860(1) 2887(2) 2952(2) 3028(3) 3128(4) 3185(5) 3229(6) 3274(7) 3361(9) 3380(9) 3391(9) 3522(12) 3555(14)

da (f^\ dClmn-r *• sr'

107(2) 11.0(4) 9.4(4) 2.0(2) 30.2(7) 0.4(1) 35.5(7) 4.3(2) 15.2(3) 9.3(9) 35(1) 9.4(5) 1.6(2) 26(1) 2.6(4) 12.4(5) 6.5(3) 8.2(6) 2.7(3) 2.4(2) 32(4) 18(3) 8.7(5) 11.6(5) 2.3(2)

and maximum differential cross sections of low-lying 2+ states of

"Previously known excited 0 + state

Previous tentative or unknown spin assignment

Table 7.3: Energies 102,106,108pd

98

102p d 106p d 108p d

E (keV)

1275.9(9)a

2138.1(6)° 2301.6(6)6

2343.0(6)6

2581.9(4) 2799.6(5)6

3195.5(2) 3368.2(4) 3432.8(2) 3511.8(5) 3586.7(2)

da i fib \ i ff lmn, \ ST '

2.1(1) 10.4(2) 20.1(4) 15.9(3) 2.5(2) 3.72(5) 2.1(1)

0.73(8) 1.5(1) 1.8(2) 1.5(1)

E (keV)

1229.1(3)° 1932.1(1)° 2077.5(2)° 2283.4(3)° 2351.2(3)° 2579.8(3) 2647.6(3)"

2704(1) 2714.9(8)'' 2737.5(3) 2753.0(3) 2774.5(3)6

2878.3(8) 2907.4(3) 3040.3(8)° 3095.8(2) 3234.2(3) 3322.7(3) 3393.8(2)° 3411.6(5) 3462.9(2) 3477.5(5) 3531.1(1) 3546.1(6)

da i lib \

4.1(4) 5.8(2) 3.9(2) 10.8(3) 1.5(2) 1.3(2) 12.7(4) 0.48(8) 0.44(8) 12.5(4) 6.4(3) 9.2(3) 0.88(9) 0.9(2) 2.7(2) 7.3(3) 1.3(2) 2.4(2) 3.9(2) 1.3(2) 4.4(4) 0.9(3) 1.6(3) 3.0(3)

E (keV)

1624.6(2)b

1958.3(1)° 1990.4(3)6

2079(1) 2476.6(2) 2556.2(1) 2656.9(1) 2706.3(3) 2797(1) 2814(1) 2913(1) 2925(2) 2969(3) 2983(3) 2993(4) 3058(4) 3146(5 3212(6) 3436(10) 3476(11) 3564(13)

da i lib \ dClmn-r ^ ST >

4.6(1) 9.0(3) 5.7(2) 2.0(1) 3.0(1) 29.5(4) 26(2)

10.9(5) 13.6(5) 1.2(2) 1.2(2)

22.7(7) 2.3(2) 7.0(3) 2.7(2) 4.9(3) 1.7(2) 2,5(3) 4.4(4) 4.9(4) 5.0(3)

Table 7.4: Energies and maximum differential cross sections of low-lying 4+ states of 102,106,108pcj

"Previously known excited 0+ state

'Previous tentative or unknown spin assignment

99

Chapter 8

Discussion

8.1 Systematics of low-lying states of the Palladium isotopes

A near complete set of the low-lying low-spin states of the stable Palladium isotopes, and

the evolution of these states as a function of neutron number is presented in Figure 8.1.

108Pd consists of 46 protons and 62 neutrons. The 46 proton configuration is a four hole

configuration of the Z = 50 closed shell. These four holes contribute two bosons to the IBM

description. Similarly, the 62 neutrons of 108Pd can be construed as 12 valence particles

beyond the N = 50 closed shell. These valence neutrons contribute an additional six bosons

to the model for a total of eight bosons required for the description of this isotope. For

the series of stable Palladium isotopes, the number of bosons increases from five for 102Pd

to eight for 108Pd. Closer to the N = 50 shell closure, the lighter Palladium isotopes

exhibit spherical vibrator-like structure. This is evidenced by the energy ratio of the first

4 + state to the energy of the first 2 + state, R.4/2- The R4/2 value for 102Pd is 2.12, close

to 2.0, the value expected at the spherical limit. As valence neutrons are added, R4//2 of

the heavier Palladium isotopes gradually increases to 2.46 for 110Pd, a value consistent

with that of transitional nuclei. The IBM calculations of the Palladium isotopes mirror

this gradual evolution from a spherical to transitional behavior. The experimental R4/2

systematics are presented in Figure 8.2. The gradual structural evolution is in contrast

100

0+

4+

2432

2302

4+ 2138 0+ S _ / JIM <5+ /

2+

0+ 0*

2+

4+

*""\ 2111

1944

1659 1593

„ ^ 1535

1276

2+

6+

2521

2250 2 + 5 - C J 2 4 5 0+ 3135 4+

0+

„ ^ , 2082

1793

2+

2^

4+ 6+ \

4+ 2* y

0+

2+

3309

„ , 2343 2078

*_f 2077

1932 , ~ \ 1909

1704

1559

2+ 0+

2+

_4+ }

6+

4+

2+

0+

0+ 4+ ~> 2+

2219 2145

2014

' - V 1958

1771

1624

1441

1314

1052 ^ 1048

931

2+ 2+ 512

0+ 0 0+ 0 0+ 0 0+

102Pd 1MPd ^Pd ^ P d

Figure 8.1: Evolution of the low-lying structure of the Palladium isotopes studied in this work. The evolution from spherical vibrator-like structure near the N = 50 shell closure to transitional behavior with the addition of valence neutrons is observed.

to the expected dramatic change for phase transitional behavior. A common benchmark

for phase transitional behavior, where the transition is accompanied by the rapid change

from spherical to deformed nuclear shapes, is one observed in Gadolinium isotopes near N

= 92 [89, 134]. The rapid change of the R4/2 value for the Gadolinium isotopes with the

addition of neutrons beyond the N = 82 shell closure is depicted in Figure 8.3 [82]. The

R4/2 value of 150Gd (N = 86) corresponds to a spherical nuclear shape. However, at N

_ go (154Gd), a dramatic change in the structure of the Gadolinium isotopes is observed.

The R4/2 value increases from 2.2 for 152Gd to approximately 3.0 with the addition of just

two valence neutrons, a change indicative of a transition from a spherical to a deformed

nucleus. In contrast to the Gadolinium isotopes, the gradual structural change observed in

the Palladium isotopes, see Figure 8.2, is indicative of an increase in collective behavior as

101

3.4 -1

3.2 H

3.0'

2.8-

J CC 2.6

2.4-

2.2>

2.0-

54

•—2, Energy •— R„

56 58 60 62 64

Neutron Number

700

650

H 600

550

500

450

400

H 350

Figure 8.2: Evolution of 2* and R4/2 values with neutron number for the palladium iso­topes. The R4/2 value for 100Pd (2.12), corresponding to spherical vibrator behavior, gradually increases with neutron number to a value of 2.46 for n 0 Pd .

a result of the addition of valence nucleons to the nuclear system rather than a signature

for phase transitional behavior.

8.2 The search for enhanced level density of excited 0+ states

Included in Figure 8.3 are the depictions of a qualitative description of the nuclear potential

as a function of the deformation parameter /?. The shape of the potential at various

points in the transition from spherical to deformed nuclei elucidates the first-order phase

transitional behavior from a spherical to deformed nucleus for the Gadolinium isotopes. At

N = 86, the nucleus behaves like a spherical vibrator. Hence, the potential has the shape

of a harmonic oscillator with a minimum at zero deformation. As the critical point is

approached with the addition of neutrons to the system (near N = 90), a second deformed

minimum forms which is characteristic for a first-order phase transition. States can form in

the two parts of the potential separated by a finite barrier: spherical states in the potential

with a minimum at zero deformation and deformed states in the larger (3 minimum. As

102

J " L I

/ . *«

1 <

/ /

/

Y i 3.5

H2.5

Figure 8.3: Evolution of R4 /2 (dashed red line) with neutron number for the Gadolinium isotopes. The increase between N = 88 and 90 indicates a rapid transition from a spherical to deformed nuclear shape. Also depicted is the relative population strength for a (p,t) reaction of the first excited 0 + state. An enhancement of the first excited 0 + s tate cross section is observed at N = 88. A qualitative depiction of the nuclear potential as a function of P is displayed for each step in the transition (see text for details).

the two minima become close in energy, the excited states associated with each minimum

are found at similar excitation energies. This leads to an enhancement in the density

of low-lying excited states in even-even nuclei near the phase-transitional region. With

the further addition of neutrons, the Gadolinium isotopes become good examples of well-

deformed nuclei (N > 92). The potential that characterizes this behavior is one in which

the single minimum is found at a non-zero value of p.

The observation of an enhanced density of excited states during rapid nuclear shape

transitions provides evidence for the presence of phase-transitional behavior in finite nuclear

systems. Figure 8.4, adopted from Ref. [135], presents the behavior of 0 + states in the U(5)

to SU(3) first-order transition in a 30 boson system as a function of r] where

V = 4(C ~ 1) 3C-4

(8.1)

and ( is denned in Section 5.1. The critical point in this transition is found at 77 = 0.8 (( =

0.5). As the system moves away from the U(5) limit, the energies of the excited 0 + states

103

Figure 8.4: IBM calculations from Ref. [135] showing the dependence of the energy of ex­cited 0 + states as a function of the parameter ?; for a 30 boson system. The results indicate an enhanced level density at the critical point (rj = 0.8) for the U(5)-SU(3) transition.

decrease rapidly with increasing rj. This effect culminates with a large 0+ state density at

the critical point in the transition between a spherical and deformed system. The origin of

the enhanced level density is the coexistence of two families of excited states formed in the

separate minima of the nuclear potential. For r\ > 0.8, toward the SU(3) limit, the density

of the excited 0+ states decreases as the energies of the spherical family of states increase

relative to the deformed states.

Recent (p,t) studies of rare earth nuclei [136, 89, 134] unearthed a number of previously

unobserved excited 0 + states used to corroborate phase transitional behavior in this mass

region. Figure 8.5, adopted from [89], was produced using sd-IBM fits of McCutchan et

al. [137] and the new set of observed excited 0+ states below 3 MeV obtained in these

experiments. Rare earth isotopes were plotted as a function of their calculated r\ values,

ranging from a rotor-like value of 0.2 for 162Dy to the vibrator behavior of 152Gd. A peak in

the number of observed excited 0+ states was observed for the isotope 154Gd which was fit

with an r\ value in close proximity to the critical point of the first-order phase transition.

This enhanced level density was interpreted as evidence for phase transitional behavior

104

in the evolution from spherical to deformed nuclei [89]. The 0 + states of the Palladium

+ o

12

10

8

6

4

2

0

,

162Dy

-

-

i

x[«Gd

'76Hf/ \

168gr 180\y \

»«Gd -

0 Rotor SU(3)

0.2 0.4 0.6 0.8 1 m,.,, Vibrator

U(5)

Figure 8.5: IBM fits for a number of rare earth isotopes and the corresponding number of excited 0 + states observed for each isotope. The number of excited 0+ states is shown to peak at 154Gd which was fit [137] with an r\ value in close proximity to that of a first-order phase transition. Figure adopted from Ref. [89].

isotopes studied in the present work are presented in Figure 8.6. The number of observed

excited 0 + states below an excitation energy of 3 MeV gradually increases with neutron

number. A comparison of the number of observed 0 + states with the number of 0 + states

generated from the sd-IBM fits of Bucurescu et al. [138] are included in Table 8.1. The

sd-IBM predicts fewer 0 + states than the number observed for 102Pd and 104Pd but this is

not completely surprising as the states not reproduced by the calculations are most likely

non-collective in nature and therefore not included in the model space. While the number

excited 0+ states below 3 MeV does increase with neutron number, this is a sign of the

increased collectivity with the addition of valence particles. In contrast to the enhanced

0 + level density of 154Gd, this gradual change provides no indication of phase transitional

behavior of the Palladium isotopes studies in this work.

105

»*

a*

»*

»•

ft-9*

mo

2 5 «

3435

31J0

MS» Wff

0* >—-Cisra

_J12L «*

awo

«*

0*

V

m

2239

i » «

M»5

l l *

1053 J£

0*

9* £

0*

Si

2805^

2<6!

— V W .

2IS0

MOf M#>

1423

Uk

EXP IBM Exp. IBM Exp. IBM I02pd loepd i o 8 p d

Figure 8.6: The energies of the observed excited 0 + states (shown in blue) below an exci­tation energy of 3 MeV for the Palladium isotopes studied in this work. The number and energies of these states are compared with the IBM description for each isotope (shown in red) using parameters from Ref. [138].

8.3 Collective model description of the two-nucleon transfer

strengths to excited 0+ states

The strength of the population of excited 0+ states in even-even nuclei using a two-nucleon

transfer reaction is a useful probe of changes in the structure of the nucleus. Save for a

few unique cases, such as pairing vibrations [139], the population of excited 0 + states in an

even-even nucleus in a two-nucleon transfer reaction is very weak (<10%) compared to the

population of the ground state of the residual nucleus. The interpretation of these results

is related to the orthogonality of the wavefunctions of the excited 0+ states to ground state

wave functions of the collective nuclei involved in the transfer reaction [140]. Amplitudes of

the population strength to excited 0+ states are hindered due to the implied orthogonality

106

Isotope Observed 0+ states sd-IBM l t o Fd lOGp^

108p d

6 6 8

2 5 10

Table 8.1: Number of observed excited 0+ for the series of Palladium isotopes studied below an excitation energy of 3 MeV. These values are compared to the results from fits of the studied isotopes using the sd-IBM framework.

with the ground state wave function.

Two-neutron transfer studies of the Gadolinium isotopes near N = 92, a region, as

previously discussed, of rapid shape evolution, provide an interesting and unique exception

to the weak population of excited 0+ states in collective nuclei. The strength of the

population of the first excited state of 154Gd in a (p,t) reaction was measured [141, 142] to be

comparable with that of the ground state population strength. The standard interpretation

of these results is based on the idea of shape coexistence in the ground state wave function

of the target nucleus [143, 106, 144]. The ground state of 154Gd is thought to be a mixture

of spherical and deformed configurations. The ground state of 152Gd however is spherical

while the first excited 0+ state is deformed. Therefore, there will be a large constructive

overlap between the ground state of 154Gd and both the ground and first excited 0 + state

of 152Gd. The ratio of the population strength for the (p,t) reaction of the first excited

0 + to the ground state of the Gadolinium isotopes is displayed in Figure 8.3. This ratio

is small (< 10% for the pickup of two neutrons from the isotopes that are not adjacent

to the rapid shape transition. For a target Gd nucleus near the transition region (N=88),

the strength of the population of the first excited 0+ state even exceeds that of the ground

state. Figure 8.7 presents the maximum population strengths of the excited 0+ states of the

Pd isotopes studied in the current work. While for each isotope displayed, the strongest

population is observed for the first excited 0+ state, this population strength is but a

fraction of the cross section of the ground state populations. The lack of an enhancement

of the excited 0 + states is consistent with the gradual structural change observed in the

Palladium isotopes.

107

1*4

•8

! 1000 -j 100-j

10-i

1-1

" " • • • - . . .

1 1 1 r 1 |

• *

1 1 '

~

• •

. ,ospd

1 ' 1 500 1000 1500 2000 2500 3000 3500 4000

l 06Pd

1 ' 1 ' 1 • r T 1 500 1000 1500 2000 2500 3000 3500 4000

'Td

500 1000 1500 2000 2500 3000 3500 4000

Ex(keV)

Figure 8.7: The maximum two-neutron transfer cross sections for each 0+ state in I02,i06,i08pcj 0k s e r v e c} j n this work. The population strength of the ground state is at least an order of magnitude larger than that of any excited state for each of the isotopes studied.

8.4 Excited 0+ populations strengths in the sd-IBM frame­

work

Using the sd-IBM framework, the strength of the population of 0+ states in even-even nuclei

and its dependence on structural change was investigated. In this model, the addition or

removal of two nucleons and the population of a 0 + state can be interpreted as the transfer

of a single s boson [86, 144]. The population strength is then proportional to the matrix

elements s or s^ connecting the wavefunction of the ground state of the target nucleus and

that of the populated state in the residual nucleus. For a transfer reaction that results

in the removal of one boson, N + 1 —> N, the ratio R of the intensity of the population

strength of the first excited 0 + state to the ground state is dependent on the structure of

108

both the initial and final nucleus. At the limits of the sd-IBM, these ratios are

R= <

0, 17(5) -» 17(5)

(4A^-l)(AT+l)(iV+3) > SU(3) - * SU(3) \ • )

where N is the boson number of the target nucleus. It is interesting to note that for the

inverse reaction, the addition of one boson, the s' matrix element connecting the ground

state wave function to excited 0+ states in the residual nucleus vanish; the population of

excited 0+ states at the three dynamical limits of the IBM is forbidden. This leads to the

the dependency of R not only on the specific reaction used (i.e. (p,t) or (t,p)), but also

on the number of valence nucleons within a shell for a target nucleus. For example, if the

target nucleus is 4 neutrons above the N = 50 shell closure, the removal of two neutrons

would be equivalent to the removal of one boson and the population of excited 0+ states

is allowed in the SU(3) or 0(6) limit. However, if the ground state of the target nucleus is

a four hole configuration, the removal of two neutrons would be equivalent to the addition

of a boson and the population of excited states would be forbidden.

The investigation of the behavior of the population strength of the first excited 0+ state

for an s boson transfer between two points in the symmetry triangle gives further insight

into its dependence on the structure of the initial and the final nucleus. The s matrix

elements were calculated using U(5) basis states to determine to population strength of

the ground state and the first nine excited 0+ states for combinations of initial and final

nuclei spanning the symmetry triangle. The s boson removal operator was used to describe

the transfer reaction for each set of initial and final nuclei and a boson number N of 10

was chosen for the initial nucleus. Before presenting the results of these calculations, a

measure of the change in structure of a nucleus must be defined between an initial and

a final nucleus in a boson transfer reaction. A popular measure to determine to general

structure of a nucleus is the value R4/2 [6]. The change in the value, 8R4/2 = (-R4/2 — ^4/2)

109

is used as a measure of structural change between the initial and final nucleus.

Calculated two nucleon transfer cross sections along the U(5)-SU(3) leg of the symmetry

triangle (x = -\/7/2) are displayed in Figure 8.8. The initial and final nuclei along this

leg of the symmetry triangle were described as a function of the single parameter £. In

total, for the results displayed in Figure 8.8, 30 discrete steps in £ along the U(5)-SU(3)

leg of triangle were taken. The population strength of excited states for all combinations

of initial and final values of £ (x = —y/l/2) were calculated using the code TRANSPT

[145]. The C values of each point used for the description of the initial and final nuclei

are presented in Table 8.2. Due to the rapid change from a spherical to deformed system

at C = 0.5, an increased density of points was enforced in this region. One of the

l.o

0.75

l o , o

0.25

•• • • • . *

Figure 8.8: Calculated relative population strengths to the first excited 0+ state for a two-nucleon removal transfer reaction on the U(5)-SU(3) leg of the symmetry triangle. All combinations of the initial and final nucleus (described by the parameters of Table 8.2) are included. The minimum cross section to the first excited 0 + state relative to the ground state population is observed to be dependent only on <5R4/2.

primary observations gleaned from Figure 8.8 is the change of the minimum population

110

strength of the first excited 0 + state relative to the ground state population strength on

the magnitude of the "change in structure" from the initial to final state. For larger values

of 5R4/2, the minimum population strength is shown to increase. According to the model,

for a £R,4/2 = 0.2, the population strength of the first excited 0+ state can be no weaker

than approximately 20 % of the ground state strength. The results of these calculations

suggest that the idea of shape coexistence as the primary source of the enhanced excited

state population strength is not viable. Similar calculations performed for the U(5)-0(6)

teg (x — 0) of the symmetry triangle suggest this increased strength is a symptom of a

much more general mechanism contrary to the traditional interpretation. The behavior

of the population strength to excited 0 + states along the U(5)-0(6) leg of the symmetry

triangle is depicted in Figure 8.9. Again, the general increase of the minimum excited state

cross section is dependent on the magnitude of SR^/2- I n these cases, the cross section to

the excited 0+ state which is most strongly populated in the transfer reaction can be no

less than 10% of the ground state strength for a magnitude of 6R4/2 of 0.2 or greater.

The behavior of the population strength of excited 0+ states as a function of the value

of £ for the initial nucleus as well as for various trajectories through the symmetry triangle

were also studied [146]. Figure 8.10, adopted from [146], displays the behavior of excited

state population strength as a function of ( for an initial nucleus on the U(5)-SU(3) leg of

the symmetry triangle. Each contour in this figure represents a different #R4/2 between the

initial and final nucleus on this leg of the triangle. For a spherical target nucleus near the

U(5) limit, the sum of the cross sections to the first nine excited 0 + states is large for each

value of 5R-4/2- The summed strength is comparable to the ground state populations and,

in some cases, is greater by an order of magnitude. The magnitude of these sums is also

shown to increase with larger 5R4/2. The magnitude of the sum of populations strengths

decreases as £ of the target nucleus decreases, with a minimum value corresponding to a

target nucleus near the phase transitional point (£ = 0.5). The sum then increases with the

further increase of £ for the target nucleus. Again, this general behavior does not depend on

the relative position of the initial and final nuclei in the symmetry triangle as emphasized

111

1.0

Figure 8.9: Calculated relative population strengths for the strongest populated excited 0 + state for a two-nucleon removal transfer reaction on the U(5)-()(6) leg of the symme­try triangle. Combinations of the initial and final nucleus are identical to those used in Figure 8.8. The same general trend is observed. The minimum of the transfer strength to an excited 0 + state in the residual nucleus is only dependent on the magnitude of the difference of their R4/2 values.

by Figure 8.11 [146]. For three separate trajectories, x = 0-0, -0-7, and -\/7/2, the sum of

the cross sections of the nine strength of the nice excited states relative to the ground state

strength for the s boson transfer between an initial and final nucleus for a fixed 5R4/2 =

0.4. The overall behavior is similar for each \ value presented: the sum of the cross section

is large for excited states for an initial £ value near the U(5) limit, decreases to a minimum

for an initial ( value near 0.5 and peaks where ( of the final nucleus nears 1.0 at the SU(3)

limit. The outcome of the series of calculations presented suggests an extraordinary result.

The enhanced population strength to excited 0 + states of even-even nuclei in two-nucleon

transfer reactions is not the consequence of shape coexistence but rather the stems from the

more general rapid structural change between the target and final nucleus. The search for

experimental results corroborating the phenomenon described in the previous paragraph

112

Figure 8.10: Calculated two-nucleon IBM transfer cross sections for the sum of the first nine excited 0 + states normalized to the ground state population strength. Results are presented in contours of £R/i/2 as a function of the £ value of the initial nucleus. The magnitude of the population strength to the excited state is observed to increase with <5R4/2- For each contour, the minimum excited state cross section of found in proximity to the location of the first-order phase transition. This figure is adopted from Ref. [146]

must begin in regions of rapid change of nuclear structure. Two-neutron transfer reactions

involving the Molybdenum isotopes near N = 60 provide a satisfactory test of the above

conclusions. This region of nuclei contain examples of spherical shapes near N = 50 and

the evolution to deformed nuclei (R4/2 ~ 3.0) as one moves away from the neutron closed

shell. More importantly however is the absence of observed phase transitional behavior

in this region. The investigation of a series of Mo(t,p) reactions [147, 148, 149] yield the

results presented in Figure 8.12 [146]. For small changes in R4/2 the sum of the (t,p) cross

sections to excited 0+ states is relatively small. However, for 100Mo(t,p)102Mo, where £R4/2

= 0.39, the excited state population strength increases dramatically. The change of R4/2

for the Palladium isotopes studied in the present work is relatively small from 102Pd to

108Pd indicating a gradual change in structure. One would not expect, according to the

described model predictions, any large population strength to excited 0+ states of these

113

100-

Figure 8.11: Calculated two-nucleon IBM transfer cross sections for the sum of the first nine excited 0 + states (normalized to the ground state population strength) for multiple trajectories through the symmetry triangle for <5R4/2 = 0.4. Results are presented as contours of different x values as a function of the £ value of the initial nucleus. This figure is adopted from Ref. [146]

isotopes via two-neutron transfer reactions. Indeed, as the results presented in Figure 8.7

indicate, there was no large cross section to excited 0+ states observed.

Configuration mixing is the primary mechanism for the enhancement of cross sections

of excited states in two-nucleon transfer reactions [146]. According to the sd-IBM, the

eigenstates of U(5) become mixed by the deformation-driving second term of Equation 5.5.

The strength of the mixing of the U(5) eigenstates by the Q • Q term is proportional to (.

This mixing results in the increased overlap of the ground state wavefunction with excited

states which would otherwise be orthogonal in the U(5) limit. This increased wavefunction

overlap due to configuration mixing leads to the enhanced population strength of excited

states in this model.

114

52 56 60 64 68 N

Figure 8.12: Cross sections for the population of the first excited 0+ state and corresponding 5R4/2 values for Mo(t,p) reactions (adopted from Ref. [146]). An enhanced population strength to the first excited 0+ state is observed for 100Mo(t,p)102Mo where there is a fairly rapid nuclear shape change, as evidenced by large SR^/o values, in the absence of a first-order phase transition.

1.15

Index C R4/2. N = 10 R.4/2, N = 9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

0.0 0.1 0.2 0.3 0.4 0.41

0.42

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.50

0.51

0.52

0.53

0.54

0.55

0.56

0.57

0.58

0.59

0.6 0.7 0.8 0.9 1.0

2.00

2.01

2.02

2.04

2.08

2.09

2.11

2.12

2.14

2.16

2.19

2.22

2.26

2.31

2.36

2.43

2.50

2.58

2.66

2.75

2.83

2.91

2.99

3.05

3.11 3.31

3.33

3.33

3.33

2.00

2.01

2.02

2.04

2.10

2.11

2.12

2.14

2.15

2.18

2.20

2.23

2.27

2.31

2.36

2.42

2.48

2.55

2.62

2.70

2.78

2.85

2.92

2.99

3.05

3.30

3.33

3.33

3.33

Table 8.2: £ and R4y2 values on the U(5)-SU(3) leg of the symmetry triangle (x = -N/7 /2)

for the points used to describe the initial and final nucleus for a s boson transfer reaction. The R4/2 value for each point is given for both a N = 10 and N = 9 system corresponding to the initial and final state, respectively. A greater density of points was chosen near ( = 0.5 in order to probe the behavior of the boson-transfer reaction in regions of rapidly changing nuclear structure.

116

Part III

Conclusions and Outlook

117

The first topic presented in this work encompassed the study of the microscopic descrip­

tion of the atomic nucleus. The structure of 215Ac was investigated to probe the evolution

of proton shell structure of the N = 126 isotones beyond 208Pb and search for evidence of

a possible subshell closure at Z — 92 predicted by RMF models. However, the study of

nuclei in this mass region is particularly difficult due to low-production cross sections and

large background from fission. To this end, the focal plane apparatus of the gas-filled sepa­

rator SASSYER was redesigned. With the introduction of a pair of DSSDs, the multi-wire

avalanche counter MACY, and all associated apparatus, the prompt and delayed gamma

decay of 215Ac was studied using the recoil-decay tagging technique. A multitude of decays

from high-spin excited states feeding the 29/2+ isomeric state were observed. A selection

of these transitions were tentatively assigned as decays from the 35/2+, 39/2+, and 41/2+

states corresponding to the (7r/igy2)(8i(7ri13/2) configuration. The 7ri13/2 quasiparticle ex­

citation was observed at an energy of 859 keV in addition to the high-spin states. Upon

comparison with the lighter N = 126 isotones, a trend in the decrease of the energy gap

between the irhg/2 and 7ri13/2 orbitals was discerned. No indication of a subshell gap at

Z — 92 was discovered in this work in agreement with the conclusions of Hauschild et al.

[27].

The primary difficulty in the gamma ray spectroscopy of 215Ac was the general lack of

statistics due to losses from both transmission and detection efficiency. Large transmission

losses were observed between MACY and the DSSDs primarily due to the broadening of the

recoil profile as a result of scattering of the exceedingly slow-moving residues. As a result,

gamma-gamma analysis of the recoil-decay tagged gamma rays proved impossible. In the

future, a less asymmetric fusion-evaporation reaction should be used for the production of

215Ac. The measurement of an excitation function for the chosen reaction is also highly

recommended to determine the optimal beam energy. The coupling of other experimental

devices available at WNSL to the target position of SASSYER is proposed. Specifically,

the coupling of a conversion electron spectrometer to the YRAST array would allow the

observation of the highly-converted, low-energy decays of large Z isotopes. These advances

118

will improve the future study of the N = 126 isotones at WNSL and will be necessary if

the gamma ray spectroscopy of the Z = 92 nucleus 217Pa is undertaken.

High-resolution, two-neutron transfer spectroscopy of the stable, even-even Palladium

isotopes probed the transition between macroscopic nuclear shapes. The observation of en­

hanced level density of excited 0 + in regions of rapid nuclear shape change was previously

proposed as an indication of first-order quantum phase transitions in nuclei. Though no

signature of this collective phenomenon in the Palladium isotopic chain was observed, 54

new 0+ , 2+ , and 4+ states below an excitation energy of 3.5 MeV were discovered. The

population strength of excited states in a two-nucleon transfer reaction was investigated in

the framework of the Interacting Boson Model. The presence of a large cross sections to

excited 0 + states, previously thought to be the consequence of nuclear shape coexistence,

was recognized to be a much more general effect. Large cross sections to excited 0+ states

are predicted for any two-nucleon transfer reaction in which there is a large structural dif­

ference between the initial and final nucleus. The increased population strength is observed

for large 5R4/2 values regardless of the presence of a first-order quantum phase transition.

With the construction of new facilities capable of the production of very neutron-rich

isotopes, new regions of nuclei will become available to test the IBM interpretation of two-

nucleon transfer reactions. The CAlifornium Rare Isotope Breeder Upgrade (CARIBU) to

the Argonne Tandem Linac Accelerator System (ATLAS) at Argonne National Laboratoy

and the Facility for Rare Isotope Beams (FRIB) will greatly extend the boundary of known

neutron-rich isotopes. New detector systems, such as the Helical Orbital Spectrometer (HE­

LIOS), are particularly suited to study transfer reactions, in inverse kinematics, involving

the short-lived radioactive beams. These future experimental capabilities will provide a

new testing ground for collective and microscopic models developed for the description of

the atomic nucleus.

119

Appendix

DSSD strip position and energy calibration

As described in Section 2.2.5, all energy and position information of each event observed

in the pair of DSSDs at the focal plane of SASSYER is contained in eight analog signals

input to peak-sensing ADCs. The output of these eight ADCs must be calibrated for both

proper strip indentification and energy assignment. The energy output of each strip will

depend not only on the strips physical properties but the characteristics of the signal pro­

cessing of the MUX-16 channel. These parameters vary from strip to strip and the energy

calibration of each strip must be carried out individually. Before an energy calibration can

be performed, one must first map the position output of each bus to a strip id. An example

103

10*

I O U

10

1

600 800 1000 1200 1400 1600 1800 Channel Number

Figure 13: Horizontal position spectrum for a single DSSD exposed to an alpha calibration source.

120

of a raw MUX-16 position output is displayed in Figure 13. This spectrum represents the

position output of the front side of a DSSD that is exposed to an alpha-emitting source.

The channel number will be proportional to the strip location and each peak corresponds

to events from a single strip on the front side of the detector. These front strip events will

be coincident with the vertical position rear strips of the DSSD. A two-dimensional hit

pattern is displayed in Figure 14. This figure also illustrates the effective pixelation one

can achieve by observing coincident events in overlapping horizontal and vertical strips.

Assuming all strips signals are present, which is not the case as evidenced by the hit pattern

of Figure 14, a 57 front strip and 39 rear strip DSSD will provide 2223 effective 1 mm2

pixels. Upon completion of the position calibration, the energy signals coincident with each

r 3

[1400

i i

^200

1000-

800-

600

400

m io

600 800 1000 1200 1400 1600 1800 front channel

Figure 14: DSSD hit pattern generated after exposure to an alpha calibration source.

position signal can then be mapped to the corresponding strip number. The energy of each

strip must be calibrated separately. Figure 15 illustrates a successful energy and position

calibration for the front strips of the beam right DSSD. The energy and relative intensity

of the alpha decays of isotopes present in the PuCm source used to produce this figure are

recorded in Table 3. The combined energy resolution of the front strips of the beam right

DSSD can be extracted the fits shown in Figure 16. This figure is the projection of the

Figure 15 onto the energy axis. It is evident that the doublets expected at each observed

121

100 200 300 400 500 600 700 800 900 1000 10keV

Figure 15: Front strip energy spectra for PuCm source.

peak energy are not resolved. Also, the energy resolution of the rear set of strips for each

DSSD is significantly worse than that of the front set. This loss of resolution in the rear

strips is most likely the result of incomplete charge collection due to shallow implantation

events. The energy difference between the front and rear strip for a given calibration event

is shown in Figure 17. Though centered at zero as one would expect, there are a large

number of events that correspond a larger measured energy in the front strip compared to

the rear strip signal. This observation supports the claim that incomplete charge collec­

tion after a shallow implant event in the DSSD is responsible for the increased peak width

observed by the rear strips.

Isotope Energy (MeV) Intensity (%)

240p u

244Cm

241Am

5.124 5.168 5.762 5.802 5.443 5.486

27.7 72.8 23.6 76.4 13.1 84.8

Table 3: Alpha decay energies of PuAmCu source used for energy calibration of DSSDs.

122

460 480 500 520 540 560 580 600 620 640 10keV

Figure 16: Combined PuCmAm source energy spectrum of front strips for beam left DSSD

cou

nts

400

300

200

100

-

i i

I i

i

-

il

l

1 A

1 / I

T500 -1000 -500 500 1000 keV

Figure 17: Energy difference between front and rear strips of the beam right DSSD.

123

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