Structure and Reactions of Exotic Nuclei, 24-26 February 2005

Francesco Cappuzzello

N* + 3n light nuclei via the (7Li,7Be) reaction

• N = 1 7He• N = 2 11Be• N = 3 15C• N = 4 19O• N = 5 23Ne• N = 6 27Mg• …

BSEC(Bound States Embedded

in the Continuum)

DCP(Dynamical Core Polarization)

Systematic study via the (7Li,7Be) reaction

What exactly?

Hard core

Softer core

An important part of the phase space is represented by

(7Li,7Be) reaction over 7Li, 11B, 15N, 19F, 23Na, 27Al

Study of single particle isovector excitations

Problem of the core polarisation

Systematic study of the (7Li,7Be) reaction at low incident energy as function of charge asymmetry and mass

References:

F.Cappuzzello et al., Excited states of 11Be, Phys.Lett B516 (2001) 21

F.Cappuzzello et al., Analysis of the 11B(7Li,7Be)11Be reaction at 57 MeV in a Microscopic Approach, Nucl. Phys. A739 (2004) 30.

F.Cappuzzello et al., Excited states of 15C, EuroPhys.Lett. 65 (2004) 766

C.Nociforo et al. Investigation of light neutron-rich nuclei via the (7Li,7Be) reaction, Acta Physica Polonica, B34 (2003) 2387.

S.E.A. Orrigo et al. On the line shape of 15C submitted to Phis. Lett. B 2004

Examples:

11B(7Li,7Be)11Be

at 57 MeV

15N(7Li,7Be)15C

at 55 MeV

Cou

nts

l = 14, 55 keV/ch.

l = 9, 14 keV/ch.

15C excitation energy (MeV)

Single particle regime

Single particle regime

DCP regime

DCP regime

7Be detected with the IPN-Orsay Split Pole

Cou

nts

11Be excitation energy (MeV)

Target LiF+Criv = 0°

7 He and 19O spectra via

(7Li,7Be) at 56 MeV

19F(7Li,7Be)19O

Results of microscopic QRPA calculations

The strength is well reproduced for single particle transitions, namely ½+ gs, ½- excited state at 0.32 MeV and 5/2+ state at 1.77 MeV

The observed fragmentation beyond 2 MeV is not reproduced

Single particle

Results of microscopic DWBA

calculations

11BeGS

11Be*1.77

No scaling factors

No scaling factors

Angular distributions reproduced without any scaling factor or parameter tuning

Direct one step mechanism

Nuclear structure model

132211 VVHH

Quasiparticle-RPA approach:

eff. Hamiltonian of the odd-mass system

n Jj

CJjnlj

C

CjJjznljzjm

'' )'()()(,

by Bogolyubov-Valatin transformation

3qp0 jmnlj

where is the g.s. correlated of the even-mass core and

0

mjjmj

jmjjm aau v)1(

1v 22 jj uwith

s.p. mixing 1qp

Quasiparticle-core coupling model (QPC) (Bohr & Mottelson)

V13 couples

state-dependent mass operator

Odd-mass system w. f. :

H. Lenske, Progr. in Part. and Nucl. Phys. A693(2001)616

15C response function

s1/2 and d5/2 strength functions of 15C calculated with Jc3

Strong fragmentation of the strength for 9<Ex<15 MeV

g.s. configuration:

83.0)0(2 2142/1 SCCs

15.0)2(1 2142/5 SCCd

0.110 MeV

[

C. Nociforo, H.Lenske, in preparation

excited configuration:dominance of core excitations (1-,2+,3-)

Some experimental consideration

Experiments need high energy resolution (1/1000), forward angles (around 0) exploration and large momentum byte (1020%)

Magnetic spectrographs

IPN-Orsay Split-Pole

Energy resolution 1/1000

Momentum byte 36 %

Solid angle 1.8 msr

The small solid angle limits the possibility to study weak narrow states above neutron emission threshold

The MAGNEX opportunity

Maximum magnetic rigidity 1.8 T• m

Solid angle 51 msr

E max /E min 1.5

Total energy resolution (target 1 mm2) (90% of full acceptance)

1000

Mass resolution 250

A.Cunsolo et al., NIMA 481 (2002) 48

A.Cunsolo et al., NIMA 484 (2002) 56

A.Cunsolo et al., NIMA 495 (2002) 216

Large solid angle and high energy resolution

Conclusions and outlooks

Exploration of excited states of light neutron rich nuclei is a rich source of information about nuclear structure

High energy resolution is crucial to that purpose

Use of refined microscopic theories is also fundamental

Challanges

Use of the MAGNEX spectrometer (starting from next weeks)

Full development of the microscopic DCP theory (on the run)

The “Charge Exchange” collaboration

 A.Cunsolo, F.C., A.Foti, A.Khouaja,

C.Nociforo, S.E.A.Orrigo, J.S.Winfield, M.Cavallaro 

INFN-LNS, Catania, Italy INFN, Sez. Catania, Catania, ItalyDipartimento di Fisica, Università di Catania, Catania, Italy

D. Beaumel, S. Fortier,

Institut de Physique Nucléaire, IN2P3-CNRS, Orsay, France

H.Lenske

Universitatat Giessen, Giessen, Germany

15N(7Li,7Be)15C reaction at 55 MeV

15C excitation energy (MeV)

= 14

(55 keV/ch)

DCP regime

single particle regime

Co

un

ts

F. Cappuzzello et al., Phys. Lett. B516, 21 (2001)C. Nociforo et al., Acta Phys. Polonica B34 ,2387 (2003)

F. Cappuzzello et al., Europhys. Lett. 65, 766 (2004)F. Cappuzzello et al., Nucl. Phys. A739, 30 (2004)

g.s.

0.74

8.5

10.3

15C Excitation Energy (MeV)

counts lab=10° 136 keV/ch

0 2 4 6 8 10 12 14 16

100

80

60

40

20

0

lab=9° 140 keV/ch

11Be Excitation Energy (MeV)

9.5

15C and 11Be spectra via (7Li,7Be) at 57 MeV

11Be state at6.05 MeV

(FWHM 320±40 keV)

F.Cappuzzello et al., Phys.Lett.B516(2001)21

counts

6.0 15C state at8.49 MeV

(FWHM 270±50 keV)

Core excitations

For large A/Z ( A-1 ) core soft

Evidence of 2+ core excitation in 11Beg.s.

1H(11Be,10Be) at 35.3 MeV/u

J.S.Winfield et al., Nucl.Phys. A683(2001)48

2+

Apparence of low energy (vibrational) states ( 2+ , 3- )

CEX transitions 19Fgs 19O

gsF190

JMNeOFQ gsJM ;,191919

jmp

JMq

CEX-QRPA

ppMJq

pppppp

qppq YXQ

)1(

Projection over isospin τ+ subspace

Average treatment of the configurations ortogonal to 2QP ones (i.e. 4QP...)

a

JMJMJaJM aQEz )()()()(

Bogoliubov-Valatin transformationpp

mjppp

ppmj

ppp

avau

avau

)1(

)1(

From HFB calculations

Green function approach to QRPA

00 )(Im1

,

qqq QEGQQER

RPAresph

RPA GVGGG 00

HEG )(

00 )( HEG

Dyson Equation

CEX-QRPA (Charge EXchange Quasi-particle Random Phase Approximation)

qQ

0 qq Q

F.T.Baker et al. Phys. Rep. 289, 235 (1997)

phresVHH 0

Response function

Need to describe effect due to the proximity of the continuum