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)
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