1. 108Sn studied with intermediate-energy Coulomb excitation
Dissertation zur Erlangung des Grades
“Doktor der Naturwissenschaften”
am Fachbereich Physik
der Johannes Gutenberg-Universität
in Mainz
Leontina Adriana Banu

2. Outline Motivation Why to study 108Sn ?
Why to study it with Coulomb excitation ?
Experimental method description
Most significant features of intermediate-energy
Coulomb excitation
Experimental set-up
Data analysis
Experimental results
Theoretical interpretation

3. Average energy of the first excited states
Why to study 108Sn ?
Average energy of the first excited states
in even- even nuclei
N=Z
Number of neutrons (N)
Number of protons (Z)
Sn(N,Z) = B(N,Z) – B(N-1,Z)
N odd
Z even 2 8 20 28 50 82
126
Neutron separation energy [MeV]
insight into the structure of 100Sn by
studying the nuclei in its vicinity
how rigid is the the doubly-magic core
when valence neutrons are being added ?
(studying A= Sn isotopes)
investigation on quadrupole polarization of
the doubly-magic core
(E2 core polarization effect)
B(E2;0+->2+)=|<f||OE2||i>|2 is the most
sensitive to E2 collective effects
100Sn
Z = 2,8,20,28,50,82
N = 2,8,20,28,50,82,126
magic numbers shell closures
Nuclear shell model
112Sn 62
108Sn 58
100Sn (N=Z=50) principle test ground

4. Why Coulomb excitation to study 108Sn ?
Electromagnetic decay of lowest excited 2+state:
transition probability
lifetime 2+ 0+ E
()
1207 keV
0 keV
Lifetime measurement
B(E2) value
B(E2) determination:
Coulomb excitation
B(E2) value
cross section
((E2) ~ B(E2)) 0+ 2+ 4+ 6+
108Sn
905
253
1206 6+
( ~ 7 ns) isomeric state E2 2+
(< 0.5 ps)
B(E2;6+->4+) = 3 W.u. E2
Z. Phys. A352 (1995) 373
(HI,xn) reaction

5. Intermediate-energy Coulomb excitation
Nuclear excitation
~ 3%
E=1.3 MeV
D = 70 cm n
Nuclear excitation (±)
Lorentz boost (+)
Doppler broadening (-)
Atomic background
radiation (-) 
Coulomb excitation
target
( in our case )
 = 0.43
Detector opening angle Dq=3°
Composite
detector
 = 0.57
DEg0/Eg0 [%]
 = 0.43
 = 0.11
1 Ge-Cluster
detector
qlab [deg]

6. GSI accelerator facility
UNILAC
SIS
ESR
FRS

7. Experimental set-up Beam direction 108Sn/112Sn Primary beam
Secondary
reaction target:
700 A•MeV
108Sn/112Sn
Primary beam
CATE (Si)
CATE (CsI)
(~ 150 A•MeV)
9Be, 4 g/cm2
projectile fragmentation (production method)
in-flight fragment separation
197Au, 0.4 g/cm2
(Bρ-E-Bρ method)

8. Fragment identification before/after target
Selection with FRS
Selection with CATE
108Sn

9. Scattering angle measurement
Beam tracking g
CATE MW MW
Target
511 keV Si
CsI Qg
 ~ 50% Qp
rest
40K
Event–by–event Doppler shift correction:
in-flight γ 2
βcosΘ 1 β E - =
Impact parameter determination:

10. Analysis of intermediate-energy Coulomb excitation
Elastic scattering dominates
Nuclear excitation contribution
grazzing = 1.5° ± 0.5°
Analysis of intermediate-energy Coulomb excitation
Fragment selection before secondary target
Fragment selection after secondary target
Scattering angle selection (1°- 2°)
Prompt  time ‘window’
Ge-Cluster multiplicity: M(E > 500 keV) = 1

11. Experimental results B(E2; 0+ -> 2+) = 0.230 (57) e2b2 Measure:
-particle coinc.
particle singles I Np
exp.
theory
Deduce B(E2) for 108Sn as follows:
0.240 (14) e2b2
--- previous work
B(E2; 0+ -> 2+) = (57) e2b2
A. Banu et al., submitted to Phys. Rev. C (2005)

12. Theoretical interpretation
theory (neutron valence + proton core excitations and
90Zr as closed-shell core)
theory (neutron valence and 100Sn as closed-shell core)
Neutron/proton single-particle states
in a nuclear shell-model potential:
t=0
t=2
t=4
Neutron number
B(E2 ) e2 b2
This work
••••••••
Proton np-nh core excitations (t=n)
&
100Sn core is open

13. Conclusion and Outlook
108Sn the heaviest Z-nucleus studied with
intermediate-energy Coulomb excitation
B(E2;0+->2+) measured for the first time
The experimental result is in agreement
with latest large scale shell model calculations
This work brings more insight into the investigation of
E2 correlations related to 100Sn core polarization
108Sn further step towards 100Sn

14. “Art is I, Science is We.” - Claude Bernard
Thanks to…
J. Gerl (GSI), J. Pochodzalla (Uni. Mainz) - thesis advisors
C. Fahlander (Lund), M. Górska (GSI) - spokespersons
H. Grawe, T.R. Saito, H.-J. Wollersheim (GSI)
M. Horth-Jensen et al. (Oslo Uni.), F.Nowacki et.al (IRES)
and last but not least…

15. The local RISING team
Thank you...

16. -residual interaction in a jn configuration
Seniority scheme in Sn isotopes: 2 6+
 = 0 2 4+
 = 0 2 2+
 = 2 0+
energy axis  jn J 6+
min   4+ j j j 2+ J j j j j J j J 0+
E(j2J) ~ V0tan(/2) for T=1, J even
-residual interaction in a jn configuration
(V12() = -V0(r1-r2))

18. Data Summary Primary beam SIS energy (MeV/nucleon)
Primary beam intensity (s-1)
124Xe
700
 6 × 107
Secondary beam
Sec. beam abundance (%)
Sec. beam rate (s-1)
Sec. beam target (MeV/nucleon)
112Sn
 60
2400
147
108Sn
 62
2480
142
E(21+->0+) (keV)
Data collection time (h)
1257
 33
1206
 58

19. Single-particle states in shell-model potential
l -> orbital angular momentum
Spectrsoscopic notation:
l= 0, 1, 2, 3, 4, 5, 6
s, p, d, f, g, h, i
••••••••
2j+1
njl
j -> total angular momentum
j = l + s
j = l ± ½
s = 1/2
2j+1 nucleons /orbital
inert core +
active valence
nucleons

20. Single-particle states in shell-model potential
l -> orbital angular momentum
Spectrsoscopic notation:
l= 0, 1, 2, 3, 4, 5, 6
s, p, d, f, g, h, i
2j+1
njl
j -> total angular momentum
j = l + s
s = 1/2
j = l ± ½
2j+1 nucleons /orbital

21. Generalized seniority scheme:
B(E2;0+ -> 2+) ~ f(1-f) where
Generalized seniority scheme:
f = (N – 50)/ 32