Coulomb-excitation of 112, 114, 116 Sn Pieter Doornenbal.
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Transcript of Coulomb-excitation of 112, 114, 116 Sn Pieter Doornenbal.
Coulomb-excitation of 112, 114, 116Sn
Pieter Doornenbal
The three faces of the shell model
Pairing interaction:large spin-orbit splitting implies a jj coupling scheme.
Seniority scheme in Sn isotopes:Seniority scheme in Sn isotopes:
E(E(jj22J) ~ -VJ) ~ -V00FFrrtan(tan(/2)/2) for T=1, even J for T=1, even J
-residual interaction gives nice simple geometric rationale for -residual interaction gives nice simple geometric rationale for Seniority IsomersSeniority Isomers from from
00++
22++
44++
66++
jjnn00
22
22
22
= 2= 2
= 0= 0
= 0= 0
22++
44++
66++
00++
minmin
ener
gy a
xis
jj
j
j
j
j
j j
JJ
JJJJ
JJ
Example of the 8+ ( h9/2)2 isomers in nuclei with Z > 82
Seniority SchemeSeniority conserving = 0
1-body even tensor
B(E2: I I – 2, I 2)
Seniority changing 0
1-body even tensor
B(E2: I I – 2, I = 2)
0+
2+
4+
6+
8+
= 0
2
2
2
2
j = (9/2)n
Fractional Filling
B(E
2)
Reduced transition probabilityin a single J-shell
ff 1
2
12
122
11 02122
1202
JjQJjj
njnJjQJj nn
122
12 2
j
j ff 1
12/ jnf
≈Nparticles*Nholes
(2j+1) ≡ nucleons/orbital
Reduced transition probability in a complex shell
ffEB 1)02;2( 11
2
2
122
12
j
jj ff 1
j
jnf 12/
≈Nparticles*Nholes
number of nucleons between shell closures.
j
jnf 12/
j
j 12
Theoretical interpretationTheoretical interpretation
Neutron numberNeutron number
B(E
2 )
eB
(E2
) e
2 2 bb
22
This workThis work
theory (theory (neutron valenceneutron valence and and 100100SnSn as closed-shell core)as closed-shell core)
••••••••
5810850Sn
Neutron/proton single-particle statesin a nuclear shell-model potential:
theory (theory (neutron valenceneutron valence + proton core excitations+ proton core excitations and and
9090ZrZr as closed-shell core)as closed-shell core)
t=0
t=2t=4
t=4
Proton np-nh core excitations (t=n)&
100Sn core is open
from A. Banu et al., cond. publ.
Previous measurements:
75Gr300.229 (5)α, 16OCoul Ex
81Ba050.256 (6)16OCoul Ex
57Al430.180 (40)αCoul Ex
61An070.33 (6)14N, 20NeCoul Ex
70St200.256 (6)α, 16OCoul Ex
Reference*Measured Value
ProjectileMethod
112Sn
1257 320 (20) fs ≙ 0.244 (13)
e2b2
114Sn
1300 300 (60) fs ≙ 0.25 (5) e2b2
116Sn
1294 374 (10) fs ≙ 0.209 (5)
e2b2
Coul Ex α 0.20 (7) 57Al43
Coul Ex 14N, 20Ne 0.25 (6) 61An07
Coulex 16O 0.25 (5) 81Ba05
DSA 112Cd(α,2n) 0.238 (77) 91VIZW
RDDS 100Mo(18O, 4n) 0.189 (39) 01Ga52
112Sn
114Sn
*From NNDC
2+
0+
2+
0+
2+
0+
Coulomb excitation experimentCoulomb excitation experiment
112,114,116Sn→58Ni at 3.6MeV/u
Ex=1257MeV, 1300MeV, 1294MeVB(E2)↑=0.244(13), 0.25(5), 0.209(5)e2b2
Sn-excitation ~ 180 mbNi-excitation ~115 mb
γ-efficiency = 0.005
beam intensity = 1pnAtarget thickness = 1mg/cm2
10 % duty factor
pγ-rate (Sn) = 1/s
Choosing the right target184W → 120Sn @ 4.7 MeV/u
120Sn
1171
1120 1250
2+
0+
114Sn
13002+
0+
58Ni
14542+
0+
154 keV
θγ = 25º
120Sn
184W
2+
4+
Transition Ratio 90º-140º
2+→0+ 1
4+→2+ 0.017
Important to know:116Sn
Secure energy:
dD
d
dD
d Ruthel 99.0
116Sn→58Ni
θγ = 25º
Conclusion:
•Very easy to perform, yet leads to interesting physical results•All necessary equipment is already available at GSI.•Only feasible using Sn ion beams
•
•We ask for a total of 3 times 7 shifts of beam time for the isotopes 112, 114, 116Sn.
)()(
)()(
)2()2(
58
116
58
114
116114
NiISnI
NiISnI
EBEBSnSn