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