Download presentation

Presentation is loading. Please wait.

1
**Coulomb-excitation of 112, 114, 116Sn**

Pieter Doornenbal

2
**The three faces of the shell model**

Pairing interaction: large spin-orbit splitting implies a jj coupling scheme.

3
**Symmetries of the shell model**

Three bench-mark solutions: No residual interaction IP shell model. Pairing (in jj coupling) Racah’s SU(2). Quadrupole (in LS coupling) Elliott’s SU(3). Symmetry triangle:

4
**Racah’s SU(2) pairing model**

Assume large spin-orbit splitting ls which implies a jj coupling scheme. Assume pairing interaction in a single-j shell: Spectrum of 210Pb:

5
**Solution of pairing hamiltonian**

Analytic solution of pairing hamiltonian for identical nucleons in a single-j shell: Seniority (number of nucleons not in pairs coupled to J=0) is a good quantum number. Correlated ground-state solution (cfr. super-fluidity in solid-state physics). G. Racah, Phys. Rev. 63 (1943) 367

6
**Superfluidity in semi-magic nuclei**

Even-even nuclei: Ground state has =0. First-excited state has =2. Pairing produces constant energy gap: Example of Sn nuclei:

7
**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+ -residual interaction gives nice simple geometric rationale for Seniority Isomers from E(j2J) ~ -V0Frtan(/2) for T=1, even J

8
**Example of the 8+ ( p1h9/2)2 isomers in nuclei with Z > 82**

Seniority Scheme Seniority conserving Dn = 0 1-body even tensor B(E2: I I – 2, I 2) Seniority changing Dn 0 B(E2: I I – 2, I = 2) 2 8+ 2 6+ 2 4+ 2 2+ j = (9/2)n n = 0 0+ B(E2) Fractional Filling

9
**e.g. Jp = (h9/2)2 coupled to 0+, 2+, 4+, 6+ and 8+. q q**

d-interaction gives nice simple geometric rationale for Seniority Isomers from DE ~ -VoFr tan (q/2) for T=1, even J 8 6 4 DE(j2J) 2 e.g. Jp = (h9/2)2 coupled to 0+, 2+, 4+, 6+ and 8+. 180 90 q 2 4 6 8 q

10
**d-interaction gives nice simple geometric rationale**

for Seniority Isomers from DE ~ -VoFr tan (q/2) for T=1, even J 2 4 6 8

11
**Reduced transition probability in a single J-shell**

≈Nparticles*Nholes (2j+1) ≡ nucleons/orbital

12
**Reduzierte Übergangswahrscheinlichkeit in einer einzelnen J-Schale**

≈NTeilchen*NLöcher (2j+1) ≡ Anzahl der Nukleonen in der j-ten Schale

13
**Reduced transition probability in a complex shell**

≈Nparticles*Nholes number of nucleons between shell closures.

14
**Reduzierte Übergangswahrscheinlichkeit in einer komplexen Schale**

≈NTeilchen*NLöcher Anzahl der Nukleonen zwischen den Schalenabschlüssen

15
**Proton np-nh core excitations (t=n)**

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: from A. Banu et al., cond. publ. 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

16
**Previous measurements:**

112Sn 2+ 112Sn (20) fs ≙ (13) e2b2 75Gr30 0.229 (5) α, 16O Coul Ex 81Ba05 0.256 (6) 16O 57Al43 0.180 (40) α 61An07 0.33 (6) 14N, 20Ne 70St20 Reference* Measured Value Projectile Method 0+ 2+ 114Sn (60) fs ≙ 0.25 (5) e2b2 114Sn 0+ Coul Ex α 0.20 (7) 57Al43 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 2+ 116Sn (10) fs ≙ (5) e2b2 0+ *From NNDC

17
**Coulomb excitation experiment**

112,114,116Sn→58Ni at 3.6MeV/u Ex=1257MeV, 1300MeV, 1294MeV B(E2)↑=0.244(13), 0.25(5), 0.209(5)e2b2 Sn-excitation ~ 180 mb Ni-excitation ~115 mb γ-efficiency = 0.005 beam intensity = 1pnA target thickness = 1mg/cm2 10 % duty factor pγ-rate (Sn) = 1/s

18
**Choosing the right target**

2+ 1454 154 keV 2+ 184W → 4.7 MeV/u 114Sn 1300 0+ 0+ 58Ni 184W 1120 1250 2+ 120Sn 1171 120Sn 2+ 0+ θγ = 25º 4+

19
**Important to know: Transition Ratio 90º-140º 2+→0+ 1 4+→2+ 0.017 116Sn**

θγ = 25º 116Sn→58Ni Secure energy:

20
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.

Similar presentations

Presentation is loading. Please wait....

OK

Coulomb excitation with radioactive ion beams

Coulomb excitation with radioactive ion beams

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on eia report 2016 Ppt on chapter 3 atoms and molecules bill Ppt on two point perspective grid Ppt on object-oriented technologies Ppt on peak load pricing strategy Ppt on two point perspective buildings Avian anatomy and physiology ppt on cells Ppt on views in dbms functions Ppt on natural numbers vs whole numbers Download ppt on teamviewer