1. Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote 3, S. Chiba 4, and J. M. Quesada 5 1 Dep. of Physics, Sejong University, Korea 2 Joint Institute for Energy and Nuclear Research, Belarus 3 Nuclear Data Section, IAEA, Austria 4 Advanced Science Research Center, JAEA, Japan 5 Universidad de Sevilla, Spain * yeon@sejong.ac.kryeon@sejong.ac.kr

2. Why Study Tin Isotopes ?  A main component of nuclear reactor material.  A candidate material for superconducting magnets in fusion reactors.  Energy splittings of yrast 0 +, 2 +, 4 + and 6 + levels are irregular. ⇒ may suggest non-harmonic vibrational states?  Sn isotopes are single-closed-shell nuclei of Z=50.  determine whether the calculations using a self- consistent CC optical model may produce different nuclear deformations for different external probes (protons, neutrons) for Sn isotopes.

3. Present soft-rotator model - Lee et al., PRC 79, 064612 (‘09) - Soukhovitskii et al., PRC 72, 024604 (‘05) - Capote et al., PRC 72, 064610 (‘05) - Soukhovitskii et al., J. Physics G 30, 905(‘04)  Non-axial quadrupole, octupole, hexadecapole deformations  γ -vibrations  Soft-octupole and rigid hexadecapole deformations  Identify positive and negative parity bands, associated with octupole surface vibrations

4. Calculations i) Nuclear Hamiltonian parameters to reproduce experimental collective levels (determined by fitting the calculated levels to the evaluated nuclear structure data ) ii) Contruct wave functions from these parameters. iii) CC optical Model calculations ⇒ “ Self-consistent ! ”

5. Present soft-rotator model ⇒ Quite successful in explaining –Nuclear collective level structures, –Nucleon interaction cross sections, –Proton non-elastic scattering cross sections, –γ -transition probabilities, for 12 C, 28 Si, 56 Fe, 58 Ni, & 238 U. - Lee et al.,, PRC 79, 064612 (‘09) - Soukhovitskii et al, PRC 72, 024604 (‘05) - Capote et al, PRC 72, 064610 (‘05) - Soukhovitskii et al., J. Physics G 30, 905(‘04) - Soukhovitskii et al., J. Nucl. Sci. Tech. 40, 69 (‘03), - Soukhovitskii et al., PRC 62, 044605(‘00), NPA 624, 305 (‘98).

6. Goals Consistent description of collective nuclear level structures & nucleon scattering properties for 116,118,120 Sn using the soft-rotator model. 50

7. Description of soft-rotator model ASSUME : An excited state of even-even non-spherical nucleus can be described as a combination of rotation, β -quadrupole and octupole vibrations, & γ -quadrupole vibration. Multipole-deformed instant nuclear shape Deformations

8. Hamiltonian of the soft-rotator model where,

9. Description of soft-rotator model ASSUME : An excited state of even-even non-spherical nucleus can be described as a combination of rotation, β -quadrupole and octupole vibrations, & γ -quadrupole vibration. Multipole-deformed instant nuclear shape Deformations (Review)

10. Deformed nuclear potential : ASSUME : is small.

11. (Non-spherical) Dispersive Optical Potential

12. (“Lane consistent dispersive CC OMP”)  deal with (p,n) charge exchange reactions [to the elastic Isobaric Analogue States(IAS)] Isospin-dependent dispersive CC OMP Lane equations Soukhovitskii et al, PRC 72, 024604 (‘05) Capote et al, PRC 72, 064610 (‘05)

13. Applications to Sn isotopes For 120 Sn(32.59%), 118 Sn (24.22%), 116 Sn (14.54%),  Collective nuclear level structures  Total neutron & proton reaction cross sections  Nucleon elastic & inelastic scattering cross sections [(n,n), (n,n’), (p,p), (p,p’)]  Quasi-elastic (p,n) reactions.

14. Collective level structures of 120 Sn & 118 Sn ⇒ All the levels are involved in CC calculations. EXP. CALCULATIONS EXP. (i) K≈0,n β =n γ =0 (g.s. rotational band) (ii) K≈0,n β =1,n γ =0 (iii) K≈2,n β =0,n γ =0 (positive parity band) (iv) K≈0,n β =0,n γ =0 (negative parity band) (v) K≈0,n β =0,n γ =1

15. 120 Sn total neutron & proton reaction cross sections

16. Neutron elastic scattering cross sections 116 Sn(n,n) 118 Sn(n,n) 120 Sn(n,n)

17. Neutron inelastic scattering cross sections 116 Sn(n,n’)2 + 118 Sn(n,n‘)2 + 120 Sn(n,n’)2 +

18. Neutron inelastic scattering cross sections 116 Sn(n,n’)3 - 118 Sn(n,n‘)3 - 120 Sn(n,n’)3 -

19. Proton elastic scattering cross sections 116 Sn(p,p) 118 Sn(p,p) 120 Sn(p,p)

20. Proton inelastic scattering cross sections 116 Sn(p,p’)2 + 118 Sn(p,p‘)2 + 120 Sn(p,p’)2 +

21. Proton inelastic scattering off 3 - state 116 Sn(p,p’)3 - 118 Sn(p,p‘)3 - 120 Sn(p,p’)3 -

22. Quasi-elastic (p,n) reactions 116 Sn(p,n) 118 Sn(p,n) 120 Sn(p,n)

23. Deformation Parameters Isotope β 20 β 30 β 40 npnp 116 Sn0.0250.0270.0500.053-0.080 118 Sn0.0290.0350.0470.049-0.060 120 Sn0.0340.0370.0430.045-0.094

24. Summary For 116 Sn, 118 Sn, 120 Sn,  Collective level structures  Total neutron cross sections  Nucleon elastic/inelastic scattering cross sections  Quasi-elastic (p,n) reactions. ⇒ well described within the soft-rotator model self-consistently. [ χ 2 : 6.882( 116 Sn), 8.369( 118 Sn), 6.74( 120 Sn) ]