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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

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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.

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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

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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 ! ”

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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).

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

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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

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Hamiltonian of the soft-rotator model where,

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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)

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Deformed nuclear potential : ASSUME : is small.

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(Non-spherical) Dispersive Optical Potential

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(“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)

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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.

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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

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120 Sn total neutron & proton reaction cross sections

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

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

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

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

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

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

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

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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

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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) ]

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