Applications of Nilsson Mean-field Plus Extended Pairing Model for Well-Deformed Nuclei

1. Liaoning Normal University Applications of Nilsson Mean-field Plus Extended Pairing Model for Well-Deformed Nuclei 关鑫，潘峰 辽宁师范大学物理学

2. Outline Introduction Extended Pairing Model Numerical results and discussions Summary

3. Introduction • Pairing is an important residual interaction that is used in nuclear physics. • The Bardeen-Cooper- Schrieffer (BCS) and Hartree-Fock-Bogolyubov (HFB) methods suffer from serious difficulties. Extended Pairing Model 1 Company Logo

4. Extended Pairing Model The standard pairing Hamiltonian The extended pairing Hamiltonian The total number of Nilsson levels The pairing strength The single-particle energies Feng Panet al., PRL. 92.112503(2004) The first step approximation The extended pairing model The standard pairing model Only the lowest energy eigenstate is taken into consideration Feng Panet al., PRC. 80, 044306 (2009)

5. Extended Pairing Model k-pair eigenstates The additional quantum number The expansion coefficient can be expressed as The undetermined variable 1 Company Logo

6. Extended Pairing Model mean-field pairing The eigenvalue equation of the model

7. Extended Pairing Model The undetermined variable is given by k-pair excitationenergies

8. Numerical results and discussions Er isotope = - 7.475 Mev = - 7.476 Mev Yb isotope = - 7. 71 Mev Hf isotope The neutron single particle energy is expressed as The average binding energy of per valence neutron in a major shell Neutron single-particle energies calculated from the Nilsson model The contribution from the core The average binding energy per valence neutron 1 Company Logo

9. Numerical results and discussions The definition of odd-even mass difference The total number of the nuclei fitted P(A)=E(A-1)+E(A+1)-2E(A) Mean-square deviation of binding energies All nuclei fitted in a chain 1 Company Logo

10. Numerical results and discussions Odd-even mass difference Binding energy

11. Numerical results and discussions BCS approximation Extended Pairing Model Nearest-orbit pairing model

12. Numerical results and discussions The first pairing excitation energy of Er

13. Numerical results and discussions The second pairing excitation energy of Er

14. Numerical results and discussions The first pairing excitation energy of Hf The second pairing excitation energy of Hf

15. Numerical results and discussions The first pairing excitation energy of Yb The second pairing excitation energy of Yb

16. Summary and perspective • Summary • Mean-field plus extended pairing interaction for the description of well-deformed nuclei in Rare-earth Region is adopted. Freezing the excitation of the proton pairs, binding energies, pairing excitation energies, even-odd mass differences of 152-169Er , 154-171Yb, 153-173Hf are calculated and compared with the corresponding experimental data. • There is a little deviation of the pairing excitation energies. • Perspective • In the future work we will calculate in both proton-proton and neutron-neutron pairing excitation cases, and also calculate and moment of inertia of low-lying excitation states and the electric quadrupole moment.

17. Liaoning Normal University Thank You ! 关鑫，潘峰 辽宁师范大学物理学

18. Numerical results and discussions The second pairing excitation energy The ground state energy The first pairing excitation energy K=0 K=2 K=0 K=0