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Understanding HFB Methods: Mean-Field Dynamics and Nuclei Interactions

This text explores the meaning and dependence of HFB (Hartree-Fock-Bogoliubov) methods, emphasizing the role of interactions in nuclear physics. It discusses mean-field wave functions, configuration mixing, and diagonalization results related to odd and even nuclei. By examining effective interactions for mean-field and pairing, key insights into rotational properties of actinides and transactinides are provided. The analysis also evaluates the interpretation of spectra in odd nuclei, offering a comprehensive view of energy configurations and quantum states relevant to nuclear structure.

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Understanding HFB Methods: Mean-Field Dynamics and Nuclei Interactions

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  1. Sp states in HFB methods • What do they mean? • How do they depend: on the interaction on N and Z P. Bonche, M. Bender, A. Chatillon, T. Duguet, PHH

  2. Beyond mean-field • Set of mean-field wave functions depending on axial q • Projection on N, Z, J: • New wave functions by mixing on q: withfJ,k (q)determined by minimizing the energy:

  3. Mean-field (HFBCS) MF projected on J=0 Configuration mixing for J=0 Four typical nuclei

  4. HFB methods • Effective interaction for mean-field and pairing:

  5. Result of diagonalization: qp energies (not fully significant with LN) The sp energies are the diagonal parts of h For an even nucleus: gs vacuum For an odd nucleus: 1qp state associated with the quantum numbersi (two operators for 2qp states in even nuclei) The only well defined quantity is the total energy of a configuration

  6. It works! • Rotational properties of actinides and transactinides (self consistent cranking): test of pairing • Interpretation of spectra of odd nuclei test of the mean-field part of the interaction

  7. 251Cf Z= 98 N=153

  8. 249Bk N= 102 Z= 97

  9. Z = 99, 101, 103

  10. Z=99

  11. Z=101

  12. Z=103

  13. (1/2)- (7/2)- : 7- (7/2)- (9/2)+ : 8- (7/2)+ (7/2)- : 7-

  14. neutrons 8-? 2-

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