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Sp states in HFB methods

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. Beyond mean-field Set of mean-field wave functions depending on axial q Projection on N, Z, J:.

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Sp states in HFB methods

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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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