Inversion of single-particle levels in nuclear Hartree-Fock and Brueckner- HF calculations with broken symmetry
Energy levels of states connected by a symmetry of the Hamiltonian normally should be degenerate. In self-consistent field theories, when only one of a pair of single-particle levels connected by a symmetry of the full Hamiltonian is occupied, the degeneracy is split and the unoccupied level often lies below the occupied one. Inversions of neutron-proton (charge) and time- reversal doublets in odd nuclei, charge doublets in even nuclei with a neutron excess, and spin-orbit doublets in spherical configurations with spin-unsaturated shells are examined. The origin of the level inversion is investigated, and the following explanation offered. Unoccupied single-particle levels, from a calculation in an A-particle system, should be interpreted as levels of the (A + 1)-particle system. When the symmetry-related level, occupied in the A-particle system, is also calculated in the (A + 1)-particle system it is degenerate with or lies lower than the other. That is, when both levels are calculated in the (A + 1)-particle system, they are not inverted. It is demonstrated that the usual prescription to occupy the lowest-lying orbitals should be modified to refer to the single-particle energies calculated in the (A + 1)- or the (A - 1)-particle system. This observation is shown to provide a justification for avoiding an oscillation of occupancy between symmetry-related partners in successive iterations leading to a self-consistency. It is pointed out that two degenerate determinants arise from occupying one or the other partner of an initially degenerate pair of levels and then iterating to self-consistency. The existence of the degenerate determinants indicates the need for introducing correlations, either by mixing the two configurations or by allowing additional symmetry- breaking (resulting in a more highly deformed non-degenerate configuration). 2 figures, 3 tables, 43 references. (auth)
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- DOE Contract Number:
- W-7405-ENG-26
- NSA Number:
- NSA-33-013711
- OSTI ID:
- 4106594
- Report Number(s):
- ORNL-TM-5174
- Resource Relation:
- Other Information: Orig. Receipt Date: 30-JUN-76
- Country of Publication:
- United States
- Language:
- English
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