Inversion of single-particle levels in nuclear Hartree-Fock and Brueckner- HF calculations with broken symmetry

Becker, R. L.; Svenne, J. P.

doi:10.2172/4106594

Title: Inversion of single-particle levels in nuclear Hartree-Fock and Brueckner- HF calculations with broken symmetry

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Abstract

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 tomore »« less

Authors:: Becker, R. L.; Svenne, J. P.

Publication Date:: Mon Dec 01 00:00:00 EST 1975

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

OSTI Identifier:: 4106594

Report Number(s):: ORNL-TM-5174

NSA Number:: NSA-33-013711

DOE Contract Number:: W-7405-ENG-26

Resource Type:: Technical Report

Resource Relation:: Other Information: Orig. Receipt Date: 30-JUN-76

Country of Publication:: United States

Language:: English

Subject:: N69210* -Physics (Nuclear)-Nuclear Theory-Nuclear Structure; 643501*; *SINGLE-PARTICLE MODES- HARTREE-FOCK METHOD; BRUECKNER METHOD; ENERGY LEVELS; ITERATIVE METHODS; SYMMETRY BREAKING

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                    Becker, R. L., and Svenne, J. P. Inversion of single-particle levels in nuclear Hartree-Fock and Brueckner- HF calculations with broken symmetry.  United States: N. p., 1975. 
        Web.  doi:10.2172/4106594.

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                    Becker, R. L., & Svenne, J. P. Inversion of single-particle levels in nuclear Hartree-Fock and Brueckner- HF calculations with broken symmetry.  United States.  https://doi.org/10.2172/4106594

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                    Becker, R. L., and Svenne, J. P. 1975.  
        "Inversion of single-particle levels in nuclear Hartree-Fock and Brueckner- HF calculations with broken symmetry".  United States.  https://doi.org/10.2172/4106594.  https://www.osti.gov/servlets/purl/4106594.

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@article{osti_4106594,

  title        = {Inversion of single-particle levels in nuclear Hartree-Fock and Brueckner- HF calculations with broken symmetry},

  author       = {Becker, R. L. and Svenne, J. P.},

  abstractNote = {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)},

  doi          = {10.2172/4106594},

  url          = {https://www.osti.gov/biblio/4106594},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Mon Dec 01 00:00:00 EST 1975},

  month        = {Mon Dec 01 00:00:00 EST 1975}

}

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