Nature of Hartree-Fock Calculations in Light Nuclei

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Abstract
The role of the two-body force, its exchange mixture, and the spin-orbit force in their effect on the Hartree-Fock wavefunctions and spectra is investigated. It is shown that the main features of the Hartree-Fock single-particle field are determined almost completely by the long-range part of the two-body force. The solutions for a long-range model are derived for various systems of different neutron excesses, and the exchange dependence of the energy "gap" between occupied and unoccupied levels is particularly considered. The main effect of the spin-orbit force and the finite range of the two-body force is to mix the orbitals. In the cases where the energy "gap" is large, the mixing is only of the occupied orbitals among themselves. Out of this study it emerges that the most natural representation for the Hartree-Fock single-particle orbitals is that associated with the axially symmetric deformed harmonic oscillator where one takes linear combinations of degenerate orbitals which are time-reversal eigenstates. This prescription results often in nonaxially-symmetric nuclei and is consistent with the results found in exact calculations with realistic forces.