Self-consistency in the application of Brueckner's method to doubly-closed-shell nuclei

Abstract

The relationships between various self-consistency conditions for the single-particle potential U are investigated. These conditions are the Brueckner-Hartree-Fock condition, the requirement that the single-particle orbitals be maximum overlap orbitals, or generalized natural orbitals. The implications of the use of the latter two sets of single-particle functions are examined in detail. It is shown that these two different choices lead to the cancellation of different sets of diagrams in the linked-cluster expansions of various quantities of physical interest. Both sets of basis functions lead to definitions of the particle-hole matrix elements of U which in lowest order coincide with each other, and with that obtained from the Brueckner-Hartree-Fock condition. The definition of the hole-hole matrix elements of U, on the other hand, as obtained from the Brueckner-Hartree-Fock condition is not related to these two sets.