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Zeitschrift für Naturforschung A

Unification of Brueckner Theory and HFB Theory

York Christian Gerstenmaier, Dieter Schütte

Published Aug 1, 1980• 5 citations
Publisher

Abstract

Abstract A cluster expansion for the expectation value of operators with correlated wave functions is presented. A variational approach to the Brueckner theory with occupation probabilities is generalized and HFB theory incorporated.
DOI
10.1515/zna-1980-0802

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A theory of correlated wave functions for finite systems is developed which systematically neglects the contribution from three-body cluster terms. The approximation made leads to a derivation of a Bethe-Goldstone equation for finite systems which includes modified occupation probabilities and self-consistent potentials for occupied states. The absence of potentials in unoccupied states follows from the neglect of three-body cluster terms. It is also shown that a careful treatment of the Pauli principle and occupation probabilities allows the application of variational techniques.
The cluster expansion for the energy for a system with Bijl-Dingle-Jastrow (BDJ) correlation structure is derived in a new form. It is shown how the theory may be related to the Brueckner-Bethe-Goldstone theory with a particular choice for the correlation operator (or wave matrix) appearing in the BDJ wave function. The three-body cluster terms are discussed. It is shown that these clusters contain a limited class of dispersive terms which may be included in the analysis of the two-body clusters. The three-body clusters are also shown to contain terms which correct for violations of the Pauli principle in the correlation operator.
A method for the accurate evaluation of the diagonal and off-diagonal matrix elements of the Hamiltonian operator within the correlated basis function scheme is presented. Considering a basis consisting of Slater determinants, correlated with a Jastrow correlation factor, the expectation value of the kinetic energy operator has been expressed in the Jackson-Feenberg form. A diagrammatic analysis is presented for the construction and evaluation of the cluster expansions of the required quantities incorporating the Fermi hypernetted chain theory.