Many-body treatment of the Coulomb hole: application to beryllium

Abstract

A many-body theoretical treatment of the Coulomb hole is presented. In contrast to the traditional density matrix approach, the interparticle separation distribution function is expressed in terms of the expectation value of the interparticle separation distribution operator. By introducing the second quantisation method, the Goldstone-type linked diagrammatic expansion of the distribution function is obtained, which provides a very clear and convenient frame for the discussion and calculation of the Coulomb hole. The effects of one-body excitation on the Coulomb hole are discussed in detail based on this formulation, and they imply that if the authors define the Coulomb hole with respect to Brueckner instead of Hartree-Fock (HF) orbitals, the Coulomb hole is expected to possess a well behaved form. To calculate the angular parts of the Coulomb hole Goldstone diagrams, the angular momentum graph-an elegant tool-is introduced. By using the formalism and techniques described above, the ground-state Coulomb hole of the beryllium atom is evaluated from a many-body wavefunction, and compared with those derived from CI wavefunctions. The formulation outlined here can be straightforwardly extended to discuss open-shell atoms.