Nonsymmetric nonlocal potentials and Hartree-Fock scattering formalisms

Abstract

Scattering formalisms that take antisymmetrization into account may result in nonsymmetric nonlocal potentials for the effective interaction. Furthermore, when the incident particle state is antisymmetrized with respect to single-particle states of the target, these states appear as redundant states in the scattering spectrum. This requires the Fredholm determinant associated with the kernel of the integral equation for the physical wave function to be zero for all wave numbers of the incident particle. Under these circumstances, a scattering solution may not exist. The conditions for existence are examined, and a consistency condition is established. Evidence is presented that the nonlocal potential in the full Hartree-Fock equation including target excitations is not symmetric, and thus that the equation will not exhibit a scattering solution unless certain consistency requirements are met in its construction. Since the scattering solution must be orthogonal to each of the single-particle states of the target, the standard procedure in Hartree-Fock scattering formalisms is to drop all terms in the potential which project onto these states. This results in the reduced Hartree-Fock equation usually considered. It is demonstrated that constructing the reduced equation without reference to the full equation may result in a failure of the solution of themore » reduced equation to meet the consistency condition required for it to be a solution of the full equation.« less