Discretized propagators in Hartree and Hartree–Fock theory. II. Responses to static electric and magnetic fields

Abstract

Discrete propagator methods that take account of the Pauli exclusion principle through the level of many-body Hartree theory are used to investigate the linear responses of inhomogeneous electron systems to static scalar and vector potentials. The induced densities and currents are obtained in the form of configurational integrals over Bessel functions, in close analogy with classical statistical mechanical partition functions that are configurational integrals over Boltzmann weight functions. In self-consistent field treatments the arguments of these Bessel functions are themselves functionals of the electron densities in the absence of external potentials. Qualitative differences between the magnetic responses predicted by Hartree and Hartree–Fock equations are pointed out. A simplified Hartree–Fock theory for magnetic responses is also derived. Here too, the responses are shown to be configurational integrals over Bessel functions.