Formulation of the Many-Body Problem for Composite Particles. III. The Projected Hamiltonian

Abstract

A previously developed representation for many-atom problems is extended by incorporation of all effects of interatomic exchange of electrons and nuclei into a ``projected Hamiltonian.'' An expression for the projected Hamiltonian is derived which is exact on the two-atom subspace, and hence incorporates those exchange effects which are important at low densities. By the use of the center-of-mass separation of atomic wavefunctions, this expression for the projected Hamiltonian is transformed into a representation in terms of atomic field operators ψν(r) and ψν†(r), where r is the center-of-mass position of an atom and v stands for all of its internal quantum numbers.