Second-quantization representation for a nonrelativistic system of composite particles. I. Generalized Tani transformation and its iterative evaluation

Abstract

A method of constructing ’’atomic second quantization’’ representations is described, based on the introduction of redundant modes (’’ideal atom variables’’) which are then given physical content by carrying out a suitable unitary transformation, the ’’generalized Tani transformation.’’ In such a representation bound atoms or molecules are described by elementary Bose or Fermi operators, the field operators for nuclei and electrons referring only to unbound particles. The Hamiltonian thus obtained contains not only nucleus–nucleus, electron–electron, and nucleus–electron Coulomb interactions, but also atom–atom, atom–nucleus, and atom–electron Coulomb and exchange interactions, including breakup and recombination terms. All possible scattering and reaction channels are exhibited simultaneously in this transformed Hamiltonian. The method is applicable to any species or mixture of species of composite particles, but for simplicity the derivation is restricted here to the case of atomic hydrogen.