Fock-Tani representation for positron-hydrogen scattering

A new second-quantization representation for low-energy positron-hydrogen scattering is derived by starting with the standard Fock representation and carrying out two canonical transformations, one to introduce the field operator for bound positronium and the other to introduce one for the bound atomic electron. The transformed "Fock-Tani representation" Hamiltonian is obtained in closed form. Its various terms have simple physical interpretations and manifest the various scattering and reaction channels. The interaction-matrix elements obtained are automatically renormalized through inclusion of bound-state-continuum orthogonality corrections. The definition of the $S$-matrix elements is simpler in the new representation since bound states are exactly redescribed therein as elementary particles. Certain constraints necessary and sufficient for the one-one property of the mapping from Fock- to Fock-Tani-state space are shown to be automatically satisfied when the asymptotic initial and final states for scattering processes are defined by the standard wave-packet method. This representation is expected to be useful for inclusion of the intermediate-state positronium channel in the standard manybody Green's-function approach to evaluation of $S$-matrix elements.