Fock-Tani transformation and a first-order theory of charge transfer

A unitary (Fock-Tani) transformation of the second-quantized Hamiltonian breaks the interaction into its component parts, e.g., elastic scattering, inelastic scattering, rearrangement interaction, etc. The interaction for a particular process is ‘‘weaker’’ than the overall interaction; this is reflected in certain orthogonality corrections which appear in a perturbation expansion of the T-matrix element. As a result, the internuclear potential makes a negligible contribution of order $m_e$/$m_p$ to the first-order amplitude for charge transfer. We find very good agreement with experimental and the best available theoretical results for the total cross section for the reaction p+H(1s)→H(1s)+p for energies greater than 10 keV and for the differential cross section at 25, 60, and 125 keV in an angular range of ∼1 mrad about the forward direction.