Nonadiabatic treatment of hydrogen-antihydrogen collisions

Abstract

We present a nonadiabatic treatment of the hydrogen-antihydrogen system. The technique used to describe $\mathrm{H}\text{\ensuremath{-}}\overline{\mathrm{H}}$ collisions is based on the coupled-rearrangement-channel method. Within this approach the total, nonadiabatic wave function of the system is divided into two parts: an inner and an outer one. To describe the inner part a set of square-integrable four-body functions is used. These functions are obtained by a diagonalization of the total Hamiltonian projected on a chosen ${L}^{2}$ subspace; they explicitly contain components of various arrangement channels expressed in terms of corresponding Jacobi coordinates. The outer part of the total wave function reflects its asymptotic character. Our procedure leads to a system of nonlocal integrodifferential equations that are solved iteratively and simultaneously determine the outer part of the solution and the coefficients in the four-body expansion of the inner part. To solve these equations the compact fine difference method was applied. Using this formalism we perform a one-channel calculation of the elastic scattering to obtain the $S$ matrix, the nonadiabatic scattering length, and the cross section for the low-energy elastic scattering in the $\mathrm{H}\text{\ensuremath{-}}\overline{\mathrm{H}}$ channel.