Separable expansions for local potentials with Coulomb interactions

Abstract

If two particles are interacting via a short range potential and a repulsive Coulomb potential the $t$ matrix can be written as a sum of the Coulomb and the "nuclear" $t$ matrices. In order to solve the three-nucleon problem with Coulomb interactions usually we need a separable representation of this nuclear $t$ matrix. A recently proposed method for finding a separable expansion for local potentials is here extended to find a rapidly convergent separable expansion, with analytic form factors, for the nuclear part of the $t$ matrix of a local potential, in the presence of Coulomb interactions. The method is illustrated for a two-term Malfliet-Tjon potential. In each rank the nuclear phase shift is close to the corresponding phase shift when the Coulomb interaction is switched off.