Calculation of one-electron two-centre exchange matrix elements in ion-atom collisions

An alternative method to that of Cheshire is presented for evaluating exchange matrix elements of the types occurring in close coupling-based treatments of ion-atom scattering. The idea consists in reducing by quadrature the matrix elements (which are expressible as two dimensional integrals in confocal elliptic coordinates) to one dimensional integrals which are then numerically calculated via Gauss-Laguerre quadrature. The scheme which has been tested in both the two-state and three-state approximations represents a considerable saving in computing time. This should enable one to subject to practical test the important question of the rate of convergence of close coupling-type expansions in these problems.