J−matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering

Abstract

The J−matrix method introduced previously for s−wave scattering is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L²), Laguerre (Slater), and oscillator (Gaussian) basis sets. The determination of the expansion coefficients of the continuum eigenfunctions in terms of the L² basis set is shown to be equivalent to the solution of a linear second order differential equation with appropriate boundary conditions, and complete solutions are presented. Physical scattering problems are approximated by a well−defined model which is then solved exactly. In this manner, the generalization presented here treats the scattering of particles by neutral and charged systems. The appropriate formalism for treating many channel problems where target states of differing angular momentum are coupled is spelled out in detail. The method involves the evaluation of only L² matrix elements and finite matrix operations, yielding elastic and inelastic scattering information over a continuous range of energies.