Modified $\mathitJ$-Matrix Method for Scattering
We modify the J-matrix technique for scattering so that problems with long-range interactions are easily solved. This is done by introducing additional terms in the asymptotic three-term recurrence relation that take into account asymptotic effects of the potential. The solutions of this modified recurrence relation are a very good approximation of the exact scattering solution. Only a small number of residual coefficients need to be calculated. As a result, the numerical effort to solve the scattering problem is seriously reduced. The technique is illustrated with a Yukawa potential.