NUMERICAL-METHOD FOR THE CALCULATION OF 2-CENTER INTEGRALS

A numerical method has been developed to calculate the two-center integrals which can be used to evaluate the charge-transfer matrix elements arising in ion-atom collisions. The initial three-dimensional integrals are first reduced to one-dimensional integrals using a Feynman-integral technique. A special routine which uses continuation in the complex plane has been designed to evaluate the integrals in the region far away from the target to remove their rapid oscillation in this region. Then a Gauss-Laguerre integral method is used to compute this analytic continuation. The four-state charge-transfer matrix elements in proton-hydrogen scattering have been calculated to illustrate the method. The resultant coupled differential equations are solved by the Runge-Kutta method. Some cross sections for proton-hydrogen scattering have been evaluated and compared with available results.