Evaluation of the Coulomb integral for scattering problems

Abstract

A six-dimensional integral in the coordinate space of two particles 1 and 2, where the integrand contains Coulomb functions for both the particles, the term $\frac{1}{|{\overrightarrow{\mathrm{r}}}_1-{\overrightarrow{\mathrm{r}}}_2|}$, and an exponential term, is reduced to a double integral in real space. The resulting integral can finally be integrated numerically with a high degree of accuracy. This technique has been verified by its application to the Nordsieck integral for bremsstrahlung with different sets of parameters and compared with the exact method of Nordsieck. The error estimate is always found to be less than 0.01%.