On the numerical evaluation of six dimensional integrals occurring in scattering problems Original Research Article

We consider integrals of the from ∫ d3r0 tf(r0) ∫ d3ri V(r0, ri)g(ri), where tf(r0) and g(ri) are complex functions. Such integrals occur frequently in scattering theory problems where typically V(r0, ri) is the Coulomb potential xt/vbr0−rivb and g contains an exponentially decaying function. tf(r0) usually contains oscillatory functions and may or may not contain an exponentially decreasing one. In the former case standard techniques such as Monte Carlo integration can be used with reasonable accuracy, however, in the latter these methods fail due to the extremely large integration region required for the outer integral. We propose a numerical 6 Dimensional Integration Method (6DIME) which can be used for either situations. In the exponentially damped case it provides faster and more accurate results. However, this methods tackles for the very first time the far more difficult problem of the undamped case. The accuracy of this approach is tested against analytically solvable integrals that occur in scattering problems.