Calculation of two-center integrals involving a rapidly oscillating free electron wave function

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Abstract
Optical potentials are used in a quantum mechanical treatment of loss processes, e.g., ionization, where the loss of flux is described by the imaginary part. We present a numerical method for calculating two-center two-electron integrals necessary to construct the imaginary part of the optical potential. By introducing Slater-type orbitals with complex-valued exponents (CSTOs), we are able to represent the free electron wave with a limited number of CSTOs. For the representation of free electron wave functions with many oscillations, i.e., in a large r range or for a high kinetic energy, these new CSTOs form a more natural set of basis functions. The introduction of CSTOs is inevitable for the calculation of integrals concerning collisions in the mK energy range, where the interaction acts over large internuclear distances. Extensive numerical checks show that the final imaginary part of the optical potentials can be calculated with an accuracy better than 2%.