Computational study of significant semi-infinite integrals in electromagnetic and atomic interactions

When deriving dyadic Green's functions for the spherical structures with uniaxial or gyrotropic anisotropic materials and studying the interaction among the neutrons, ions and atoms, some semi-infinite integrals whose integrant function consists of two spherical Bessel functions and a power function needs to be evaluated. Furthermore, those kinds of integrals are of great importance to the research of atomic particle collisions, multipole moments and relativistic processes. During the recent work associated with the formulations, we evaluated in detail the integrals of two spherical Bessel functions given in C.T. Whelan (1986), but found the mistakes in the solution given in C.T. Whelan (1986). Therefore, this paper revisited the evaluation of the integral and provided the correct solution to the integral in spherical coordinates in terms of distribution, step functions and delta functions. The formulation was further extended and it is also found that the solution varies differently in the cases of even and odd values of l - l'