An asymptotic method for calculation of radial matrix elements for atomic transitions

The decisive factor for calculation of the oscillator strengths of ions and atoms in the central-field approximation is the radial matrix element of the transition between stationary electron states [l]. A method is proposed for calculation of thjs matrix element by numerical integration near the nucleus and analytic cal­ culation of the radial integral with the aid of an asymptotic expansion of the exact Coulomb wave functions in the range where the electroncore interaction potential is Coulombic. The results of integration in this region are repre­ sented in the form of asymptotic series in reciprocal powers of the radius at the boundary of the core, and can be used to calculate photoionization and photo­ recombination cross sections.