Summary: Slater integrals are two-dimensional radial integrals whose integrand is constructed from normalized eigenfunctions of the Schrödinger equation. These integrals occur in many atomic structure and scattering computations. However, in two-dimensional R-matrix propagation they represent a significant computational bottleneck. The problem involves two steps, that is, the numerical solution of the Schrödinger equation and the computation of the integrals, respectively.
By exploiting the characteristic features of the problem we seek to devise a two-stage computational strategy, where the second stage is influenced and informed by the first. In particular, we focus on the development of extended frequency-dependent quadrature rules that improve the accuracy and significantly reduce the computation time of the integrals. The performance of these ad hoc rules is examined and compared to the currently used Newton-Cotes method in the construction of Hamiltonian matrices involving up to \(300\times 10^6\) integrals. A gain of two orders of magnitude in the CPU time is obtained.