Hybrid Gaussian–B-spline basis for the electronic continuum: Photoionization of atomic hydrogen

As a first step towards meeting the recent demand for new computational tools capable of reproducing molecular-ionization continua in a wide energy range, we introduce a hybrid Gaussian--B-spline basis (GABS) that combines short-range Gaussian functions, compatible with standard quantum-chemistry computational codes, with B splines, a basis appropriate to represent electronic continua. We illustrate the performance of the GABS hybrid basis for the hydrogen atom by solving both the time-independent and the time-dependent Schr\"odinger equation for a few representative cases. The results are in excellent agreement with those obtained with a purely B-spline basis, with analytical results, when available, and with recent above-threshold ionization spectra from the literature. In the latter case, we report fully differential photoelectron distributions which offer further insight into the process of above-threshold ionization at different wavelengths.