High-accuracy calculation of nonrelativistic Compton profile for H-like ions

In collision processes such as Compton scattering, radiative electron capture (REC) and resonant transfer and excitation (RTE) and so on, the shape of their cross sections in the impulse approximation can be determined by the so-called Compton profile (CP), which reflects the initial distribution in the momentum space for bound electrons in atomic and molecular targets. In this paper, the pseudospectral-fitting (PSF) method is proposed to obtain the radial wave function in position space numerically, which is proved equivalent to the analytical solution, and then the radial wave function in momentum space can be calculated by the series method analytically in order to avoid the numerical difficulties in highly oscillatory integrals. Finally, taking the ns(n=1−10) orbitals of hydrogenic ions as examples, high-accuracy Compton profile has also been calculated at an arbitrary momentum with enough significant digits by using the Gauss–Legendre quadrature.