K-Shell photoionization cross sections of one-electron uranium cation by relativistic complex basis function method

Abstract

The complex basis function (CBF) method is a square-integrable (L2) function method that represents continuum wave functions, and has been applied successfully to various problems, including the calculation of resonance state energies and photoionization cross sections. The previous applications of this method have been limited to non-relativistic problems, and no serious attempt has been made for the relativistic Hamiltonian. In this study, we calculated the photoionization cross sections from the imaginary part of the frequency-dependent polarizability by applying the CBF method to the inhomogeneous Dirac equation of the one-electron uranium cation. The results obtained by employing a pure Coulomb potential to the K-shell photoionization cross sections were in good agreement with previous theoretical values and experimental values for the neutral uranium atom. Phase shifts were obtained by matching the CBF solutions with the numerical ones, which were further propagated by the fourth-order Runge–Kutta method, and thus, the photoionization differential and total cross sections were successfully calculated. The calculated results were analyzed from various viewpoints, including the multipole effect of electromagnetic fields, momentum conservation of photon and photoelectron, interference of multiple perturbation terms, and difference in the orbital angular momentum of the small component wave functions. These analyses demonstrate the effectiveness of the CBF method for the inhomogeneous Dirac equation and thus its applicability to multielectron systems.