Photoionization of atoms and molecules studied by Crank-Nicolson method

TL;DR

This paper demonstrates the application of the Crank-Nicolson method combined with B-spline basis sets for calculating photoionization cross sections in atoms and molecules, showing good agreement with previous results and extending to two-electron systems.

Contribution

It introduces a versatile approach using the Crank-Nicolson method with B-splines for both time-dependent and time-independent photoionization calculations, including excited and continuum states.

Findings

C-N method converges to ground, excited, and continuum states via imaginary-time propagation.

Results agree well with previous studies.

Method extends to two-electron systems.

Abstract

Crank-Nicolson (C-N) Method combined with $ B $-spline basis set can be used in both time-dependent and time-independent calculations of the photoionization cross sections of atoms and molecules. For time-independent systems, it is found that C-N method in imaginary-time propagation (ITP) can converge directly to not only the ground state, but also excited and continuum states by controlling the time step size. The C-N method can also be directly applied in time-dependent calculations. Both time-dependent and time-independent calculations agree very well with previous results. This method can also be extended to two-electron systems directly.