Role of intermediate continuum states in exterior complex scaling calculations of two-photon ionization cross section

TL;DR

This paper improves the calculation of two-photon ionization cross sections using exterior complex scaling by introducing a modified procedure that yields reliable partial ionization amplitudes, validated on helium and applicable to autoionizing states.

Contribution

It presents a minor modification to existing exterior complex scaling methods, enabling accurate partial ionization amplitude calculations for two-photon ionization processes.

Findings

Calculated cross sections agree well with literature.

Modified procedure reliably extracts partial amplitudes.

Applicable to autoionizing states for simplified modeling.

Abstract

The calculation of partial two-photon ionization cross sections in the above-threshold energy region is discussed in the framework of exterior complex scaling. It is shown that with a minor modification of the usual procedure, which is based on the calculation of the outgoing partial waves of the second-order scattering wave function, reliable partial ionization amplitudes can be obtained. The modified procedure relies on a few-term least-squares fit of radial functions pertaining to different partial waves. To test the procedure, partial and total two-photon ionization cross sections of the helium atom have been calculated for a broad range of incident photon energies. The calculated cross sections may be seen to agree well with the results found in the literature. Furthermore, it is shown that, using a similar approach, partial photoionization cross sections of an atom in an autoionizing (resonance) state may be calculated in a relatively straightforward way. Such photoionization cross sections may find their use in enhanced few-parameter models describing the atom-light interaction in cases where a direct solution of the time-dependent Schroedinger equation becomes too resource-intensive.