# Application of the time-dependent surface flux method to the time-dependent multiconfiguration self-consistent-field method

## TL;DR

This paper introduces an extension of the tSURFF method for multielectron systems within the TD-MCSCF framework, enabling efficient and accurate computation of photoelectron spectra under intense laser fields.

## Contribution

The authors develop a numerical implementation of tSURFF for TD-MCSCF, allowing direct extraction of photoelectron spectra from multielectron wave functions with reduced computational cost.

## Key findings

- Successfully applied to Ne photoionization with attosecond XUV pulses.
- Accurately computed above-threshold ionization of Ar with mid-infrared lasers.
- Demonstrated improved efficiency and accuracy over traditional projection methods.

## Abstract

We present a numerical implementation of the time-dependent surface flux (tSURFF) method [New J. Phys. 14, 013021 (2012)], an efficient computational scheme to extract photoelectron energy spectra, to the time-dependent multiconfiguration self-consistent-field (TD-MCSCF) method. Extending the original tSURFF method developed for single particle systems, we formulate the equations of motion for the spectral amplitude of orbital functions constutiting the TD-MCSCF wave function, from which the angle-resolved photoelectron energy spectrum, and more generally, photoelectron reduced density matrices (RDMs) are readiliy obtained. The tSURFF method applied to the TD-MCSCF wave function, in combination with an efficient absorbing boundary offered by the infinite-range exterior complex scaling, enables accurate {\it ab initio} computations of photoelectron energy spectra from multielectron systems subject to an intense and ultrashort laser pulse with a computational cost significantly reduced compared to that required in projecting the total wave function onto scattering states. We apply the present implementation to the photoionization of Ne exposed to an attosecond extreme-ultraviolet (XUV) pulse and above-threshold ionization of Ar irradiated by an intense mid-infrared laser field, demonstrating both accuracy and efficiency of the present method.