# Density-based one-dimensional model potentials for strong-field simulations in $\text{He}$, $\text{H}_{2}^{+}$ and $\text{H}_{2}$

## TL;DR

This paper develops and tests improved one-dimensional models for atomic and molecular systems under strong laser fields, achieving high accuracy in simulating dynamics and harmonic spectra compared to full 3D models.

## Contribution

It introduces corrected 1D Coulomb potentials derived from 3D density corrections, enhancing the accuracy of strong-field simulations for He, H2+, and H2.

## Key findings

- 1D models closely match 3D simulation results.
- High-order harmonic spectra agree well with 3D results.
- Significant improvement in atomic quantity dynamics accuracy.

## Abstract

We present results on the accurate one-dimensional (1D) modeling of simple atomic and molecular systems excited by strong laser fields. We use atomic model potentials that we derive from the corrections proposed earlier using the reduced ground state density of a three-dimensional (3D) single-active electron atom. The correction involves a change of the asymptotics of the 1D Coulomb model potentials while maintaining the correct ground state energy. We present three different applications of this method: we construct correct 1D models of the hydrogen molecular ion, the helium atom and the hydrogen molecule using improved parameters of existing soft-core Coulomb potential forms. We test these 1D models by comparing the corresponding numerical simulation results with their 3D counterparts in typical strong-field physics scenarios with near- and mid-infrared laser pulses, having peak intensities in the $10^{14}-10^{15}\,\mathrm{W/cm}^2$ range, and we find an impressively increased accuracy in the dynamics of the most important atomic quantities on the time scale of the excitation. We also present the high-order harmonic spectra of the He atom, computed using our 1D atomic model potentials. They show a very good match with the structure and phase obtained from the 3D simulations in an experimentally important range of excitation amplitudes.