Recombination Amplitude Calculations of Noble Gases, in Length and Acceleration Forms, beyond Strong Field Approximation

TL;DR

This study compares different theoretical models for calculating recombination amplitudes in noble gases, revealing significant dependence on wavefunction choice and dipole form, and identifying models that best match experimental data for high-order harmonic generation.

Contribution

It provides a detailed comparison of recombination amplitude calculations beyond the strong field approximation, highlighting the importance of wavefunction and dipole form choices in noble gases.

Findings

Recombination amplitudes vary significantly with wavefunction and dipole form.

Outgoing scattering eigenstates with length form best predict Cooper minima.

Recombination cross sections agree better with RRPA when using length form and scattering eigenstates.

Abstract

Transition of an electron from a free to a bound state is critical in determining the qualitative shape of the spectrum in high-order harmonic generation (HHG), and in tomographic imaging of orbitals. We calculate and compare the recombination amplitude, from a continuum state described by a plane wave and an outgoing scattering eigenstate, to the bound state for the noble gases that are commonly used in HHG. These calculations are based on the single active electron model and the Hartree-Fock-Slater method, using both the length form and the acceleration form of the dipole matrix element. We confirm that the recombination amplitude versus emitted photon energy strongly depends upon the wavefunction used to describe the free electron. Depending on the choice of the wavefunction and the dipole form, the square of the absolute value of the recombination amplitude can differ by almost two orders of magnitude near the experimentally measured Cooper minima. Moreover, only the outgoing scattering eigenstates with the length form roughly predict the experimentally observed Cooper minimum for Ar (~50 eV) and Kr (~85 eV). We provide a detailed derivation of the photorecombination cross sections (PRCSs) from photo ionization cross sections (PICSs) calculated by the relativistic random phase approximation (RRPA)., For Ar, Kr and Xe, compare the total PICSs calculated using our recombination amplitudes with that obtained from RRPA. We find that PICS calculated using the outgoing scattering eigenstates with the length form is in better agreement with the RRPA calculations than the acceleration form.