Analytical model for laser-assisted recombination of hydrogenic atoms

TL;DR

This paper presents an analytical model for laser-assisted hydrogen recombination, deriving explicit cross sections and field-enhancement coefficients using Coulomb-Volkov wave functions and a soft photon approximation.

Contribution

It introduces a new analytical approach to calculate laser-assisted recombination cross sections with explicit formulas and a simplified model for practical analysis.

Findings

Derived explicit cross section formulas for laser-assisted recombination.

Expressed the field-enhancement coefficient in terms of a dimensionless parameter.

Analyzed the process within a soft photon approximation.

Abstract

We introduce a new method that allows one to obtain an analytical cross section for the laser-assisted electron-ion collision in a closed form. As an example we perform a calculation for the hydrogen laser-assisted recombination. The $S$-matrix element for the process is constructed from an exact electron Coulomb-Volkov wave function and an approximate laser modified hydrogen state. An explicit expression for the field-enhancement coefficient of the process is expressed in terms of the dimensionless parameter $\kappa= |{e\epsilon_{0}}/{q\omega_{0}}|^{2}$, where $e$ and $q$ are the electron charge and momentum respectively, and $\epsilon_{0}$ and $\omega_{0}$ are the amplitude and frequency of the laser field respectively. The simplified version of the cross section of the process is derived and analyzed within a soft photon approximation.