Analytical model for laser-assisted recombination of hydrogenic atoms

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 wavefunction 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 = vertical bar e epsilon(0)/q omega(0)vertical bar(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.