  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.
