  We present a theoretical study on the recombination of a free electron into
the ground state of a hydrogen-like ion in the presence of an external laser
field. Emphasis is placed on the effects caused by the laser dressing of the
residual ionic bound state. To investigate how this dressing affects the total
and angle-differential cross section of laser assisted radiative recombination
(LARR) we apply first-order perturbation theory and the separable
Coulomb-Volkov-continuum ansatz. Using this approach detailed calculations were
performed for low-$Z$ hydrogen like ions and laser intensities in the range
from $I_L=10^{11}\text{W/cm}^2$ to $I_L=10^{13}\text{W/cm}^2$. It is seen that
the total cross section as a function of the laser intensity is remarkably
affected by the bound state dressing. Moreover the laser dressing becomes
manifest as asymmetries in the angular distribution and the (energy) spectrum
of the emitted recombination photons.
