Laser-Phase Dependence for Electron Capture in Laser-Assisted Proton -- Hydrogen Collisions*

We calculate electron capture probabilities for ion--atom collisions in a strong laser field ($5\times10^{13}~\mathrm{W/cm^2}$) by numerically solving the 3-dimensional time--dependent Schr\"{o}dinger equation. For circularly polarized laser fields and an impact energy of $1.2~\mathrm{keV}$, we find a substantial modification of the electronic dynamics in the $p$--$H$ collision system as compared to field-free collisions. In particular, we observe a strong dependence on the laser phase and the impact parameter for electron capture, which can be explained using semi-classical arguments.