Three-body recombination for protons moving in a strong magnetic field

Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom: $e+e+\overrightarrow{p}\mathrm{H}+e)$ in strong magnetic fields. The proton is allowed its full motion whereas the motion of the electron is given by the guiding center approximation. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated anti-hydrogen. When the proton has the same temperature as the electrons, the recombination rate for the more elaborate equations of motion is roughly 60% larger than for the $\overrightarrow{B}\infty$ approximation. The recombination rate decreases as the proton speed approaches the electron thermal speed; the variation of this rate has implications for the directionality of the anti-atoms formed in recent experiments. We report on several properties of the atoms formed by three-body recombination in strong magnetic fields.