The Doppler profiles of Ba(P-3(2)) atoms desorbed from the surface of argon clusters following the deactivation of Ba(P-1(1)) have been measured. These measurements have been performed for desorption from pure ATN clusters and as a function of a known average number of CH4 molecules deposited on the cluster. Analysis of the profile widths with respect to the kinetic energy release from deactivation indicates that desorption occurs along a single Ba-Ar and Ba-CH4 coordinate in the former and latter cases, respectively. By comparing the kinetic energy distributions in the desorbed barium with the relative kinetic energy available at the temperature of the cluster it is found that the collisions leading to deactivation in both cases are gas kinetic at the temperature of the cluster (35 K). The residual anisotropies in the Doppler profiles reveal the Ba-Ar deactivation to be a relatively inefficient process allowing the barium to undertake a full migration on the cluster surface before desorbing. This results in an essentially isotropic distribution of recoil velocities. In contrast Ba-CH4 deactivation is sufficiently fast to preserve some degree of anisotropy in the desorbed barium velocity distribution. The anisotropy results from the depolarization of the barium orbital due to bath the migration of the barium on the cluster surface and axial relaxation of the orbital by collisions with neighboring argon atoms. Calculations of the anisotropies resulting from both reorientating mechanisms show a significant degree of relaxation and migration to occur before the barium is desorbed.