HEATING DUE TO LONG-RANGE PHOTON EXCHANGE INTERACTIONS BETWEEN COLD ATOMS

We have calculated the long-range part of the momentum diffusion coefficient of two atoms in a radiation field using an S-matrix expansion to first order in the dipole-dipole interaction between the atoms. This perturbative treatment is limited to the low-saturation regime and large detunings (\delta\ much greater than gamma). The physical processes arise from the interaction with the coherent and incoherent parts of the scattered spectrum. We find that in the regime of a constant density the extra diffusion term when averaged over the trap volume depends on the total number of trapped atoms to the third power and is independent of the atom laser detuning.