Photoassociation in a gas of cold alkali atoms: I. Perturbative quantum approach

We develop a quantum-mechanical approach to the photoassociation phenomenon in a sample of cold atoms initially at thermal equilibrium with temperature T. We calculate the rate of formation of molecules in the weak field regime using a perturbative approach. Analytical expressions are obtained for the overlap between the initial and final molecular wavefunctions, and are shown to agree with numerical calculations. The photoassociation rate is found to decrease with increasing atomic mass m, from Li to Cs. Also considered is the heating of the atomic sample through spontaneous photodissociation.