Multipole analysis of radio-frequency reactions in ultracold atoms

Using the multipole expansion, we analyze photoinduced reactions in an ultracold atomic gas composed of identical neutral bosons. While the Franck-Condon factor dominates the photoinduced spin-flip reactions, we have found that for a frozen-spin process in which the atomic spins are conserved, the reaction rate is governed by the monopole r2 and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number k acquires an extra k4 factor in comparison to the spin-flip process. Comparing the relative strength of the r2 and quadrupole modes in dimer photoassociation, we predict that the mutual importance of these two modes changes with temperature and scattering length.