Multipole Analysis of Radio-Frequency Reactions in Ultra-Cold Atoms
Abstract
Using the multipole expansion we analyze photo induced reactions in an ultra-cold atomic gas composed of identical neutral bosons. While the Frank-Condon factor dominates the photo induced spin-flip reactions, we have found that for frozen-spin process where the atomic spins are conserved the reaction rate is governed by the monopole
r
2
and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number
k
acquires an extra
k
4
factor in comparison to the spin-flip process. Comparing the relative strength of the
r
2
and quadrupole modes in dimer photoassociation we predict that the mutual importance of these two modes changes with temperature and scattering length.