Reflection approximation in photoassociation spectroscopy - art. no. 052705

We construct an analytical wave function in the phase-amplitude formalism t o describe collisions between two neutral atoms. This wave function is vali d from intermediate to asymptotic internuclear distance over a large energy range near zero energy, and is especially suitable for cold and ultracold collisions. We have used this analytic wave function with the reflection ap proximation formula for calculating Franck-Condon factors for photoassociat ive spectroscopy. Numerical tests show very satisfactory agreement between the resulting analytic formula and the fully quantum numerical results in m ost cases investigated. Finally, we show in a model case that our analytica l wave function enables us to relate the scattering length directly to a pr easymptotic node in the ground-state wave function, which in principle can be measured by photoassociative spectroscopy.