Reflection approximation in photoassociation spectroscopy

We construct an analytical wave function in the phase-amplitude formalism to describe collisions between two neutral atoms. This wave function is valid 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 approximation formula for calculating Franck-Condon factors for photoassociative spectroscopy. Numerical tests show very satisfactory agreement between the resulting analytic formula and the fully quantum numerical results in most cases investigated. Finally, we show in a model case that our analytical wave function enables us to relate the scattering length directly to a preasymptotic node in the ground-state wave function, which in principle can be measured by photoassociative spectroscopy.