Mapped Fourier methods for long-range molecules: Application to perturbations in the Rb2(0u+) photoassociation spectrum

Numerical calculations of vibrational levels of alkali dimers close to the dissociation limit are developed in the framework of a Fourier Grid Hamiltonian method. The aim is to interpret photoassociation experiments in cold atom samples. In order to avoid the implementation of very large grids we propose a mapping procedure adapted to the asymptotic $R^{\mathrm{-n}}$ behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to ${\text{500a}}_0$ using a minimal number of grid points. Calculations with two electronic states, ${\mathrm{A }}^1{\Sigma }_u^{+}$ and ${\mathrm{b }}^3{\Pi }_u$ states, both correlated to the $\mathrm{Rb}\text{(5s)+}\mathrm{Rb}\text{(5p)}$ dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the ${\mathrm{Rb}}_{\mathrm{2}}{\text{(0}}_u^{+}$ ) spectrum, manifested under the $\text{5s,}$ ${\text{5p\hspace{0.05em}}}^2{P}_{\text{1/2}}$ dissociation limit by an oscillatory behavior of the rotational constants.