Mapped Fourier methods for long-range molecules: Application to perturbations in the Rb₂(0_u ⁺) 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^-n behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to 500a₀ using a minimal number of grid points. Calculations with two electronic states, A ¹Σ_u ⁺ and b ³Π_u states, both correlated to the Rb(5s) + Rb(5p) dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the Rb₂(0_u ⁺) spectrum, manifested under the 5s, 5p ²P_I/2 dissociation limit by an oscillatory behavior of the rotational constants.