Context. The high degree of deuteration observed in some prestellar cores depends on the ortho-to-para H 2 ratio through the H + 3 fractionation. Aims. We want to constrain the ortho/para H 2 ratio across the L183 prestellar core. This is required to correctly describe the deuteration amplification phenomenon in depleted cores such as L183 and to relate the total (ortho+para) H 2 D + abundance to the sole ortho-H 2 D + column density measurement. Methods. To constrain this ortho/para H 2 ratio and derive its profile, we make use of the N 2 D + /N 2 H + ratio and of the ortho-H 2 D + observations performed across the prestellar core. We use two simple chemical models limited to an almost totally depleted core description. New dissociative recombination and trihydrogen cation-dihydrogen reaction rates (including all isotopologues) are presented in this paper and included in our models. Results. We estimate the H 2 D + ortho/para ratio in the L183 cloud, and constrain the H 2 ortho/para ratio: we show that it varies across the prestellar core by at least an order of magnitude, being still very high (≈0.1) in most of the cloud. Our time-dependent model indicates that the prestellar core is presumably older than 1.5−2 × 10 5 years but that it may not be much older. We also show that it has reached its present density only recently and that its contraction from a uniform density cloud can be constrained. Conclusions. A proper understanding of deuteration chemistry cannot be attained without taking into account the whole ortho/para family of molecular hydrogen and trihydrogen cation isotopologues as their relations are of utmost importance in the global scheme. Tracing the ortho/para H 2 ratio should also place useful constraints on the dynamical evolution of prestellar cores.

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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 Ϫn behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to 500a 0 using a minimal number of grid points. Calculations with two electronic states, A 1 ⌺ u ϩ and b 3 ⌸ u states, both correlated to the Rb(5s)ϩRb(5 p) dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the Rb 2 (0 u ϩ ͒ spectrum, manifested under the 5s, 5p 2 P 1/2 dissociation limit by an oscillatory behavior of the rotational constants.