Context. The high degree of deuteration observed in some prestellar cores depends on the ortho-to-para H2 ratio through the H3+ fractionation. Aims. We want to constrain the ortho/para H2 ratio across the L183 prestellar core. This is mandatory to correctly describe the deuter- ation amplification phenomenon in depleted cores such as L183 and to relate the total (ortho+para) H2D+ abundance to the sole ortho-H2D+ column density measurement. Methods. To constrain this ortho/para H2 ratio and derive its profile, we make use of the N2D+ /N2H+ ratio and of the ortho-H2D+ 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 H2D+ ortho/para ratio in the L183 cloud, and constrain the H2 ortho/para ratio : we show that it is varying 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 x 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 H2 ratio should also give useful constraints on the dynamical evolution of prestellar cores.
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