  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.
