  Barnard B1b has revealed as one of the most interesting globules from the
chemical and dynamical point of view. It presents a rich molecular chemistry
characterized by large abundances of deuterated and complex molecules.
Furthermore, it hosts an extremely young Class 0 object and one candidate to
First Hydrostatic Core (FHSC). Our aim was to determine the cosmic ray
ionization rate and the depletion factors in this extremely young star forming
region. We carried out a spectral survey towards Barnard 1b as part of the IRAM
Large program ASAI using the IRAM 30-m telescope at Pico Veleta (Spain). This
provided a very complete inventory of neutral and ionic C-, N- and S- bearing
species with, up to our knowledge, the first secure detections of the
deuterated ions DCS+ and DOCO+. We used a state-of-the-art
pseudo-time-dependent gas-phase chemical model to determine the value of the
cosmic ray ionization rate and the depletion factors. The observational data
were well fitted with $\zeta_{H_2}$ between 3E-17 s$^{-1}$ and 1E-16 s$^{-1}$.
Elemental depletions were estimated to be ~10 for C and O, ~1 for N and ~25 for
S. Barnard B1b presents similar depletions of C and O than those measured in
pre-stellar cores. The depletion of sulfur is higher than that of C and O but
not as extreme as in cold cores. In fact, it is similar to the values found in
some bipolar outflows, hot cores and photon-dominated regions. Several
scenarios are discussed to account for these peculiar abundances. We propose
that it is the consequence of the initial conditions (important outflows and
enhanced UV fields in the surroundings) and a rapid collapse (~0.1 Myr) that
permits to maintain most S- and N-bearing species in gas phase to great optical
depths. The interaction of the compact outflow associated with B1b-S with the
surrounding material could enhance the abundances of S-bearing molecules, as
well.
