Spin-state chemistry of deuterated ammonia
  Aims. We aim to develop a chemical model that contains a consistent
description of spin-state chemistry in reactions involving chemical species
with multiple deuterons. We apply the model to the specific case of deuterated
ammonia, to derive values for the various spin-state ratios.
  Methods. We apply symmetry rules in the complete scrambling assumption to
calculate branching ratio tables for reactions between chemical species that
include multiple protons and/or deuterons. Reaction sets for both gas-phase and
grain-surface chemistry are generated using an automated routine that forms all
possible spin-state variants of any given reaction with up to six H/D atoms.
Single-point and modified Bonnor-Ebert models are used to study the density and
temperature dependence of ammonia and its isotopologs, and the associated
spin-state ratios.
  Results. We find that the spin-state ratios of the ammonia isotopologs are,
at late times, very different from their statistical values. The ratios are
rather insensitive to variations in the density, but present strong temperature
dependence. We derive high peak values ($\sim$ 0.1) for the deuterium fraction
in ammonia, in agreement with previous (gas-phase) models. The deuterium
fractionation is strongest at high density, corresponding to a high degree of
depletion, and also presents temperature dependence. We find that in the
temperature range 5 to 20 K, the deuterium fractionation peaks at $\sim$ 15 K
while most of the ortho/para (and meta/para for $\rm ND_3$) ratios present a
minimum at 10 K (ortho/para $\rm NH_2D$ has instead a maximum at this
temperature).
  Conclusions. Owing to the density and temperature dependence found in the
abundances and spin-state ratios of ammonia and its isotopologs, it is evident
that observations of ammonia and its deuterated forms can provide important
constraints on the physical structure of molecular clouds.
