Ammonia and its deuterated isotopologues probe physical conditions in dense molecular cloud cores. With the aim of testing the current understanding of the spin-state chemistry of these molecules, we observed spectral lines of NH3, NH2D, NHD2, ND3, and N2D+ towards a dense, starless core in Ophiuchus with the APEX, GBT, and IRAM 30-m telescopes. The observations were interpreted using a gas-grain chemistry model combined with radiative transfer calculations. The chemistry model distinguishes between the different nuclear spin states of light hydrogen molecules, ammonia, and their deuterated forms. High deuterium fractionation ratios with NH2D/NH3=0.4, NHD2/NH2D=0.2, and ND3/NHD2=0.06 were found in the core. The observed ortho/para ratios of NH2D and NHD2 are close to the corresponding nuclear spin statistical weights. The chemistry model can approximately reproduce the observed abundances, but predicts uniformly too low ortho/para-NH2D, and too large ortho/para-NHD2 ratios. The longevity of N2H+ and NH3 in dense gas, which is prerequisite to their strong deuteration, can be attributed to the chemical inertia of N2 on grain surfaces. The discrepancies between the chemistry model and the observations are likely to be caused by the fact that the model assumes complete scrambling in principal gas-phase deuteration reactions of ammonia, which means that all the nuclei are mixed in reactive collisions. If, instead, these reactions occur through proton hop/hydrogen abstraction processes, statistical spin ratios are to be expected. The present results suggest that while the deuteration of ammonia changes with physical conditions and time, the nuclear spin ratios of ammonia isotopologues do not probe the evolutionary stage of a cloud.
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