  Ammonia is one of the most widely observed molecules in space, and many
observations are able to resolve the hyperfine structure due to the electric
quadrupole moment of the nitrogen nucleus. The observed spectra often display
anomalies in the satellite components of the lines, which indicate substantial
deviations from the local thermodynamic equilibrium. The interpretation of the
spectra thus requires the knowledge of the rate coefficients for the hyperfine
excitation of NH$_3$ induced by collisions with H$_2$ molecules, the dominant
collider in the cold interstellar medium. In this paper we present the first
such calculations using a recoupling approach. The rate coefficients are
obtained for all hyperfine levels within rotation-inversion levels up to $j=4$
and temperatures up to 100 K by means of quantum scattering close-coupling
calculations on an accurate, five-dimensional, potential energy surface. We
show that the rate coefficients depart significantly from those obtained with
the statistical approach and that they do not conform to any simple propensity
rules. Finally, we perform radiative transfer calculations to illustrate the
impact of our new rate coefficients by modelling the hyperfine line intensities
of the inversion transition in ground state para-NH$_3$ ($j_k=1_1$) and of the
rotational transition $1_0\rightarrow 0_0$ in ortho-NH$_3$.
