  We theoretically study slow collisions of NH$_3$ molecules with He atoms,
where we focus in particular on the observation of scattering resonances. We
calculate state-to-state integral and differential cross sections for collision
energies ranging from 10${}^{-4}$ cm$^{-1}$ to 130 cm$^{-1}$, using fully
converged quantum close-coupling calculations. To describe the interaction
between the NH${}_3$ molecules and the He atoms, we present a four-dimensional
potential energy surface, based on an accurate fit of 4180 {\it ab initio}
points. Prior to collision, we consider the ammonia molecules to be in their
antisymmetric umbrella state with angular momentum $j=1$ and projection $k=1$,
which is a suitable state for Stark deceleration. We find pronounced shape and
Feshbach resonances, especially for inelastic collisions into the symmetric
umbrella state with $j=k=1$. We analyze the observed resonant structures in
detail by looking at scattering wavefunctions, phase shifts, and lifetimes.
Finally, we discuss the prospects for observing the predicted scattering
resonances in future crossed molecular beam experiments with a
Stark-decelerated NH$_3$ beam.
