  We carried out a parameter-space exploration of the ammonia abundance in the
pre-stellar core L1544, where it has been observed to increase toward the
center of the core with no signs of freeze-out onto grain surfaces. We
considered static and dynamical physical models coupled with elaborate chemical
and radiative transfer calculations, and explored the effects of varying model
parameters on the (ortho+para) ammonia abundance profile. None of our models
are able to reproduce the inward-increasing tendency in the observed profile;
ammonia depletion always occurs in the center of the core. In particular, our
study shows that including the chemical desorption process, where exothermic
association reactions on the grain surface can result in the immediate
desorption of the product molecule, leads to ammonia abundances that are over
an order of magnitude above the observed level in the innermost 15000 au of the
core - at least when one employs a constant efficiency for the chemical
desorption process irrespective of the ice composition. Our results seemingly
constrain the chemical desorption efficiency of ammonia on water ice to below
1%. It is increasingly evident that time-dependent effects must be considered
so that the results of chemical models can be reconciled with observations.
