  The variation of remotely sensed neutron count rates is measured as a
function of cratercentric distance using data from the Lunar Prospector Neutron
Spectrometer. The count rate, stacked over many craters, peaks over the crater
centre, has a minimum near the crater rim, and at larger distances, it
increases to a mean value that is up to 1% lower than the mean count rate
observed over the crater. A simple model is presented, based upon an analytical
topographical profile for the stacked craters fitted to data from the Lunar
Orbiter Laser Altimeter (LOLA). The effect of topography coupled with neutron
beaming from the surface largely reproduces the observed count rate profiles.
However, a model that better fits the observations can be found by including
the additional freedom to increase the neutron emissivity of the crater area by
~0.35% relative to the unperturbed surface. It is unclear what might give rise
to this effect, but it may relate to additional surface roughness in the
vicinities of craters. The amplitude of the crater-related signal in the
neutron count rate is small, but not too small to demand consideration when
inferring water-equivalent hydrogen (WEH) weight percentages in polar
permanently shaded regions (PSRs). If the crater-wide count rate excess is
concentrated into a much smaller PSR, then it can lead to a significantly
biased inferred WEH weight percentage. For instance, it may increase the
inferred WEH for Cabeus crater at the Moon's South Pole from ~1% to ~4%.
