  Interstellar grain mantles present in dense interstellar clouds are in
constant exchange with the gas phase via accretion and desorption mechanisms
such as UV, X-ray photodesorption, cosmic ray induced sputtering, grain thermal
fluctuations, and chemical reaction energy release. The relative importance of
the various desorption mechanisms is of uttermost importance for astrophysical
models to constrain the chemical evolution in such high density dense cloud
regions. In this experimental work we investigated the sputtering yield as a
function of ice mantle thickness, exposed to Xe ions at 95MeV. The ion induced
ice phase transformation and the sputtering yield were simultaneously monitored
by IR spectroscopy and mass spec- trometry, respectively. The sputtering yield
is constant above a characteristic ice layer thickness and starts to decrease
below this thickness. An estimate of the sputtering depth corresponding to this
length can be evaluated. In these experiments the measured desorption depth
corresponds to 30 ice layers. Assuming an effective cylindrical shape for the
volume of sputtered molecules, the aspect ratio is close to unity; in the
semi-infinite ice film case this ratio is the diameter to height of the
cylinder. This result shows that most ejected molecules arise from a rather
compact volume. The measured infinite thickness sputtering yield for water ice
mantles scales as the square of the ion electronic stopping power (Se). We
expect that the desorption depth dependence varies with Se^a , where a=0.5.
Astrophysical models should take into account the thickness dependence
constraints of these ice mantles in the interface regions when ices are close
to their extinction threshold. In the very dense cloud regions, most of the
water ice mantles are above this limit for the bulk of the cosmic rays.
