  Motivated by recent studies of inclusive neutrino nucleus processes and muon
capture within a correlated local Fermi gas model (LFG), we discuss the
relevance of nuclear finite size effects in these reactions at low energy, in
particular for muon capture. To disentangle these effects from others coming
from the reaction dynamics we employ here a simple uncorrelated shell model
that embodies the typical finite size content of the problem. The integrated
decay widths of muon atoms calculated with this shell model are then compared
for several nuclei with those obtained within the uncorrelated LFG, using in
both models exactly the same theoretical ingredients and parameters. We find
that the two predictions are in quite good agreement, within 1--7%, when the
shell model density and the correct energy balance is used as input in the LFG
calculation. The present study indicates that, despite the low excitation
energies involved in the reaction, integrated inclusive observables, like the
total muon capture width, are quite independent of the fine details of the
nuclear wave functions.
