  We calculate the spallative production of light elements associated with the
explosion of an isolated supernova in the interstellar medium, using a
time-dependent model taking into account the dilution of the ejected enriched
material and the adiabatic energy losses. We first derive the injection
function of energetic particles (EPs) accelerated at both the forward and the
reverse shock, as a function of time. Then we calculate the Be yields obtained
in both cases and compare them to the value implied by the observational data
for metal-poor stars in the halo of our Galaxy, using both O and Fe data. We
find that none of the processes investigated here can account for the amount of
Be found in these stars, which confirms the analytical results of Parizot and
Drury (1999). We finally analyze the consequences of these results for Galactic
chemical evolution, and suggest that a model involving superbubbles might
alleviate the energetics problem in a quite natural way.
