  Observations of the middle-aged supernova remnants IC 443, W28 and W51C
indicate that the brightnesses at GeV and TeV energies are correlated with each
other and with regions of molecular clump interaction, but not with the radio
synchrotron brightness. We suggest that the radio emission is primarily
associated with a radiative shell in the interclump medium of a molecular
cloud, while the gamma-ray emission is primarily associated with the
interaction of the radiative shell with molecular clumps. The shell interaction
produces a high pressure region, so that the gamma-ray luminosity can be
approximately reproduced even if shock acceleration of particles is not
efficient, provided that energetic particles are trapped in the cooling region.
In this model, the spectral shape \ga 2 GeV is determined by the spectrum of
cosmic ray protons. Models in which diffusive shock acceleration determines the
spectrum tend to underproduce TeV emission because of the limiting particle
energy that is attained.
