  The proof of cosmic ray (CR) origin in supernova remnants (SNR) must hinge on
full consistency of the CR acceleration theory with the observations; direct
proof is impossible because of the orbit stochasticity of CR particles. Recent
observations of a number of galactic SNR strongly support the SNR-CR connection
in general and the Fermi mechanism of CR acceleration, in particular. However,
many SNR expand into weakly ionized dense gases, and so a significant revision
of the mechanism is required to fit the data. We argue that strong ion-neutral
collisions in the remnant surrounding lead to the steepening of the energy
spectrum of accelerated particles by \emph{exactly one power}. The spectral
break is caused by a partial evanescence of Alfven waves that confine particles
to the accelerator. The gamma-ray spectrum generated in collisions of the
accelerated protons with the ambient gas is also calculated. Using the recent
Fermi spacecraft observation of the SNR W44 as an example, we demonstrate that
the parent proton spectrum is a classical test particle power law $\propto
E^{-2}$, steepening to $E^{-3}$ at $E_{br}\approx7GeV$.
