  We present a simple analytic model for the various contributions to the
non-thermal emission from shell type SNRs, and show that this model's results
reproduce well the results of previous detailed calculations. We show that the
\geq 1 TeV gamma ray emission from the shell type SNRs RX J1713.7-3946 and RX
J0852.0-4622 is dominated by inverse-Compton scattering of CMB photons (and
possibly infra-red ambient photons) by accelerated electrons. Pion decay (due
to proton-proton collisions) is shown to account for only a small fraction,
\lesssim10^-2, of the observed flux, as assuming a larger fractional
contribution would imply nonthermal radio and X-ray synchrotron emission and
thermal X-ray Bremsstrahlung emission that far exceed the observed radio and
X-ray fluxes. Models where pion decay dominates the \geq 1 TeV flux avoid the
implied excessive synchrotron emission (but not the implied excessive thermal
X-ray Bremsstrahlung emission) by assuming an extremely low efficiency of
electron acceleration, K_ep \lesssim 10^-4 (K_ep is the ratio of the number of
accelerated electrons and the number of accelerated protons at a given energy).
We argue that observations of SNRs in nearby galaxies imply a lower limit of
K_ep \gtrsim 10^-3, and thus rule out K_ep values \lesssim 10^-4 (assuming that
SNRs share a common typical value of K_ep). It is suggested that SNRs with
strong thermal X-ray emission, rather than strong non-thermal X-ray emission,
are more suitable candidates for searches of gamma rays and neutrinos resulting
from proton-proton collisions. In particular, it is shown that the neutrino
flux from the SNRs above is probably too low to be detected by current and
planned neutrino observatories (Abridged).
