  We compare the $\gamma$-ray spectra from 10 middle-aged supernova remnants
(SNRs), which are interacting with molecular clouds (MCs), with the model
prediction from widely used escaping scenario and direct interaction scenario.
It is found that the $\gamma$-ray data is inconsistent with the escaping
scenario statistically, as it predicts a diversity of spectral shape which is
not observed. The inconsistency suggests that the free escape boundary adopted
in the escaping model is not a good approximation, which challenges our
understanding of cosmic ray (CR) escaping in SNRs. In addition, we show that
ambient CRs is potentially important for the $\gamma$-ray emission of
illuminated MCs external to W28 and W44. In direct interaction scenario, the
model involving re-acceleration of pre-existing CRs and adiabatic compression
is able to explain the emission from most SNRs. The dispersion shown in the TeV
data is naturally explained by different acceleration time of CR particles in
SNRs. Re-acceleration of pre-existing CRs suggests a transition of seed
particles, which is from thermal injected seed particle in young SNRs to
ambient CRs in old SNRs. The transition needs to be tested by future
multi-wavelength observation. In the end, we propose that radiative SNR without
MC interaction is also able to produce a significant amount of $\gamma$-ray
emission. A good candidate is S147. With accumulated Fermi data and CTA in
future we expect to detect more remnants like S147.
