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RX~J1713.7$-$3946 is a prototype in the $\gamma$-ray-bright supernovaremnants (SNRs) and is in continuing debates on its hadronic versus leptonicorigin of the $\gamma$-ray emission. We explore the role played by thediffusive relativistic protons that escape from the SNR shock wave in the$\gamma$-ray emission, apart from the high-energy particles' emission from theinside of the SNR. In the scenario that the SNR shock propagates in a clumpymolecular cavity, we consider that the$\gamma$-ray emission from the inside ofthe SNR may arise either from the inverse Compton scattering or from theinteraction between the trapped energetic protons and the shocked clumps. Thedominant origin between them depends on the electron-to-proton number ratio.The diffusive protons that escaped from the shock wave during the expansionhistory can provide an outer hadronic $\gamma$-ray component by bombarding thesurrounding dense matter. The broadband spectrum can be well explained by thistwo-zone model, in which the $\gamma$-ray emission from the inside governs theTeV band, while the outer emission component substantially contributes to theGeV $\gamma$-rays. The two-zone model can also explain the TeV $\gamma$-rayradial brightness profile that significantly stretches beyond the nonthermalX-ray-emitting region. In the calculation, we present a simplified algorithmfor Li & Chen's (2010) "accumulative diffusion" model for escaping protons andapply the Markov Chain Monte Carlo method to constrain the physical parameters.

The role of the diffusive protons in the gamma-ray emission of supernova remnant RX J1713.7$-$3946 --- a two-zone model