Xiao

RX~J1713.7$-$3946 is a prototype in the $gamma$-ray-bright supernova remnants (SNRs) and is in continuing debates on its hadronic versus leptonic origin of the $gamma$-ray emission. We explore the role played by the diffusive relativistic protons that escape from the SNR shock wave in the $gamma$-ray emission, apart from the high energy particles’ emission from the inside of the SNR. In the scenario that the SNR shock propagates in a clumpy molecular cavity, we consider that the $gamma$-ray emission from the inside of the SNR may either arise from the IC scattering or from the interaction between the trapped energetic protons and the shocked clumps. The dominant origin between them depends on the electron-to-proton number ratio. The surrounding molecular cavity wall is considered to also produce $gamma$-ray emission due to the “illumination” by the diffusive protons that escaped from the shock wave during the expansion history. We simplify the algorithm for Li & Chen’s (2010) “accumulative diffusion” model for diffusive escaping protons. This two-zone model is fit to the broad-band spectrum of the SNR that incorporates the updated 5-yr Fermi data, with application of the MCMC method. The broad-band spectrum can be well explained by this two-zone model, in which the $gamma$-ray emission from the inside governs the TeV band, while the outer emission component substantially contributes to the GeV $gamma$-rays. The two-zone model can also explain the TeV $gamma$-ray radial brightness profile that significantly stretches beyond the nonthermal X-ray emitting region.