Gamma rays from molecular clouds illuminated by accumulated diffusive protons from supernova remnant W28

W28 is one of the archetype supernova remnants (SNRs) interacting with molecular clouds. H.E.S.S. observation found four TeV sources which are coincident with the molecular clouds (MCs) around W28, but Fermi LAT detected no prominent GeV counterparts for two of them. An accumulative diffusion model is established in this Letter and the energetic protons colliding the nearby MCs are considered to be an accumulation of the diffusive protons escaping from the shock front throughout the history of the SNR expansion. We have fitted the gamma ray spectra of the four sources and naturally explained the GeV spectral break of the northeastern source (source N) and the nonsignificant GeV emission of the southern sources A and C. The distances of sources A and C from the SNR centre are found to be much larger than those of sources N and B, which may be the basic reason for the faint GeV gamma rays of the two former sources.