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Gamma-ray sources like V407 Cygni in Symbiotic Stars

Using a simple accelerating model and an assumption that $γ$-rays originate from $p-p$ collisions for a $π^0$ model, we investigate $γ$-ray sources like V407 Cygni in symbiotic stars. The upper limit of their occurrence rate in the Galaxy is between 0.5 and 5 yr$^{-1}$, indicating that they may be an important source of the high-energy $γ$-rays. The maximum energies of the accelerated protons mainly distribute around $10^{11}$ eV, and barely reach $10^{15}$ eV. The novae occurring in D-type SSs with ONe WDs and long orbital periods are good candidates for $γ$-ray sources. Due to a short orbital period which results in a short acceleration duration, the nova occurring in symbiotic star RS Oph can not produce the $γ$-ray emission like that in V407 Cygni.