  We study the neutrino pairs annihilation into electron-positron pairs
($\nu+{\bar \nu}\to e^- + e^+$) near the surface of a neutron star. The
analysis is performed in the framework of extended theories of gravity. The
latter induce a modification of the minimum photon-sphere radius ($R_{ph}$) and
the maximum energy deposition rate near to $R_{ph}$, as compared to ones of
General Relativity. These results might lead to an efficient mechanism for
generating GRBs.
