Collision-induced flavor instability in dense neutrino gases with energy-dependent scattering

We investigate the collision-induced flavor instability in homogeneous, isotropic, dense neutrino gases in the two-flavor mixing scenario with energy-dependent scattering. We uncover a simple expression of the growth rate of this instability in terms of the flavor-decohering collision rates and the electron lepton number distribution of the neutrino. This growth rate is common to the neutrinos and antineutrinos of different energies, and is independent of the mass splitting and vacuum-mixing angle of the neutrino, the matter density, and the neutrino density, although the initial amplitude of the unstable oscillation mode can be suppressed by a large matter density. Our results suggest that neutrinos are likely to experience collision -induced flavor conversions deep inside a core-collapse supernova even when both the fast and slow collective flavor oscillations are suppressed.