Do neutrinos become flavor unstable due to collisions with matter in the supernova decoupling region?

In core-collapse supernovae, the neutrino density is so large that neutrino flavor instabilities, leading to flavor conversion, can be triggered by the forward scattering of neutrinos among each other, if a crossing between the angular distributions of electron neutrinos and antineutrinos exists (fast instability in the limit of vanishing vacuum frequency) or in the presence of perturbations induced by the neutrino vacuum frequency (slow instability). Recently, the conjecture has been advanced that neutrino collisions with the medium could be another mean to kick start flavor change (collisional instability). Inspired by a spherically symmetric core-collapse supernova model with mass $18.6M_{\odot }$, we compute the neutrino angular distributions solving the kinetic equations for an average energy mode and investigate the occurrence of flavor instabilities at different postbounce times, ranging from the accretion phase to the early cooling phase. We find that fast and slow flavor instabilities largely dominate over the collisional ones in the decoupling region for all postbounce times. While more work is needed to assess the relevance of collisional instabilities in neutrino-dense environments, our findings suggest that neutrino collisions with matter affect the flavor evolution in the decoupling region but are not responsible for triggering flavor conversion, if crossings in the neutrino lepton number angular distribution exist.