  Fast-pairwise collective neutrino oscillation represents a key uncertainty in
the theory of core-collapse supernova (CCSN). Despite the potentially
significant impact on CCSN dynamics, it is usually neglected in numerical
models of CCSN because of the formidable technical difficulties of
self-consistently incorporating this physics. In this paper, we investigate the
prospects for the occurrence of fast flavor conversion by diagnosing electron
neutrino lepton number (ELN) crossing in more than a dozen state-of-the-art
three-dimensional CCSN models. ELN crossings is a necessary condition for
triggering flavor conversion. Although only zeroth and first angular moments
are available from the simulations, our new method enables us to look into the
angular distributions of neutrinos in momentum space and provide accurate
insight into ELN crossings. Our analysis suggests that fast flavor conversion
generally occurs in the post-shock region of CCSNe, and that explosive models
provide more favorable conditions for the flavor conversion than failed CCSNe.
We also find that there are both common and progenitor-dependent
characteristics. Classifying ELN crossings into two types, we analyze the
generation mechanism of each case by scrutinizing the neutrino radiation field
and matter interactions. We find key ingredients of CCSN dynamics driving the
ELN crossings: proto-neutron star (PNS) convection, asymmetric neutrino
emission, neutrino absorptions and scatterings. This study suggests that we
need to accommodate fast flavor conversions in realistic CCSN models.
