  Fast-pairwise neutrino oscillations potentially affect many aspects of
core-collapse supernova (CCSN): the explosion mechanism, neutrino signals, and
nucleosynthesis in the ejecta. This particular mode of collective neutrino
oscillations has a deep connection to the angular structure of neutrinos in
momentum space; for instance, the appearance of electron neutrinos lepton
number (ELN) angular crossings in momentum space is a good indicator of
occurrences of the flavor conversions. However, many multi-dimensional
(multi-D) CCSN simulations are carried out with approximate neutrino transport
(such as two-moment methods), which limits the access to the angular
distributions of neutrinos, i.e., inhibits ELN-crossing searches. In this
paper, we develop a new method of ELN-crossing search in these CCSN
simulations. The required data is the zero-th and first angular moments of
neutrinos and matter profile, all of which are available in CCSN models with
two-moment method. One of the novelties of our new method is to use a
ray-tracing neutrino transport to determine ELNs in the direction of the
stellar center. It is designed to compensate for shortcomings of the crossing
searches only with the two angular moments. We assess the capability of the
method by carrying out a detailed comparison to results of full Boltzmann
neutrino transport in 1D and 2D CCSN models. We find that the ray-tracing
neutrino transport improves the accuracy of crossing searches; indeed, the
appearance/disappearance of the crossings is accurately detected even in the
region of forward-peaked angular distributions. The new method is
computationally cheap and has a benefit of efficient parallelization; hence, it
will be useful for ELN-crossing searches in any CCSN models employed two-moment
neutrino transport.
