  Core-collapse supernova neutrinos undergo a variety of phenomena when they
travel from the high neutrino density region and large matter densities to the
Earth. We perform analytical calculations of the supernova neutrino fluxes
including collective effects due to the neutrino-neutrino interactions, the
Mikheev-Smirnov-Wolfenstein (MSW) effect due to the neutrino interactions with
the background matter and decoherence of the wave packets as they propagate in
space. We predict the numbers of one- and two-neutron charged and
neutral-current electron-neutrino scattering on lead events. We show that, due
to the energy thresholds, the ratios of one- to two-neutron events are
sensitive to the pinching parameters of neutrino fluxes at the neutrinosphere,
almost independently of the presently unknown neutrino properties. Besides,
such events have an interesting sensitivity to the spectral split features that
depend upon the presence/absence of energy equipartition among neutrino
flavors. Our calculations show that a lead-based observatory like the Helium
And Lead Observatory (HALO) has the potential to pin down important
characteristics of the neutrino fluxes at the neutrinosphere, and provide us
with information on the neutrino transport in the supernova core.
