Solution (source code)

= Solution

A <Positron> signal is correct for the reactor's \b[antineutrinos], through <inverse beta decay>,
$$
\bar\nu_e+p\to e^++n,\qquad E_{\bar\nu,\rm th}\simeq1.806\ \mathrm{MeV}.
$$
A true <electron neutrino> <charged current> interaction instead produces an <electron>, for example $\nu_e+n\to e^-+p$. This corrects the source's loose use of “neutrino” for the reactor beam.

After slowing, the <Positron> annihilates with an <electron>, generally producing two $511$ keV <photons>. The prompt visible <energy> includes both the <Positron> kinetic <energy> and annihilation <energy>; neglecting the small <neutron> recoil,
$$
E_{\rm prompt}\simeq T_{e^+}+2m_e\simeq E_{\bar\nu}-0.782\ \mathrm{MeV}.
$$
A delayed <neutron> capture supplies a powerful coincidence tag. Detecting only two annihilation <photons> discards useful prompt <energy> and does not uniquely identify the <charged current> event.