  The paradigm-changing possibility of collective neutrino-antineutrino
oscillations was recently advanced in analogy to collective flavor
oscillations. However, the amplitude for the backward scattering process
$\nu_{\mathbf{p}_1}\overline\nu_{\mathbf{p}_2}\to\nu_{\mathbf{p}_2}\overline\nu_{\mathbf{p}_1}$
is helicity-suppressed and vanishes for massless neutrinos, implying that there
is no off-diagonal refractive index between $\nu$ and $\overline\nu$ of a
single flavor of massless neutrinos. For a nonvanishing mass, collective
helicity oscillations are possible, representing de-facto $\nu$--$\overline\nu$
oscillations in the Majorana case. However, such phenomena are suppressed by
the smallness of neutrino masses as discussed in the previous literature.
