  We investigate the non-radiative decay during nucleosynthesis of a massive
tau neutrino with mass 0.1 - 1 MeV into an electron neutrino and a scalar or
pseudoscalar particle, $\phi$. The full Boltzmann equation is used and shown to
give markedly different results than the usual non-relativistic formalism for
relativistic or semi-relativistic neutrino decays. Indeed, the region we
investigate is where the formalism that has previously been applied to solving
this problem is expected to break down. We also compare the nucleosynthesis
predictions from this scenario with results from the standard model and with
some of the available observational determinations of the primordial
abundances. It is found that for relativistic or semi-relativistic decays the
helium abundance can be significantly lowered without changing other light
element abundances. Since a problem with the standard model of Big Bang
nucleosynthesis is that helium appears to be overproduced, a decay of the type
we discuss can be a possible solution.
