  We calculate the Legendre expansion of the rate of the process $\nu +
\bar{\nu} \leftrightarrow e^+ + e^-$ up to 3rd order extending previous results
of other authors which only consider the 0th and 1st order terms. Using
different closure relations for the moment equations of the radiative transfer
equation we discuss the physical implications of taking into account quadratic
and cubic terms on the energy deposition outside the neutrinosphere in a
simplified model. The main conclusion is that 2nd order is necessary in the
semi-transparent region and gives good results if an appropriate closure
relation is used.

Astrophysics