The neutrino emission processes play an important role in different astrophysical scenarios, in particular during the stellar core collapse and the cooling of a protoneutron star. Recently, several authors have studied some processes such as neutrino-electron scattering (Smit et al. 1996 and Cernohorsky J. 1994), neutrino coherent scattering off nuclei (Leinson 1992), effects of nucleon spin fluctuations in the weak interaction rates (Janka et al. 1996) or neutrino reactions with strange matter (Reddy & Prakash 1997) in order to obtain the rates to be used in transport calculations. We will focus on the thermal pair emission-absorption process (TP in the next). In the stellar core collapse scenario, discrepancies in the efficiency of TP in the heating of matter outside the neutrinosphere have been noticed (see, e.g., Janka 1990 and references therein) and in order to obtain meaningful calculations of the energy deposition rate it is necessary to carefully consider the angular dependence of the distribution function.

In some calculations involving neutrino transport, only the
and terms of the Legendre expansion of the collision
kernel are included as in Bruenn (1985) and Suzuki (1989).
This approach could suffice where the diffusion
approximation remains valid. The justification of that approach
relies on the fact that the and order
terms appear multiplying and order terms of the
Legendre expansion of the
neutrino distribution function (*I*) and they
vanish in the diffusion limit.
However, if a general closure relation is used which is
different to , these higher order
terms of *I* do not vanish, and their contribution becomes
especially important in the semi-transparent region.
In this paper we will also analyze the influence of
the different closure relations that have been considered in recent
years.

This work is organized as follows: In Sect. 2 we present the Legendre expansion of the TP production and absorption kernels and we give explicit expressions for the to order terms. In Sect. 3 we study how these new terms affect the sources in the two-moment closure transport equations. In Sect. 4 we discuss the effects of the new terms and the influence of the closure relation.