We have seen how the treatment of the energy dependence in the transport equation leads to the multi-group formulation. Let us now tackle the problem of the angular dependence of the neutron flux. The approximations used for all practical reactor calculations are characterized by the methods and assumptions with which the angular dependence is treated.

These methods substitute the angular-dependent Boltzmann equation with a system of differential equations in which the angular dependence has been eliminated.

We can distinguish the following approaches:

1. Numerical discretization of the angular dependence (S„ method).

2. Expansion in eigenfunctions (spherical harmonics): Pi or B„ method.

3. Pi expansion truncated to / = 1 and assumption of slowly varying collision density (diffusion approximation).

A rather different approach consists of writing the Boltzmann equation in an integral form in which angular dependence does not explicitly appear (collision probability methods).