Until now we have considered spectrum calculations based on B„ or Pi approxima­tion to transport theory. Subject to the assumptions discussed in § 4.10 it is possible to calculate neutron spectra using the multi-group diffusion formulation. This would be rather inaccurate in case of scattering by light nuclides like hydrogen, but it is usually sufficient for graphite. The computer codes based on this method are very fast and often used for HTR calculations.

These codes are based on a multi-group formulation of eqn. (4.63)

(8.7)

This is a homogeneous system of algebraic linear equations and ксЯ is its greatest eigenvalue. First ксЯ has to be calculated and then the can be obtained for all groups i.

If В2 is not specified as a function of energy it is also possible to set ксЯ = 1 and B2 is then the eigenvalue of the problem. The programme can then calculate the smallest eigenvalue. This is equivalent to calculate the dimensions of the critical bare reactor whose material properties are defined by the parameters of eqn. (8.7).

Both approaches are possible in the MUPO code/7’8’ which solves eqns. (8.7) in forty-three groups. This code which is largely used in Europe for HTR calculations has the advantage of being extremely fast in comparison with most other spectrum calculations. Being based on multi-group diffusion theory it cannot be used for light moderators like water, but is sufficiently accurate for graphite or beryllium. Besides in this code only slowing down due to collisions with the moderator is considered, so that inelastic scattering with heavy atoms is neglected. This is also quite an acceptable approximation for most thermal reactors.

The equivalence relation is used in MUPO for resonance calculations.