The averaging of cross-section for the reflector regions can be done with any of the codes for homogeneous spectrum calculations which have been analysed.

A fission source is usually specified in order to provide neutrons to start the calculation. The error due to the introduction of this source can usually be neglected. The effect of the neutrons leaking from the core in the reflector can be taken into account using negative bucklings. Unfortunately, these bucklings are very important in the neutron balance of the reflector and usually they are not known to a very high accuracy. This can strongly influence the neutron spectrum, and negative fluxes can be easily obtained, so that it is usually better to calculate with zero bucklings. These calculations have to be repeated for the various parts of the reflectors, having different composition, density and temperature.

This rather crude method is often sufficiently accurate, but the problems posed by these calculations show that in this case the assumption made in performing space — independent spectrum calculation is no longer valid, since the spectrum, in this case, is not only determined by the characteristics of the region under consideration, but also greatly influenced by the neighbouring regions.

The thermal diffusion length varies from 10 to 30 cm depending on the core loading, and in this range very important spectral changes occur. An example is shown in Fig. 8.2<20) where the thermal spectrum is plotted at different positions. This is a rather extreme example because its fuel loading corresponds to the ratio C/U = 2500 which is very high for an HTR power station, but may occur in experimental reactors. If a high accuracy is needed a one-dimensional diffusion calculation with a high number of groups (e. g. 26 in the Fort St. Vrain case) can be performed including core and reflector. The space-dependent spectrum obtained in this way can be used for the condensation of cross-sections for the whole reflector or for some part of it. Similar methods can be used at other interfaces between regions with strong spectral differences.

In highly simplified calculations it is possible to avoid the explicit treatment of the reflector, increasing the size of the core by an amount (reflector saving) defined in such a way as to give to the bare reactor the same kcя of the actual reflected reactor. This

treatment neglects all spectral changes between core and reflector and therefore gives usually a very inaccurate power distribution.