The calculation of scattering kernels with the full treatment of the crystal binding is a very lengthy procedure. In practice it is not possible to compute a kernel for each calculation, but these data are stored on computers for various discrete values of temperature. For high moderator temperatures this full treatment is no longer neces­sary. Table 6.2 shows that whereas at 300 К chemical binding effects can reduce ксЯ by up to 2.4% at 1200 К the reduction is only up to 0.4%; the latter is small and shows that the free gas treatment is adequate above 1200 K. For this reason at high temperatures even solid moderators can be treated as ideal monoatomic gases (free gas model).

In this case the calculation of the scattering kernel becomes very simple. Supposing that the gas atoms have a Maxwellian velocity distribution, the following expression based on simple classical hard sphere collision has been derived by Wigner and Wilkins (ref. 9; see also ref. 1, § 10.1, and ref. 2, p. 26):

ME’- E> = І f erf [, ~ P V#]

+erf [, v|- p VS] — (•-“«* NS+о V5]

-e“”ertNS+WS])if^fi) <6’14)

where crsf is the free atom-scattering cross-section here supposed to be energy independent, T the temperature and

A + 1 A — 1

V 2VA P 2VA ’

This expression can be quickly calculated by a computer so that in some cases the free gas kernels are not even stored, but directly calculated for each case. One must notice that when developing a set of scattering kernels at various temperatures it is important to have a smooth variation of kernel with temperature in order that calculated reactor quantities vary smoothly with temperature. This means that chemical binding should be considered to temperatures somewhat above what might otherwise be thought neces­sary.