Perturbation theory deals with the calculation of the effect of small changes in the properties of a reactor. If the perturbation is sufficiently small it is not necessary to perform a complete new calculation of the reactor, but the adjoint function of the transport operator can be used to obtain the response to the small change (perturba­tion). Perturbation theory used to be a very important tool for reactor calculations before the general introduction of high-speed computers. It was used to calculate temperature coefficients, control rod worths, etc. In practice the so-called perturbations are seldom very small and therefore the accuracy of the method is rather limited. Because of this reason it is nowadays preferred to perform two numerical calculations one on the unperturbed and one on the perturbed system, obtaining as a difference the

effect of the perturbation (e. g. reactivity variation due to control rod insertion). It is very important that these two calculations are absolutely identical (e. g. same meshes) except for the perturbation. Only in cases where the perturbation is really small can perturbation theory be more accurate than numerical methods.

Because of the above considerations we will not discuss this method, for which we refer the reader to the existing literature (e. g. ref. 2, chap. 6).

We will simply here recall the definition of neutron importance. This quantity, which is seldom used for reactor calculation, is frequently used to give qualitative explana­tions and to get a “feeling” of what happens in a reactor.

The neutron importance ф*(г, SI, E) can be defined as the increase in the neutron population of a critical reactor due to the introduction of one neutron in point r, with energy E in the solid angle SI. It can be simply demonstrated (ref. 2, § 6. Id) that the neutron importance is the adjoint function of the transport operator. The definition of importance can be extended to the group diffusion approximation of transport theory. In one group theory the importance is coincident with the neutron flux. It is intuitively clear that the neutron importance is high in the centre of the core, while it is zero at the outer surface for the outward direction. Perturbation theory is often used in order to obtain the parameters for point model kinetics calculations (see § 12.3).