We begin this appendix by considering neutron cross-sections. There is some simplification in the case of neutrons, since they are electrically neutral and do not interact through the long-range Coulomb force. To a good approximation they can be considered to interact only through the short-range nuclear force. The concepts developed for neutrons may be applied almost immediately to other electrical neutral particles, such as photons. We then turn to the case of charged particles.

A.1 Neutron and photon cross-sections

We consider a neutron approaching from a distance a nucleus which is at rest. (Any interactions between the neutron and the atomic electrons will be neglected.) We suppose that, if the nucleus were not present, the probability of the neutron passing anywhere through a circle of radius a, centred on the nucleus and perpendicular to the direction of the neutron's motion, would be uniform (Fig. A.1), i.e. the probability of it passing through an area 𝛿A would be 𝛿A/(ℼa2). We can think of the neutron as a classical particle, or better, as a quantum-mechanical wave-packet. The radius a must be large compared with both the size of the wave-packet and the size of the nucleus. With the nucleus present, an interaction can take place, for example scattering, induced fission, or radiative capture. It is found that, provided a is large enough, the probability of an interaction is inversely proportional to the area ℼa2, i.e.