3.1. Potential scattering and resonance reactions

All reactions between neutrons and atomic nuclei can be divided into two main categories.

1. Potential scattering. The neutron is deflected by the potential field of the nucleus. If the neutron wavelength is much greater than the radius of the nucleus, the potential scattering cross-section is approximately energy independent.

2. Resonance reactions. A compound nucleus is formed. This compound nucleus is in an excited state the energy of which consists of the binding energy between nucleus and neutron and of the neutron kinetic energy. In heavy nuclides there is a high density of possible excited states. Compound nuclei are easily formed when the sum of binding and collision energy corresponds to quantum states of the compound nucleus so that the cross-section presents sharp peaks around these energies (resonances). The compound nucleus decays in different ways (“channels”): neutron emission (scatter­ing), у emission (capture), fission, etc., each mode having a different probability of occurrence.

In the case of resonance scattering we can distinguish the case in which after neutron emission the nucleus returns to normal unexcited state (elastic scattering) and the case in which part of the neutron energy is retained as excitation energy of the nucleus (inelastic scattering). In light nuclides excited states have too high an energy level to be of interest in nuclear reactors, while in heavy nuclides these energies are much lower. If A; is the decay constant of the compound nucleus along the ith channel, the probability of decay along this channel is

where Г, = ЙА, partial width,

Г = X Гі total level width.

These widths correspond to the energy uncertainty of each compound state. We have then Г„, neutron width (probability of neutron emission), I, radiation width (capture with у radiation emission), etc.