In order to understand nuclear reactions, we have first in Section 2.1 to name the arrangement of nucleons in a nucleus in terms of the quantum-mechanical state of a nucleus, and then describe the different ways in which these nucleons may be rearranged during nuclear reactions. Reactions which proceed quickly, and thus called direct reactions, are distinguished in Section 2.2 from the comparatively slow reactions that also occur, which are called compound nucleus reactions. Almost all reactions involve the collision of two nuclei, and Section 2.3 shows how the conservations of mass, energy and momentum may be described in either non-relativistic or relativistic kinematics. Section 2.4 describes how the rates of nuclear reactions are measured in terms of cross sections, which have units of area. We show how these cross sections are different in the laboratory and center of- mass coordinate frames of reference, then in the final subsection 2.4.4 how the cross sections may be determined from the wave functions that are solutions of a Schrödinger equation for the pair of reacting nuclei.

Kinds of states and reactions

States of nuclei

Nuclei are aggregations of Z protons and N neutrons in a particular configuration or state described by a wave function φ determined from quantum mechanics, given the strong and electromagnetic potentials V between the A=N + Z constituent nucleons. A state is called bound if energy is needed to remove one or more nucleons to large distances.