### Abstract

In elementary physics, collisions are usually studied by employing the conservation of momentum, and sometimes also the conservation of kinetic energy. However, in nuclear reactions, changes of mass that complicate the situation often occur. To illustrate the latter, we shall cite two examples of endoergic nuclear reactions,^{1} i.e., those for which energy must be supplied to make the reaction proceed. A typical situation is given by the equation *A* + *B* → *C* + *D* + *Q*, (1) where particles *A, B, C*, and *D* are expressed in terms of the energy‐equivalent of the particle masses, according to the Einstein relation *E* = *mc* ^{2}, and where *Q* is a negative energy quantity, corresponding to the excess of mass of (*C* + *D*) over that of (*A* + *B*). Equation (1) is just an alternate statement of the conservation of total energy. Typically, in the lab system (L), energy is supplied as kinetic energy “*T*” of particle *A*, and particle *B* is at rest. Thus, to conserve momentum, particles *C* and *D* must compensate for the momentum corresponding to *T*. Often, it is desirable to know the minimum value of *T* that will conserve both energy and momentum, i.e., the threshold value of *T*, known as *T* _{th}, that will just allow the reaction to proceed. At threshold, the particles *C* and *D* will have their minimum possible kinetic energies. In the center‐of‐mass system of coordinates (Z) in which the input momentum is zero, at threshold, the products *C* and *D* are each stationary, and this requirement will allow us to calculate the corresponding *T* _{th} in the lab system (L). The Z system is often termed the “center‐of‐mass” system, but it is more properly termed the “zero‐momentum” system.

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