The binding energy B of a nucleus consisting of Z protons and N=A-Z neutrons is defined implicitly in the atomic mass
where is the mass of a hydrogen atom. (Note that B is positive for a bound system). The atomic mass scale is determined by defining the mass of the carbon ( C) atom to be exactly 12.0 atomic mass units (amu, symbol: u). This in turn determines 1 u to have the value 931.49432(28) MeV.
We can also define the mass excess
where M is measured in amu. (Often is expressed in MeV: M will then be in MeV, and A will have to be multiplied by 1 u).
The atomic mass may be determined in mass spectrometers or by nuclear reactions. The binding energy per nucleon B(A,Z)/A for 342 beta-stable nuclei from the 1993 mass tabulation is plotted as a function of A in Figure .
This figure gives us an overview nuclear stability and the possible rearrangement of nucleons (at least in the stable nuclei). Note that greater stability of a nucleus implies a greater binding energy per nucleon. The physics of the shape of this curve will be discussed below. The following may be noted at this stage:
The binding energy for massive nuclei (A;SPMgt;60) thus grows roughly as A; if the nuclear force were long range, one would expect a variation in proportion to the number of possible pairs of nucleons, i.e. as . The variation as A suggests that the force is saturated; the effect of the interaction is only felt in a neighbourhood of the nucleon.