Binding energy

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:

• For most nuclei, the binding energy per nucleon is about 8 MeV.
• Binding is less for light nuclei (these are mostly surface) but there are peaks for A in multiples of 4. (But note that the peak for is slightly lower than that for . What does this imply?)
• The most stable nuclei ( and ) are in the region .
• Light nuclei can gain binding energy per nucleon by fusing; heavy nuclei by fissioning.
• There is no striking structure that might indicate shell effects.
• The decrease in binding energy per nucleon for A;SPMgt;60 can be ascribed to the repulsion between the (charged) protons in the nucleus: the Coulomb energy grows in proportion to the number of possible pairs of protons in the nucleus, .

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.