The Nucleus and the Strong Interaction 229
This can be tested by studying the interaction of photons with deuterons.
If the energy of the photon is not very great, the deuteron will scatter the
photon. If the energy of the photon becomes large enough, however, the
photon is capable of destroying the nuclear bond and disintegrating the
deuteron. The process of the photo-disintegration of the deuteron may
be represented as follows: γ + D → p + n. The threshold energy for
which this reaction occurs is exactly 2.22 MeV, the binding energy of
the deuteron. Unless the photon provides enough energy to provide the
necessary mass, the deuteron will not disintegrate.
The nuclear binding energy for other nuclei is determined in exactly
the same way we determined it for the deuteron. Let us consider an
arbitrary nucleus of Z proton and N neutrons with a mass M. The binding
energy of the nucleus, EB, is obtained by subtracting the mass of
the nucleus from the mass of the nucleons and hence EB = Zmpc^2 +
Nmnc^2 – Mc^2.
The binding energy turns out to be basically proportional to the
number of nucleons A = Z + N. This indicates that the nucleons inside a
nucleus do not interact with all the other nucleons but rather the nucleus
force is saturated and each nucleon only interacts with two or three other
nucleons in the nucleus. If the nucleons were interacting with all the
nucleons in the nucleus, there would be A(A – 1)/2 individual nucleon-
nucleon interactions among the A nucleons in the nucleus. If the
potential energy of each nucleon-nucleon interaction were equal to ENN,
then one would expect the binding energy EB to equal A(A – 1) ENN /2.
One would then find the binding energy proportional to A^2 and not A.
The saturation of the nuclear force indicated by the behaviour of EB is
another reflection of the finite range of the nuclear force.
The neutron and the proton have the same nuclear force. This fact is
reflected in the fact that the number of neutrons and protons in the stable
nuclei are about the same. The reason that stable nuclei composed
exclusively or principally of either neutrons or protons does not occur is
because of the Pauli exclusion principle. The proton and the neutron
are both spin ½ particles and hence are affected by the Pauli exclusion
principle, which does not allow more than one proton or one neutron
to have the same quantum numbers. A proton and a neutron may have
the same quantum numbers in the nucleus because they are different
particles. The nucleons in a nucleus assume different energy states
somewhat like the electrons surrounding the nucleus. If a nucleus were
filled exclusively with protons, the higher energy states would become