The Nucleus and the Strong Interaction 227
strong since the protons are so close to each other. The electric force
between two protons at a distance of one fermi from each other equals
250 Newtons. This force acting on a free proton would produce an initial
acceleration of over 10^29 m/sec^2 or 10^28 times the acceleration of a body
falling at the surface of the earth. How is the stability of the nucleus to
be explained in terms of this enormously strong repulsive force? The
neutron carries no charge and therefore cannot contribute any attractive
force. The gravitational force is attractive but much, much weaker than
the electric force by a factor of 10^40 and hence can be completely
ignored. The magnetic forces, which arise from the magnetic moments of
the proton and the neutron are also much weaker than the electric force
and are not necessarily always attractive. The only way we can account
for the stability of nuclei, which, implies a net attractive force between
all the nucleons is to assume the existence of another force much
stronger than the electric force, which we shall appropriately call the
nuclear force.
The nuclear force is also referred to as the strong interaction because
of its great strength. The nucleus force is the same for neutrons as it is for
protons. The force is a short-range force, which acts only when the
separation of the nucleons is less than 1 or 2 fermis. The force in this
range is extremely strong about 100 times the electric force and basically
attractive. If the separation of the nucleons becomes really small,
however, less than ½ a fermi, then the force becomes repulsive. The size
of the nucleus is determined by the nature of the nuclear force. The
radius of nucleus can never be more than a few fermis otherwise there
would be no attractive force to hold it together. It also cannot be much
less than a fermi, on the other hand, because the nuclear force becomes
repulsive at really small distances preventing a general collapse of the
nucleus. Much has been learned about the nuclear force by studying the
scattering of protons by protons. We shall discuss this interaction in
greater detail in the next chapter on elementary particles. For the purpose
of discussing nuclear physics the above description of the nuclear force
will suffice.
Nuclear Binding Energy
One of the earliest indications of the strength of the nuclear force was the
size of the nuclear binding energy compared with atomic binding energy.
If two particles form a bound state due to an attractive force, then the