Atomic and Nuclear Physics
Liquid Drop Model of a Nucleus
The nucleus is held together by the attractive nuclear force between nucleons, which was
discussed in a previous chapter. The characteristics of the nuclear force are listed below.
range, with essentially no effect beyond nuclear dimensions
( 10-13 cm)
stronger than the repulsive electrostatic forces within the nucleus
independent of nucleon pairing, in that the attractive forces between pairs of
neutrons are no different than those between pairs of protons or a neutron and a
saturable, that is, a nucleon can attract only a few of its nearest neighbors
One theory of fission considers the fissioning of a nucleus similar in some respects to the splitting
of a liquid drop. This analogy is justifiable to some extent by the fact that a liquid drop is held
together by molecular forces that tend to make the drop spherical in shape and that try to resist
any deformation in the same manner as nuclear forces are assumed to hold the nucleus together.
By considering the nucleus as a liquid drop, the fission process can be described.
Referring to Figure 18(A), the nucleus in the ground state is undistorted, and its attractive nuclear
forces are greater than the repulsive electrostatic forces between the protons within the nucleus.
When an incident particle (in this instance a neutron) is absorbed by the target nucleus, a
compound nucleus is formed. The compound nucleus temporarily contains all the charge and
mass involved in the reaction and exists in an excited state. The excitation energy added to the
compound nucleus is equal to the binding energy contributed by the incident particle plus the
kinetic energy possessed by that particle. Figure 18(B) illustrates the excitation energy thus
imparted to the compound nucleus, which may cause it to oscillate and become distorted. If the
excitation energy is greater than a certain critical energy, the oscillations may cause the
compound nucleus to become dumbbell-shaped. When this happens, the attractive nuclear forces
(short-range) in the neck area are small due to saturation, while the repulsive electrostatic forces
(long-range) are only slightly less than before. When the repulsive electrostatic forces exceed
the attractive nuclear forces, nuclear fission occurs, as illustrated in Figure 18(C).