Question

238 U nucleus has a 0+ ground state and the first four excited states are The 2 (0.045 MeV), 4 (0.148 MeV), 6 (0.309 MeV) and 8 (0.523 Mev) Briefly characterise the collective motion of this nucleus, and motivate your answer. (c) (2 marks)

Answer 1

In addition to individual nucleons changing orbits to create excited states of the
nucleus as described by the Shell Model, there are nuclear transitions that involve many
(if not all) of the nucleons. Since these nucleons are acting together, their properties are called collective, and their transitions are described by a Collective Model of nuclear
structure.

High-mass nuclei have low-lying excited states that are described as vibrations
or rotations of non-spherical nuclei. Many of these collective properties are similar to
those of a rotating or vibrating drop of liquid, and in its early development the Collective
Model was called the Liquid-Drop Model. The first important application of the Liquid-
Drop model was in the analysis of nuclear fission, in which a massive nucleus splits into
two lower-mass fragments. The Liquid Drop Model calculates an energy barrier to fission
as a sum of the repulsive Coulomb forces between the protons of the nucleus and the
attractive surface tension of the skin of the “liquid drop” nucleus. If the barrier is low
enough the nucleus might fission spontaneously. For higher barriers, it takes a nuclear
reaction to induce fission.

The quantum numbers, level spacings, and gamma ray transition probabilities identify these levels as rotational states of a non-spherical nucleus. Nuclei showing collective properties are usually those with many valence nucleons, that is, those with proton or neutron numbers that are far from
filled shells. As with the Shell Model, the Collective Model permits the calculation of
spin-parity assignments and transition probabilities that are in good agreement with the
measured properties of collective nuclei