Why we use collective model in nuclear physics?

Answer 1

When liquid drop and shell models fail to explain different phenomena like, electric quadrupole moment, magnetic dipole moment 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 figure above shows the energy levels of 238U. 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.

Answer 2

The collective model in nuclear physics is used to describe the vibrational and rotational motion of atomic nuclei as a whole, treating them as a single entity rather than individual nucleons. This model simplifies calculations and provides insights into nuclear properties such as excitation energies and electromagnetic transitions. It is particularly useful for medium to heavy nuclei where the interaction between nucleons gives rise to collective motion.