The discussion in chapter 2 of the change in energy, both kinetic and potential, when a spherical nucleus is deformed, showed that many nuclei would be expected to have quite significant quadrupole moments, in agreement with experiment. Moreover, a deformed shell model description was shown by Nilsson to provide a good quantitative description of the shape and spin of many nuclear ground states. However, what was not clear was what aspect of the Nilsson model accounted for nuclei being mainly prolate (cigar-shaped), as can be seen clearly in figure 2.15, and Lemmer and Weisskopf's argument that it is because of the shape of the nuclear potential is first presented.

After discussing the ground-state deformation of nuclei, a microscopic description of collective motion in terms of an independent-particle model is developed in the rest of this chapter. The ground state of the nucleus is generally described by a deformed intrinsic wavefunction. If the deformation is significant, then a variational approach to the motion of deformed nuclei, which avoids the problem of redundant variables inherent in the collective model, is shown to give rise to a rotational spectrum of excited states. The cranking-model expression for the moment of inertia is then derived and the influence of the pairing residual interaction is discussed.

In the shell model, if the residual interaction is diagonalised, then collective features are reproduced. In an approximate treatment of the residual interaction, the schematic model, collective vibrational states are found to correspond in the shell model to a coherent superposition of one-particle one-hole states.