Higher Order Perturbation Calculation for Deformed Nuclei

The shape of the nucleus plays an important role in various nuclear phenomena. It is now generally agreed, in the nuclear shell model, that nuclei with each shell filled with nucleons have a spherical shape, and that those nuclei with some protons and neutrons missing from the last shell, deviate from a sphere. The problem of spheroidal shape has been investigated by several methods. Investigation of asymmetric nuclear deformations, which have been suggested by experimental evidence, is still in its early stages due mainly to the mathematical complexity involved in solving the wave equation for an asymmetric potential. Lee and Inglis have investigated asymmetric deformations using the spheroidal harmonic oscillator potential and a perturbation which causes a pear-shape. They were, however, unable to show that such a nucleus is stable in the second order approximation. This problem has recently been investigated further by Lee and others by employing Nilsson\u27s model where the spherical harmonic oscillator is chosen as the basic representation. It is, however, interesting to compare the results from the two procedures since the wave functions used by Lee and Inglis are correct ones, although they have ignored the spin-orbit coupling term. To further pursue the investigation of asymmetric deformations using the perturbed spheroidal harmonic oscillator, it is necessary to extend perturbation theory to include the fourth order term as given in Chapter II. In Chapter III, the matrix elements allowed by the harmonic oscillator quantum numbers are calculated. In Chapter IV the fourth order energy term resulting from the incorporation of these matrix elements is given