Similarity between Shell Model and Deformed Nucleus Wave Functions

A body coordinate system x^'y^'z^' is defined in which the density of nuclear matter is assumed axially symmetric about the z^' axis, the angular momentum j_z^' of each of the A nucleons in the nucleus about this axis being quantized. The wave function of a nucleon is φ_κ, with j_z^'φ_κ=κφ_κ. The system x^'y^'z^' is rotated relative to a system xyz fixed in space in such a way that the nucleus is in a state of total angular momentum J, with z component M, while the z^' component remains K=κ₁+⋯+κA. The nuclear wave function is ΨMKJ. The φ_κ are so defined that the ΨMKJ are similar to wave functions obtained for shell-theoretical calculations. In order to represent at least 13 low states with A=18 and 19, three φ_κ are needed. These φ_κ resemble χ_κ, the wave functions of particles in a slightly deformed harmonic-oscillator well. Calculated ft values and magnetic moments are also similar to those for shell theory.