THE SHELL-MODEL DISTRIBUTION OF NUCLEAR SHAPES

Nuclei have giant resonance and low-energy quadrupole shape-changing degrees of freedom. It is shown that the giant-resonance degrees of freedom can be factored out by restricting to states in which the nucleus is in its giant-resonance vibrational ground state. The set of possible nuclear shapes then becomes a discrete countable set and is in one-to-one correspondence with the set of irreducible sp(3, R) representations in the nuclear shell-model Hilbert space. The relationship between observable deformation parameters and the labels of sp(3, R) irreps is given. Methods are presented for classifying sp(3, R) irreps and ordering them such that the most relevant ones for the description of low-lying states can be selected. It is shown that high-lying shell-model configurations are needed to obtain the deformations observed in deformed nuclei and that such configurations are brought down into the low-energy arena by deformation and spin-orbit interactions.