Dependence of Nuclear Energy on Axial Asymmetry and its Consequences

Abstract

An investigation is carried out to determine whether or not on the basis of theory one expects axial asymmetry in heavy nuclei. The average one-body potential well is taken as an anisotropic harmonic oscillator, modified by the usual ℓ ∙ s and ℓ² forces. The method of matrix diagonalisation is used to find the eigenvalues. Residual interaction between nucleons is also treated in the pairing approximation. The calculations show that prolate axial symmetry is favoured in each of the nuclei considered. It is possible to indicate the underlying physical reasons for this result. Assuming equilibrium prolate axial symmetry an attempt is made to understand the collective excited levels in the transition region, i.e. the region between spherical nuclei and permanently deformed nuclei. A model calculation is done to show how the levels can be obtained.