Calculations of the question of axial asymmetry in nuclei

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·sandl2 forces. The method of matrix diagonalization 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; the incompressibility of nuclear matter is one of these.The eigenvalues for single particle states in the N = 3, 4, 5 and 6 shells are listed for β = 0.3 and γ = 0(112π)13π.