On the Axial Symmetry of the Nilsson Model Nucleus

The shape of the oscillator potential necessary to give the minimum energy for a systsm of single fermions in an anisotropic oscillator with Nilsson spin-orbit coupling is calculated. The number of particles is limited to 50 or less and is even. The preferred distortion parameters ( beta and gamma ) are plotted vs. number of particles, and energy maps (energy vs. beta ) are given for various amounts of spin-orbit coupling. Implications of the calculations, e.g., that the Bohr strong coupling approximation and the Davydov- Filippov model cannot easily be justified, are discussed. (D.L.C.)