Abstract
Light neutron-rich even-even nuclei, of which the ground state is oblately deformed, are looked for, examining the Nilsson diagram based on realistic Woods-Saxon potentials. One-particle energies of the Nilsson diagram are calculated by solving the coupled differential equations obtained from the Schrödinger equation in coordinate space with the proper asymptotic behavior for for both one-particle bound and resonant levels. The eigenphase formalism is used in the calculation of one-particle resonant energies. Large energy gaps on the oblate side of the Nilsson diagrams are found to be related to the magic numbers for the oblate deformation of the harmonic-oscillator potential where the frequency ratios () are simple rational numbers. In contrast, for the prolate deformation the magic numbers obtained from simple rational ratios of () of the harmonic-oscillator potential are hardly related to the particle numbers, at which large energy gaps appear in the Nilsson diagrams based on realistic Woods-Saxon potentials. The argument for an oblate shape of Si is given. Among light nuclei the nucleus C is found to be a good candidate for having the oblate ground state. In the region of the mass number the oblate ground state may be found in the nuclei around Ni in addition to Ni.
- Received 18 February 2014
- Revised 10 April 2014
DOI:https://doi.org/10.1103/PhysRevC.89.057301
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