Oblate deformation of light neutron-rich even-even nuclei

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 $r\to \infty$ 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 (${\omega }_{\perp }:{\omega }_z$) are simple rational numbers. In contrast, for the prolate deformation the magic numbers obtained from simple rational ratios of (${\omega }_{\perp }:{\omega }_z$) 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 ${}_{14}^{42}$Si${}_{28}$ is given. Among light nuclei the nucleus ${}_6^{20}$C${}_{14}$ is found to be a good candidate for having the oblate ground state. In the region of the mass number $A\approx 70$ the oblate ground state may be found in the nuclei around ${}_{28}^{76}$Ni${}_{48}$ in addition to ${}_{28}^{64}$Ni${}_{36}$.

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References in corpus (6)

• Shape transitions in exotic Si and S isotopes and tensor-force-driven Jahn-Teller effect
• A new effective interaction for $0\hslash \omega$ shell model calculations in the sdpf valence space
• Well-developed deformation in 42Si
• Nilsson diagrams for light neutron-rich nuclei with weakly-bound neutrons
• Neutron shell structure and deformation in neutron-drip-line nuclei
• A further look at prolate dominance in nuclear deformation

Cited by in corpus (4)

• Examining possible neutron-halo nuclei heaver than ${}^{37}$Mg
• Shell-structure of one-particle resonances in deformed potentials
• Low-energy Coulomb excitation of ${}^{62}$Fe and ${}^{62}$Mn following in-beam decay of ${}^{62}$Mn
• Interplay between one-particle and collective degrees of freedom in nuclei