Anharmonicity in light nuclei near drip lines

Abstract

Abstract Single-particle energy levels of nucleons moving in an anisotropic harmonic oscillator potential along with a spin-orbit and an orbit-orbit interaction have been calculated. The model proposed herein incorporates shapes generated by higher multipolar anisotropies other than the quadruple one. The gaps among the energy levels are strongly dependent on the degree of anisotropy and hence, affect the nucleonic separation energies. For large anisotropies, this characteristic disturbs the occurrences of the usual magic numbers and the sequential ordering of the shells characterized by principal quantum number, N, associated with the elementary shell model. For large asymmetries, the states characterized by higher N, may come down and lie below the energies of the states with lower N and vice versa. This feature of the model provides a natural explanation of intruder states or the island of inversion observed experimentally. For certain choices of the parameters, the large gaps in single nucleonic separation energies could occur at neutron numbers, 10,18,30, and 32 as observed, respectively, in 20Ne, 28Ne, 52Ti, and 54Ti. For neutron as well as proton number 14, the magnitude of this energy gap depends strongly on the choice of the strength of the spin-orbit and orbit-orbit terms. The model provides a simple understanding of the observed fact that some nuclei with proton or neutron number 14 sometimes exhibit this gap but not others. It also provides an interesting insight of having a low-laying (1/2 − ) state in 7He, and confirms the ground state spin and parity of 11Be to be (1/2+) and those of 9He to be (1/2+), both of which have been contentious. This investigation indicated the density distribution, i.e., the shapes of many of nuclei near drip line to be anisotropic having a symmetry about their body-fixed z-axis.