We studied the role of the tensor interaction in He isotopes systematically on the basis of the tensor-optimized shell model (TOSM). We use a bare nucleon-nucleon interaction AV8 obtained from nucleon-nucleon scattering data. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM + UCOM approach, we investigate the role of tensor interaction on each spectrum in He isotopes. It is found that the tensor interaction enhances the LS splitting energy observed in 5 He, in which the p 1/2 and p 3/2 orbits play different roles on the tensor correlation. In 6,7,8 He, the low-lying states containing extra neutrons in the p 3/2 orbit gain the tensor contribution. On the other hand, the excited states containing extra neutrons in the p 1/2 orbit lose the tensor contribution due to the Pauli-blocking effect with the 2p2h states in the 4 He core configuration.

One of the most striking features in neutron-rich nuclei is the disappearance of magic number N = 8 or 20, which indicates a change of single-particle energy spectra and the disappearance of a large energy gap at the magic number. A sum-rule method is formulated, based on the shell model, for the evaluation of single-particle energies. It is shown that the triplet-even central component of the NN interaction plays a decisive role through the monopole interaction for a change of single-particle energy spectra, leading to a rapid decrease of the energy gap at N = 8 and 20. The triplet-even attraction is due partly to the original central interaction and partly to the second-order tensor correlations of the one-pion exchange potential. A multipole expansion analysis of NN interactions shows that the contribution to the single-particle energy from the monopole interactions between two orbits depends on the nodal quantum numbers of the orbits.

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We study the Li isotopes systematically in terms of the tensor-optimized shell model (TOSM) by using a bare nucleon-nucleon interaction as the AV8 ′ interaction. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM+UCOM approach, we investigate the role of the tensor force on each spectrum of the Li isotopes. It is found that the tensor force produces quite a characteristic effect on various states in each spectrum and those spectra are affected considerably by the tensor force. The energy difference between the spin-orbit partner, the p 1/2 and p 3/2 orbits of the last neutron, in 5 Li is caused by opposite roles of the tensor correlation. In 6 Li, the spin-triplet state in the LS coupling configuration is favored energetically by the tensor force in comparison with jj coupling shell model states. In 7,8,9 Li, the low-lying states containing extra neutrons in the p 3/2 orbit are favored energetically due to the large tensor contribution to allow the excitation from the 0s-orbit to the p 1/2 orbit by the tensor force. Those three nuclei show the jj coupling character in their ground states which is different from 6 Li.

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