Single-particle energies in neutron-rich nuclei by shell model sum rule

Abstract

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.

Evolution of single-particle states beyond132Sn

“…It is worth noting that the ESPEs coincide [25] with the energy centroids defined in [27] more than 40 years ago. The practical use of the latter definition, however, requires knowledge of all energies and spectroscopic factors corresponding to a given angular momentum, whereas expression (1) makes the computation of the ESPEs straightforward.…”

“…These quantities are the effective single-particle energies (ESPEs) [25,26] where ρ and ρ ′ stand for neutron and proton index, respectively, or viceversa. For a given j ρ , ǫ jρ denotes the corresponding energy in the one-valence system and N jρ the occupation number in the ground state of the eveneven system, while…”

Systematic study of shell-model effective interaction insdshell

“…Two-body interaction of central, spin-orbit, and tensor forces can be described in details by the singlet-triplet even-odd representation [14,15,19]. When antisymmetrizing two-nucleon states, the condition L + S + T = odd has to be fulfilled, which restricts the channels to be singlet-odd (SO), triplet-even (TE), singlet-even(SE), and triplet-odd (TO) [14,15,19]. The central force has all these four channels [14,15,19].…”

“…When antisymmetrizing two-nucleon states, the condition L + S + T = odd has to be fulfilled, which restricts the channels to be singlet-odd (SO), triplet-even (TE), singlet-even(SE), and triplet-odd (TO) [14,15,19]. The central force has all these four channels [14,15,19]. The spin-orbit forceV LS and the tensor forceV T only have spin triplet states [14,15,19].…”

“…One of the key methods to analyze effective interaction is spin-tensor-decomposition method [11,14,[16][17][18]. To do this, we first transform the jj-coupled two-body-matrixelements (TBMEs) into LS-coupled representations, in which various components of the interaction (central, tensor, spin-orbit, and antisymmetric spin-orbit) can be explicitly separated [19].…”