The structure of the sd shell nuclei

Abstract

The shell model with the phenomenologic~l effective interaction is applied to study level structures of 2°Ne, Z~Ne, 2~-Nc, 22Na and 24Mg. The full basis in the sd shell is taken in 2°Ne to diagonalize the energy matrices. This example confirms that SUn symmetry and the supermultiplet provide a very good way of truncation. This truncation is used to calculate level schemes of many nuclei beyond 2°Ne. Even though deviations of the effective interaction from the pure Q-Q interaction and the spin-orbit interaction break the SU3 symmetry and the supermultiplct, the main components of calculated wave functions in low-lying energies can be very well labelled by these two symmetries. Generally, good agreement with observations is found. Particularly, the lowest rotational bands are nicely explained. Exceptions are the level structure of 22Na and ½+ in tPO and 2~Ne, which are too low in the calculation, and the K = 2 bandsin 22Ne and 2~'Mg, which are again too low in the calculation.

Systematics of the Quadrupole–Quadrupole Interaction and Convergence Properties

“…Calculations of states in 22Na using SU(3) basis states, but with realistic interactions, were performed by Akiyama et al [27].…”

Pseudo SU(3) shell model: Normal parity bands in odd-mass nuclei

“…The ground state is now predicted to have J = reamains ordered correctly. The wave functions of all the states in all these three bands are dominated (more than 95%) by the leading SU(3) irrep (28,8), (10,4) π (18,4) ν . We will return to this point when discussing the wave functions in Section 5.…”

“…Within the SU(3) algebraic framework, large shell-model spaces can be truncated in a very natural way. While in general realistic interactions mix irreducible representations (irreps) of SU(3), the ground state wavefunction of well-deformed light nuclei are typically dominated by a few SU(3) irreps [4,5,6]. The strong spin-orbit interaction renders the SU(3) truncation scheme useless in the heavier nuclei of the f p-shell, while at the same time for rare earth and actinide species pseudo-spin emerges as a good symmetry and with it the pseudo-SU(3) model [7,8,9].…”

A Comparison of Spectroscopic Models of Low Excitation 2+ States in 24Mg and 28Si from Inelastic Proton Scattering

“…This single representation model, and the choice of the (8,4) case in particular, has been used with some success (Akiyama et al 1969;Strottman 1972) albeit that the 2t is known to occur at too Iowan excitation energy. We retain it nevertheless, not only because of its simplicity but also to enable a comparison of the results discussed herein with those of the 3+ state excitation reported previously (Nesci et al 1979).…”