L-S coupling and the magnetic moment of⁶Li from three-body models

Abstract

Recently, the shell structure of⁶Li was calculated from three-body models (αpn) where the only input is the required nucleon-nucleon and alpha-nucleon interactions. There it was learned, within the framework ofj-j coupling for the two valence nucleons with their coordinate's origin on the alpha particle, that orbitals beyond thep-shell, e.g. thes-d shell, play a significant role in the structure of⁶Li. In the present work, we extend these calculations to thef-shell. Thef-shell orbital probabilities add ∼4% to the normalization, thus bring all the models to within 3–5% of complete convergence. We then use thej-j coupling orbital amplitudes up to thef-shell to construct the corresponding amplitudes forL-S coupling. We find theL-S orbital probabilities, and compare them with theL-S component probabilities calculated directly by recoupling the three-body wave function from its “natural” Jacobi-coordinate form. The⁶Li magnetic moment is determined from the directL-S probabilities. The most realistic models yield magnetic moments about 2.5% higher than experiment.