An Effective Lagrangian with Broken Scale and Chiral Symmetry Applied to Nuclear Matter and Finite Nuclei

Abstract

We study nuclear matter and finite nuclei with a chiral Lagrangian which generalizes the linear $σ$ model and also accounts for the QCD trace anomaly by means of terms which involve the $σ$ and $\vmgπ$ fields as well as the glueball field $ϕ$. The form of the scale invariant term leading to an omega meson mass, after symmetry breaking, could involve coupling to $ϕ^2$ or $σ^2$ or some linear combination thereof. In fact an $ω_μω^μϕ^2$ form is strongly favored by the bulk properties of nuclei, which also rather strongly constrain the other parameters. A reasonable description of the closed shell nuclei oxygen, calcium and lead can be achieved, although the spin-orbit splittings are somewhat smaller than the experimental values.