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 $\sigma$ model and also accounts for the QCD trace anomaly by means of terms which involve the $\sigma$ and $\vmgπ$ fields as well as the glueball field $\varphi$. The form of the scale invariant term leading to an omega meson mass, after symmetry breaking, could involve coupling to ${\varphi }^2$ or ${\sigma }^2$ or some linear combination thereof. In fact an ${\omega }_{\mu }{\omega }^{\mu }{\varphi }^2$ 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.

25 pages, NUC-MINN-93/21-T (7 figures in postscript obtainable from authors)

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