Relativistic mean field theory for nuclei

Abstract

The phenomenology of relativistic mean field theory of nuclei is discussed for general scalar potential functions U( φ) with a minimum at zero scalar field φ = 0. The cubic-plus-quartic scalar self-interaction model U 34 is discussed as an important special case. We obtain general conditions on U required by the saturation properties including the incompressibility coefficient K. The effective mass M ∗ is uniquely related to the vector coupling. The pathologies of the U 34 model are discussed and modifications are proposed which cure the model when the quartic term is negative as phenomenologically required. It is argued that the equation of state (at T = 0) is effectively independent of the form of U if the parameters are adjusted to a given K, M ∗ , and that the phenomenology of finite nuclei, in particular the spin-orbit splitting in light nuclei, determines M ∗ ≈ 0.6 M essentially independently of U. The resulting (stiff) e.o.s. is then determined within narrow limits independently of the form of U.