Validity of the Hartree Approximation in the Walecka Model

Abstract

This work addresses the issue of when the Hartree approximation is valid in the Walecka model by computing the correlation energy (i.e., two loop corrections or lowest order Fock terms) in nuclear matter. It is shown that these corrections are quite large when one includes vacuum polarization. Two types of convergence and validity are discussed, strong and weak, with the large correlation energy implying that the Hartree approximation is not strongly valid in the Walecka model until one reaches densities near thirty times nuclear matter density. This raises questions about what validity of the Hartree approximation might mean in this model, and about the interpretation of the Walecka model as a held theory as opposed to an effective Aeld theory.

Supported in part by NSF grant PHY-8719526.