Static properties of nuclear matter within the Boson Loop Expansion

The use of the Boson Loop Expansion is proposed for investigating the static properties of nuclear matter. We explicitly consider a schematic dynamical model in which nucleons interact with the scalar-isoscalar σ meson. The suggested approximation scheme is examined in detail at the mean field level and at the one- and two-loop orders. The relevant formulas are provided to derive the binding energy per nucleon, the pressure and the compressibility of nuclear matter. Numerical results of the binding energy at the one-loop order are presented for Walecka's σ-ω model in order to discuss the degree of convergence of the Boson Loop Expansion.