Variation in Nuclear-Matter Binding Energies with Phase-Shift-Equivalent Two-Body Potentials

For any given two-body Hamiltonian, there exists a large class of unitarily equivalent Hamiltonians that lead to the same scattering phase shifts at all energies. The purpose of this paper is to exhibit typical saturation curves for reasonable equivalent potentials. The binding energy per particle changes by several MeV in either direction, and the saturation minimum shifts to higher or lower density as the binding increases or decreases. Softening the potential increases the binding. The separation approximation for the reaction matrix provides qualitative insight into these effects. Our exact calculations start with simple local $s$-wave potentials with either a hard core or a Yukawa core. The binding energy per particle is calculated in the Brueckner approximation with self-consistent single-particle energies below the Fermi level. For our examples we use unitary transformations that differ from the identity by a short-range operator of rank 2 and transformations induced by distortions of the radial scale. The latter class of transformations alters the core radius and produces potential terms that are linear in the square of the momentum.