Relativistic effects in phenomenological nucleon-nucleon potentials and nuclear matter

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Abstract
For any conventional phenomenological nucleon-nucleon potential, we derive a relativistic two-body Hamiltonian. With this two-body Hamiltonian we construct an approximately relativistic many-body Hamiltonian that is used to find the lowest order relativistic corrections to the Brueckner theory of nuclear matter. These corrections are explicity presented as a sum of terms that are linear and quadratic functions of the nonrelativistic reaction matrix. Numerical results are obtained for the Reid soft core potential, the Ueda-Green potential, and several separable potentials. Due to extensive cancellations of the individual terms, the total correction is considerably smaller than that which would be expected from simple estimates. For the Reid potential the total correction to the energy per particle at saturation is only +0.22 MeV, and the change in the saturation density is negligible. The correction at saturation is also positive for all the other potentials considered.