Vacuum corrections in nuclear matter are evaluated on basis of the modified relativistic Hartree approximation, applied to the Walecka sigma-omega model, and the relativistic Hartree approximation, employed on the non-linear model. Comparing the two approaches, we have determined the physical constraint between the compression modulus of nuclear matter and the nucleon effective mass. Moreover, the results in our work suggest we can find, for same pairs of these quantities, additional physical roots for the quartic order scalar meson self-coupling parameter of the non-linear treatment.
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