Relativistic fermion gas interacting through a scalar field. I. Hartree approximation

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Abstract
A high-density fermion gas interacting through a scalar field is studied in the relativistic Hartree approximation, as a model for superhigh-density astrophysical systems. The Hartree quasiparticle states are the superposition of positive- and negative-energy states and can be constructed by a Bogoliubov-type canonical transformation. The resulting effective mass is strongly field-dependent, and approaches 0 as the density increases into the ultrarelativistic domain. The ensuing equation of state exhibits a phase transition and a bound state in the intermediate-density range, but becomes perfect-gas-like at high densities. There is no collapse, and stronger coupling enhances the perfect-gas-like behavior. An alternate picture is provided by considering the fermion gas in the background of zero-momentum bosons. Numerical comparisons with existing scalar-meson coupling data are provided, with emphasis on regions of neutron-star densities.