$\Delta$ (1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars

TL;DR

This paper extends the density-dependent relativistic Hartree-Fock theory to include $$-isobars, analyzing their effects on dense nuclear matter and neutron star properties, revealing early $$-isobar appearance and their influence on the equation of state.

Contribution

The study introduces a method to incorporate $$-isobars into DDRHF theory and evaluates their impact on neutron star structure, providing new insights into dense matter composition.

Findings

$$-isobars appear at $ ho_B\,\sim0.27$fm$^{-3}$, similar to hyperons.

$$-isobars soften the equation of state mainly through reduced Fock contributions.

Neutron stars with $$-isobars can reach masses comparable to observed massive pulsars.

Abstract

The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\Delta$-isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\Delta$-isobars' self-energies are evaluated in details. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\Delta$-isobars is recognized at $\rho_B\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that the $\Delta$-isobars' softening of the equation of state is found to be mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are found negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\Delta$-isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars.