Chebyshev-expanded covariant density functional from relativistic Brueckner theory

Abstract

We construct a density-dependent covariant energy density functional (CE-ME1) from full-Dirac-space relativistic Brueckner--Hartree--Fock (RBHF) self-energies and the corresponding equation of state. The space-like component $U_V$ is incorporated at the Fermi surface through reduced scalar and time-like self-energies, which are mapped onto local Hartree $\sigma$, $\omega$, $\delta$, and $\rho$ channels. The density-dependent couplings are represented by cubic Chebyshev polynomials over the density range $0.08\le \rho \le 0.48{\mathrm{fm}}^{-3}$. A constrained thermodynamic calibration uses 199 RBHF energy-per-particle values from published microscopic computations at six isospin asymmetries, while maintaining positive, monotonic couplings. The Bonn-A RBHF saturation point, incompressibility $K_{\infty }=258$ MeV, symmetry energy $J=33.1$ MeV, and slope $L=65.2$ MeV are reproduced. The predicted curvature $K_{\mathrm{sym}}=33$ MeV differs from the published RBHF value of $-67$ MeV, illustrating the derivative sensitivity of the local reduction. The combined energy RMS is $0.613$ MeV, measuring model discrepancy rather than statistical uncertainty. Uniform matter remains mechanically stable and causal above saturation within the calibrated range. In cold charge-neutral $npe\mu$ matter, CE-ME1 reasonably reproduces the interpolated RBHF pressure and proton fraction over most of the interval, although the pressure discrepancy increases near its upper edge. The DD-ME2 benchmark is stiffer and predicts a lower proton fraction at high density.

arXiv comment6 pages, 3 figures; uses elsart style