Time-dependent relativistic Hartree-Fock model with spherical symmetry

This work establishes the time-dependent relativistic Hartree-Fock (TD-RHF) model with spherical symmetry. The time-dependent integral differential Dirac equations are solved by expanding Dirac spinors on the spherical Dirac Woods-Saxon (DWS) basis. The numerical verification demonstrates the high conservation qualities for both the total binding energy and the particle number, as well as the time-reversal invariance of the system, which ensures the precision and reliability of the newly developed TD-RHF model. Subsequently, the isoscalar giant monopole resonance (ISGMR) mode of $^{208}\mathrm{Pb}$ is investigated using the RHF Lagrangian PKO1. The constrained energy of the ISGMR calculated by PKO1 is found to be in close agreement with the experimental data, and the strength function is similar to the results given by the relativistic Hartree-Fock plus random phase approximation. Based on the advantage of the TD-RHF model that avoids complicated calculations of the residual interactions, the ISGMR mode of $^{208}\mathrm{Pb}$ is calculated by 12 relativistic effective Lagrangians. The results indicate that the value of the incompressibility of nuclear matter ${K}_{\ensuremath{\infty}}$ constrained by relativistic effective Lagrangians is in the range of 237--246 MeV, which is lower than the previous investigations based on the relativistic models.