Time-dependent Relativistic Hartree-Fock model with spherical symmetry

TL;DR

This paper introduces the first time-dependent relativistic Hartree-Fock model with spherical symmetry, demonstrating its accuracy and applying it to study nuclear resonances, providing new insights into nuclear matter properties.

Contribution

The paper develops the first TD-RHF model with spherical symmetry and applies it to analyze nuclear resonances, improving computational efficiency and constraining nuclear matter incompressibility.

Findings

High conservation of energy and particle number in simulations

Close agreement of ISGMR energy with experimental data

Incompressibility of nuclear matter constrained to 237-246 MeV

Abstract

This work establishes the time-dependent relativistic Hartree-Fock (TD-RHF) model with spherical symmetry for the first time. The time-dependent integro-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 $^{208}$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 in avoiding complicated calculations of the residual interactions, the ISGMR mode of $^{208}$Pb is calculated by twelve relativistic effective Lagrangians. The results indicate that the value of the incompressibility of nuclear matter $K_\infty$ constrained by relativistic effective Lagrangians is in the range of $237\sim246$ MeV, which is lower than the previous investigations based on the relativistic models.