Properties of $^{208}$Pb predicted from the relativistic equation of state in the full Dirac space

TL;DR

This paper extends the relativistic Brueckner-Hartree-Fock theory to finite nuclei, specifically $^{208}$Pb, and demonstrates its predictions align well with experimental data on nuclear properties and charge densities.

Contribution

It introduces a method to apply RBHF theory in the full Dirac space to finite nuclei, providing detailed predictions for $^{208}$Pb's properties and charge densities.

Findings

Predicted neutron and proton density distributions match experimental data.

Calculated charge form factors agree with electron scattering measurements.

Uncertainty analysis shows robustness of the model predictions.

Abstract

Relativistic Brueckner-Hartree-Fock (RBHF) theory in the full Dirac space allows one to determine uniquely the momentum dependence of scalar and vector components of the single-particle potentials. In order to extend this new method from nuclear matter to finite nuclei, as a first step, properties of $^{208}$Pb are explored by using the microscopic equation of state for asymmetric nuclear matter and a liquid droplet model. The neutron and proton density distributions, the binding energies, the neutron and proton radii, and the neutron skin thickness in $^{208}$Pb are calculated. In order to further compare the charge densities predicted from the RBHF theory in the full Dirac space with the experimental charge densities, the differential cross sections and the electric charge form factors in the elastic electron-nucleus scattering are obtained by using the phase-shift analysis method. The results from the RBHF theory are in good agreement with the experimental data. In addition, the uncertainty arising from variations of the surface term parameter $f_0$ in the liquid droplet model is also discussed.