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

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 ${}^{208}\mathrm{Pb}$ 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 ${}^{208}\mathrm{Pb}$ 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.

Figure 1

Neutron and proton density distributions for ${}^{208}\mathrm{Pb}$ calculated by the RBHF theory in the full Dirac space with the potential Bonn A. The solid lines and dashed lines are obtained by using $f_0=60$ $\mathrm{MeV}{\mathrm{fm}}^5$ and $f_0=70$ $\mathrm{MeV}{\mathrm{fm}}^5$, respectively.

Figure 2

Energy per nucleon $E/A$ for ${}^{208}\mathrm{Pb}$ and the charge radius $r_c$ calculated by the RBHF theory in the full Dirac space, in comparison with the results obtained by the BHF theory [49] with the Argonne V18 or Bonn B two-nucleon potentials plus their corresponding microscopic three-nucleon forces, the RBHF theory within the momentum-independence approximation [20], and the EFT including only two-neutron forces at $\mathrm{N}{}^4\mathrm{LO}$ [22]. The solid black star represents the experimental data.

Figure 3

Elastic DCS for electron-nucleus scattering in ${}^{208}\mathrm{Pb}$ as a function of the scattering angle $\theta$ at the electron beam energies 502 MeV. The results from the RBHF theory in the full Dirac space are compared with the measured DCS (Exp) [55].

Figure 4

Squared charge form factor for ${}^{208}\mathrm{Pb}$ as a function of the momentum transfer $q$ at the electron beam energies 502 MeV.