Fully self-consistent relativistic Brueckner-Hartree-Fock theory for finite nuclei

Starting from the relativistic form of the Bonn potential as a bare nucleon-nucleon interaction, the full relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for finite nuclei in a fully self-consistent basis. This provides a relativistic ab initio calculation of the ground state properties of finite nuclei without any free parameters and without three-body forces. The convergence properties for the solutions of these coupled equations are discussed in detail for the example of the nucleus ${}^{16}\mathrm{O}$. The binding energies, radii, and spin-orbit splittings of the doubly magic nuclei ${}^4\mathrm{He}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$ are calculated and compared with the earlier RBHF calculated results in a fixed Dirac Woods-Saxon basis and other nonrelativistic ab initio calculated results based on pure two-body forces.

Figure 1

The difference between the single-particle cutoff and the pair cutoff is illustrated for the example of orbital angular momentum coupling for $l_{\mathrm{cut}}=15\hslash$ or $l_{\mathrm{cut}}=20\hslash$ (left panel) and for $L_{\mathrm{cut}}=15\hslash$ or $L_{\mathrm{cut}}=20\hslash$ with $L=l_1+l_2$ (right panel).

Figure 2

Total energy $E$ and charge radius $r_c$ of ${}^{16}\mathrm{O}$ as a function of angular momentum cutoff $l_{\mathrm{cut}}$ calculated in RBHF theory.

Figure 3

Total energy $E$ and charge radius $r_c$ of ${}^{16}\mathrm{O}$ as a function of the energy cutoff ${\varepsilon }_{\mathrm{cut}}$ calculated in RBHF theory.

Figure 4

Total energy $E$ and charge radius $r_c$ of ${}^{16}\mathrm{O}$ as a function of energy cutoff in the Dirac sea ${\varepsilon }_{\mathrm{Dcut}}$ calculated in RBHF theory.

Figure 5

Total energy $E$ and charge radius $r_c$ of ${}^{16}\mathrm{O}$ calculated in RBHF theory as a function of total angular momentum cutoff $J_{\mathrm{cut}}$ introduced in Eq. (33).

Figure 6

Total energy $E$ and charge radius $r_c$ of ${}^{16}\mathrm{O}$ as a function of box size $R$ calculated in RBHF theory.

Figure 7

Total energies at each RBHF iteration step for PAV and PBV.

Figure 8

Single-particle spectra in $s$ and $p$ blocks at each RBHF iteration step for PAV and PBV.

Figure 9

Total energies at each iteration step calculated by RBHF in the self-consistent RHF basis (solid symbols) and in the fixed DWS basis (open symbols).

Figure 10

Single-particle spectrum of ${}^{16}\mathrm{O}$ calculated by RBHF theory with the interaction Bonn $A$ for different choices of the single-particle potential $U_{ab}$ of particle states in Eq. (18).

Figure 11

Energy per nucleon $E/A$ for ${}^{16}\mathrm{O}$ as a function of the charge radius $r_c$ calculated in RBHF using the interactions Bonn $A$, $B$, and $C$, in comparison with BHF and the relativistic effective density approximation (EDA) [97].

Figure 12

Charge density distributions of ${}^{16}\mathrm{O}$ calculated by RBHF theory with the interactions Bonn $A$, $B$, and $C$, in comparison with experimental data [98].

Figure 13

Extrapolation of total energy and charge radius with respect to the box size. Solid points are included in the fit of Eq. (D1), whereas open points are not. The uncertainties are evaluated by the jackknife resampling method.