Nuclear matter within the continuous choice in the full Dirac space

The relativistic Brueckner-Hartree-Fock equations are solved self-consistently for symmetric nuclear matter in the full Dirac space within the continuous choice for the single-particle potential. Inspired from the nucleon-nucleon scattering in the free space, the energy denominator of the scattering equation in the nuclear medium is rewritten and a complex Thompson equation for the effective interaction $G$ matrix is derived. By decomposing the matrix elements of the single-particle potential operator in the full Dirac space, both the real and the imaginary parts of the single-particle potential are determined uniquely. The single-particle energy and Dirac mass behave continuously through the Fermi surface as expected. By comparing the equation of state obtained within the continuous choice with that obtained within the gap choice and in-between choice, the convergence of the hole-line expansion is discussed.

Figure 1

The real (left) and the imaginary (right) parts of the matrix elements for the singe-particle potential operator ${\mathrm{\Sigma }}^{++}$, ${\mathrm{\Sigma }}^{-+}$, and ${\mathrm{\Sigma }}^{--}$ as functions of the momentum $p$ calculated by the RBHF theory in the full Dirac space within the continuous choice. The total nucleon density $\rho$ is chosen at $0.16{\text{fm}}^{-3}$.

Figure 2

The real (left) and the imaginary (right) parts of the single-particle potentials $U_S$, $U_0$, and $U_V$ as functions of the momentum $p$ calculated by the RBHF theory in the full Dirac space within the continuous choice. The total nucleon density $\rho$ is chosen at $0.16{\text{fm}}^{-3}$.

Figure 3

The single-particle energy (left) and the Dirac mass (right) as functions of the momentum $p$ calculated by the RBHF theory in the full Dirac space within the continuous (red solid), in-between (green dashed), and gap (blue dotted) choices. The total nucleon density $\rho$ is chosen at $0.16{\text{fm}}^{-3}$.

Figure 4

Binding energy per nucleon $E/A$ for SNM as functions of the density $\rho$ calculated by the RBHF theory in the full Dirac space within the continuous, in-between, and gap choices. The shaded area indicates the empirical values.

Figure 5

Binding energy per nucleon $E/A$ for SNM as functions of the density $\rho$ calculated by the RBHF theory in the full Dirac space within the continuous, in-between, and gap choices and with realistic $NN$ interactions Bonn A, B, and C. The gray shaded area indicates the empirical values.