Momentum, density, and isospin dependence of symmetric and asymmetric nuclear matter properties

Properties of symmetric and asymmetric nuclear matter have been investigated in the relativistic Dirac-Brueckner-Hartree-Fock approach based on projection techniques using the Bonn A potential. The momentum, density, and isospin dependence of the optical potentials and nucleon effective masses are studied. It turns out that the isovector optical potential depends sensitively on density and momentum, but is almost insensitive to the isospin asymmetry. Furthermore, the Dirac mass $m_D^{*}$ and the nonrelativistic mass $m_{\mathit{NR}}^{*}$ which parametrizes the energy dependence of the single particle spectrum, are both determined from relativistic Dirac-Brueckner-Hartree-Fock calculations. The nonrelativistic mass shows a characteristic peak structure at momenta slightly above the Fermi momentum $k_F$. The relativistic Dirac mass shows a proton-neutron mass splitting of $m_{D,n}^{*}<m_{D,p}^{*}$ in isospin asymmetric nuclear matter. However, the nonrelativistic mass has a reversed mass splitting $m_{\mathit{NR},n}^{*}>m_{\mathit{NR},p}^{*}$ which is in agreement with the results from nonrelativistic calculations.

Figure 1

Symmetry energy as a function of the nucleon density $n_B$. The DBHF result is compared to various phenomenological RMF models.

Figure 2

The nucleon optical potential in isospin symmetric nuclear matter as a function of the momentum $k=\left|k\right|$ at different densities.

Figure 3

The effective mass in isospin symmetric nuclear matter as a function of the momentum $k=\left|k\right|$ at different densities.

Figure 4

The nonrelativistic effective mass in isospin symmetric nuclear matter extracted from the single particle energy (7) as a function of the momentum $k=\left|k\right|$ at different densities.

Figure 5

The effective mass in isospin symmetric nuclear matter at $k=\left|k\right|=k_F$ as a function of the Fermi momentum $k_F$ for the various models.

Figure 6

The neutron and proton optical potential in isospin asymmetric nuclear matter as a function of the momentum $k=\left|k\right|$ at different densities.

Figure 7

The isovector optical potential as a function of momentum k for three densities and several isospin asymmetries.

Figure 8

The isovector optical potentials from the various models in asymmetric nuclear matter ($\beta =0.4$) as a function of momentum k at $n=0.5n_0$ and $n_0$. The isovector optical potential from our DBHF approach is compared to the ones from the nonrelativistic BHF approach [26], the phenomenological RMF [20], Gogny [42], and Skyrme [43] forces and from a relativistic $T-\rho$ approximation [44].

Figure 9

Neutron effective mass as a function of the momentum $k=\left|k\right|$ for various values of the asymmetry parameter β at fixed nuclear density $n_B=0.166{\text{fm}}^{-3}$.

Figure 10

Neutron and proton effective mass as a function of the momentum $k=\left|k\right|$ for a value of the asymmetry parameter $\beta =1$ at fixed nuclear density $n_B=0.166{\text{fm}}^{-3}$. In addition, the effective mass in symmetric nuclear matter is given.

Figure 11

Neutron effective mass in symmetric nuclear matter and in pure neutron matter as a function of the momentum $k=\left|k\right|$ at different nuclear densities.

Figure 12

Neutron effective mass obtained in the RMF approximation as a function of the momentum $k=\left|k\right|$ at fixed nuclear density $n_B=0.166{\text{fm}}^{-3}$.