Role of relativistic effects and three-body forces in nuclear matter properties

The role of three-body force (TBF) and the relativistic corrections (RC) on the equations of state of nuclear matter and $\beta$-stable matter (BSM) within the relativistic lowest-order constrained variation (RLOCV) approach are studied. The AV14 potential and its relativistic version $\left({\tilde{v}}_{14}\right)$ as well as the AV18 potential are considered as the bare two-body potentials by employing the nuclear many-body Hamiltonian. It is shown that by using ${\tilde{v}}_{14}$, all properties of cold nuclear matter can be correctly reproduced if TBF is used in RLOCV framework. The energy and proton abundance of BSM are calculated for a wide range of baryon number densities, which are of interest in astrophysics. It is also shown that by adding RC or TBF to our calculations, the maximum proton abundance is pushed toward lower densities. Furthermore, the particle number densities decrease by including RC and increase when TBF is added to the interactions. The opposite behaviors for the role TBF and RC on saturation properties of nuclear matter as well as proton number densities of nuclear $\beta$-stable matter are found. It is also shown that the effects of three-body forces are much larger than those of relativistic corrections.

Figure 1

The binding energy per nucleon versus density for AV14 as well as ${\tilde{v}}_{14}$. Dot curves are drawn by using $H_{\mathrm{NR}}$ in LOCV method without including TBF, dot-dashed curves by using $H_R$ in RLOCV method only by using two-body force (2BF), dashed curves are used for both 2BF and TBF in our LOCV calculations, and solid curves are related to RLOCV method with including TBF to their two-body interactions.

Figure 2

The comparison of asymmetric nuclear matter binding energy against density for various proton to neutron ratio for both versions of interactions, i.e., $A{V}_{14}$ (dashed curves) and ${\tilde{v}}_{14}$ (solid curves). Panels (a) and (b) show the results of 2BF potentials in LOCV and RLOCV calculations, respectively, and panels (c) and (d) are devoted to the results of 2BF+TBF potentials in LOCV and RLOCV methods, respectively.

Figure 3

The comparison of the saturation energy per nucleon versus asymmetry parameter for both 2BF interactions AV14 and ${\tilde{v}}_{14}$ in LOCV method (dot curves), in RLOCV method (dot-dashed curves), as well as 2BF+TBF potentials (AV14+UIX and ${\tilde{v}}_{14}$+UIX) in LOCV and RLOCV frameworks (dashed and solid curves), respectively.

Figure 4

The same as Fig. 3 but for the saturation density of nuclear matter.

Figure 5

(a) The LOCV and RLOCV calculations of the quadratic dependence of the nuclear symmetry energy as a function of ${\delta }^2$ using two different versions of 2BF as well as 2BF+TBF interactions at $\rho =0.17 {\mathrm{fm}}^{-3}$. (b) The same as (a) but at $\rho =0.35 {\mathrm{fm}}^{-3}$.

Figure 6

(a) The exact (solid curves) and approximate (dashed curves) values of density dependence of symmetry energy obtained by LOCV approach for different potentials. (b) The same as panel (a) but for RLOCV approach.

Figure 7

The comparison of the nuclear symmetry energy against density calculated in this work with other potentials and many-body techniques.

Figure 8

The energy of BSM without considering baryon rest masses as a function of baryon densities. Dot (dot-dashed) curves represent our results for LOCV (RLOCV) calculation using only 2BF and dashed (solid) curves are used for LOCV (RLOCV) methods using 2BF+TBF.

Figure 9

The same as Fig. 8 but for PNM.

Figure 10

The EOS of PNM as well as BSM using AV18 with and without including TBF. The solid curves represent the calculated EOS of BSM and broken curves show the results of PNM.

Figure 11

(a) The comparison of the relative proton abundance against baryon number density using AV14. Dot (dot-dashed) curves show the results by using 2BF in LOCV (RLOCV) treatment and dashed (solid) curves show the results by using 2BF+TBF in these approaches, respectively. (b) The same as panel (a) but for ${\tilde{v}}_{14}$.

Figure 12

The proton abundance ${\rho }_p/{\rho }_B$ as a function of baryon density calculated in this work as well as other methods and interactions.

Figure 13

(a) The particle densities of proton, electron and muon versus baryon density, for AV14 potentials with and without adding TBF to our interactions in both RLOCV (solid and dot-dashed curves) and LOCV (dashed and dot curves) frameworks. (b) The same as panel (a) but for ${\tilde{v}}_{14}$. (c) The same as panel (a) but for AV18 only in LOCV method.