The symmetry energy of isospin asymmetric nuclear matter (IANM), the density dependence of symmetry energy and also the equation of state (EOS) of the β-stable matter (BSM) are considered within relativistic corrections in the lowest order constrained variation approach (RLOCV) by using AV18 potential, with and without including Urbana (UIX) three-body force (TBF). The relative proton abundance for a wide range of baryon number density is calculated by including TBF in RLOCV approach. It is observed that if the bare two-body force (2BF) interaction AV18 is used, the relative proton abundance (ρp/ρB) increases by increasing baryon number density which tends to be saturated at high densities in both relativistic and non-relativistic treatments, while including TBF to our potential produces the ρp/ρB with higher values at low densities, which is saturated at the moderate densities in both LOCV and RLOCV frameworks. Moreover, adding the relativistic corrections (RC) to the results of β-stable matter decreases the value of proton abundance. In contrast, including TBF increases the value of ρp/ρB at low baryonic densities, which is saturated at the moderate baryon number densities. The opposite behaviors are also found on the saturation properties of nuclear matter by including TBF and RC to our calculations. It is also shown that the effect of TBF is much larger than that of the RC. Our results agree with other interactions and methods. © 2020 Elsevier B.V. All rights reserved.
