Role of symmetry potential in nuclear symmetry energy and its density slope parameter

Using a density dependent finite-range effective interaction of Yukawa form the nuclear mean field in asymmetric nuclear matter is expanded in terms of power series of asymmetry β (=ρn−ρpρ) as uτ(k,ρ,β)=u0(k,ρ)±usym,1(k,ρ)β+usym,2(ρ)β2. The behavior of nuclear symmetry potential usym,1(k,ρ) around the Fermi momentum kf is found to be connected to the density dependence of symmetry energy Esym(ρ) and nucleon effective mass m0⁎m (k=kf,ρ) in symmetric nuclear matter. Two different trends of momentum dependence for nuclear symmetry potential is observed depending on the choice of strength parameters of exchange interaction, but at Fermi momentum it is found to be independent of the choice of parameters. The nuclear symmetry energy Esym(ρ) and its slope L(ρ) are expressed analytically in terms of nuclear mean field in isospin asymmetric nuclear matter using the same interaction. We find that the second order nuclear symmetry potential usym,2(ρ) cannot be neglected while calculating the density slope of symmetry energy L(ρ) as well as the nuclear mean field in extremely neutron (proton) rich nuclear matter.