Symmetry Energy and the Isotopic Spin Dependence of the Single-Particle Potential in Nuclear Matter

Abstract

Nuclear matter with a given neutron excess is treated within the frame of the i£-matrix theory. General expressions for the symmetry energy € S ym and the single-particle potential are obtained with the help of the reaction matrix which depends on two different Fermi momenta for neutrons and protons. In particular, an expression for the isotopic spin-dependent part U\ of the single-particle potential is obtained, and then specialized for single particles at the Fermi surface. With suitable approximations numerical values of e sym and Ui at the Fermi surface are obtained with the help of the Bruckner-Gammel solution for nuclear matter. The results are: € eym = 64 MeV, Ui{k F ) = l26 MeV.

Nuclear Symmetry Energy Extracted from Laboratory Experiments

“…At the mean-field level, using the Bruckner theory [16,17] or the Hugenholtz-Van Hove (HVH) theorem [18], the E sym (ρ) and its density slope L(ρ) ≡ [3ρ(∂E sym /∂ρ)] ρ at an arbitrary density ρ can be expressed generally as [19][20][21] …”

Cross-section measurement of theBa130(p,γ)La131reaction forNetterdon1, Endres2, Kiss3 et al. 2014Phys. Rev. C250260View full textAdd to dashboardCite

“…They are based on BruecknerHartree-Fock approximation [44] nucleon-nucleon interaction [45] and adopting a local density approximation. However, beside the fact that different theoretical nuclear densities are used, the optical-model parameters obtained by fitting to experimental data are different as well.…”

Origins and impacts of high-density symmetry energy

“…The ± sign indicates that the symmetry potential is repulsive for neutrons and attractive for protons in neutron-rich matter consistent with findings from optical model analyses of nucleon-nucleus scattering data since the 1960's. Using the Brueckner theory [58,59] or more generally the Hugenholtz-Van Hove (HVH) theorem [60], the E sym (ρ) and its slope L(ρ) at an arbitrary density ρ can be expressed as…”