Effect of the splitting of the neutron and proton effective masses on the nuclear symmetry energy at finite temperatures

Abstract

We present the temperature and density dependence of symmetry energy for nuclear matter at finite temperature based on the approach of the thermodynamics with Skyrme energy density functional. We first classify the Skyrme interactions into 7 groups according to the range of neutron and proton effective mass in neutron matter limit(99.99 per cent neutron in the matter). We find that there is obvious correlation between the temperature dependence of the symmetry energy and the splitting of the neutron and proton effective mass. For some Skyrme interactions with m * n > m * p and strong splitting of the neutron and proton effective mass in asymmetric nuclear matter, a transition of the temperature dependence of symmetry energy from decreasing with temperature at low densities to increasing with temperature at high densities appears. For other Skyrme interactions, we do not observe such phenomenon. Our study show that the symmetry energy in hot asymmetric matter not only depends on symmetry potential part but also on the splitting of the neutron and proton effective mass to a certain extent.Keywords: nuclear symmetry energy, nuclear symmetry energy at finite temperature, Skyrme density functional, Splitting of neutron and proton effective mass

Neutron–proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon–nucleus scattering data within an isospin dependent optical model

“…[36], we simply have U τ (E, δ) = U τ (T τ (E), δ) (10) but one has to be very careful about the different dispersion relationship T τ (E) for neutrons and protons because of the momentum dependence of their isovector potential. In symmetric nuclear matter, the dispersion relationship T (E) can be readily obtained from manipulating the single-nucleon energy E = T + U 0 (T ) (11) once the momentum dependence of the isoscalar potential U 0 (T ) is known. For the same nucleon energy E, by expanding the U τ (T τ ) to the first-order in δ, one obtains the kinetic energy T τ (E) for protons and neutrons in asymmetric matter in terms of the (12) where μ = (1 + dU 0 /dT ) −1 .…”

“…For instance, among the 94 Skyrme interactions examined within the Skyrme-Hartree-Fock approach in Ref. [11], 48/29/17 of them predict a positive/negative/zero value for the neutron-proton effective mass splitting. One of the main reasons for this unfortunate situation is our poor knowledge about the in-medium properties of nuclear isovector interaction and the lack of reliable experimental probes of the neutron-proton effective mass splitting.…”

Constraining simultaneously nuclear symmetry energy and neutron-proton effective mass splitting with nucleus giant resonances using a dynamical approach

“…The isospin splitting of the in-medium nucleon effective mass is thus related to the momentum dependence of the symmetry potential in non-relativistic models [12]. It has been found that the isospin splitting of the nucleon effective mass is as important as the nuclear symmetry energy in understanding the isospin dynamics in nuclear reactions [13][14][15][16][17][18][19], and has ramifications in the thermodynamic properties of isospin * corresponding author: xujun@sinap.ac.cn asymmetric nuclear matter as well [20,21]. Moreover, the neutron-proton effective mass splitting is actually inter-related to the nuclear symmetry energy through the Hugenholtz-Van Hove theorem [10,22].…”

Interdependence of different symmetry energy elements

“…The shroud of uncertainty looms even larger on the higher derivatives of the symmetry energy [e.g., K 0)] and on the difference between the neutron and proton effective masses ∆m * 0 [=(m * n − m * p )/m] in neutron-rich matter at ρ 0 . The values of K 0 sym and Q 0 sym , in different parametrizations of the Skyrme energy density functional (EDF) lie in very wide ranges [−700 MeV < K 0 sym < 400 MeV; −800 MeV < Q 0 sym < 1500 MeV ] [9, 10] whereas there are divergent predictions on the value of ∆m * 0 from theoretical studies based on microscopic many-body theories [11,12] or phenomenological approaches [13][14][15][16]. Such large uncertainties belie a satisfactory understanding of the nuclear isovector interaction.There is a sliver of expectation that the entities C 0 2 (= C 2 (ρ 0 )), L 0 , K 0 sym , etc.…”