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Register a new userIsospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions
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Within an isospin and momentum dependent transport model, the dynamics of isospin particles (nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The mass splitting of $m^{*}_{n}>m^{*}_{p}$ and $m^{*}_{n}<m^{*}_{p}$ in nuclear matter and the different stiffness of symmetry energy are used in the model. The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of $^{112}$Sn+$^{112}$Sn and $^{124}$Sn+$^{124}$Sn at the incident energies of 50 and 120 MeV/nucleon, respectively. It is found that the both effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail (larger than 20 MeV). Specific constraints are obtained from the double ratio spectra, which are evaluated from the ratios of isospin observables produced in $^{124}$Sn+$^{124}$Sn over $^{112}$Sn+$^{112}$Sn collisions. A mass splitting of $m^{*}_{n}<m^{*}_{p}$ is constrained from the available data at the energy of 120 MeV/nucleon. A soft symmetry energy with the stiffness of $gamma_{s}=$0.5 is close to the experimental double ratio spectra at both energies.
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A new version of the improved quantum molecular dynamics model has been developed to include standard Skyrme interactions. Four commonly used Skyrme parameter sets, SLy4, SkI2, SkM* and Gs are adopted in the transport model code to calculate the isospin diffusion observables as well as single and double ratios of transverse emitted nucleons. While isospin diffusion observables are sensitive to the symmetry energy term, they are not very sensitive to the nucleon effective mass splitting parameters in the interactions. Our calculations show that the high energy neutrons and protons and their ratios from reactions at different incident energies provide a robust observable to study the momentum dependence of the nucleon effective mass splitting. However the sensitivity of effective mass splitting effect on the n/p yield ratios decreases with increasing beam energy, even though high energy proton and neutron are produced more abundantly at high beam energy. Our calculations show that the optimum incident energy to study nucleon effective masses is between 100-200 MeV per nucleon.
The isospin splitting of the nucleon mean field is derived from the Brueckner theory extended to asymmetric nuclear matter. The Argonne V18 has been adopted as bare interaction in combination with a microscopic three body force. The isospin splitting of the effective mass is determined from the Brueckner-Hartree-Fock self-energy: It is linear acording to the Lane ansatz and such that $m^*_n > m^*_p$ for neutron-rich matter. The symmetry potential is also determined and a comparison is made with the predictions of the Dirac-Brueckner approach and the phenomenological interactions. The theoretical predictions are also compared with the empirical parametrizations of neutron and proton optical-model potentials based on the experimental nucleon-nucleus scattering and the phenomenological ones adopted in transport-model simulations of heavy-ion collisions. The direct contribution of the rearrangement term due to three-body forces to the single particle potential and symmetry potential is discussed.
The decomposition of nuclear symmetry energy into spin and isospin components is discussed to elucidate the underlying properties of the NN bare interaction. This investigation was carried out in the framework of the Brueckner-Hartree-Fock theory of asymmetric nuclear matter with consistent two and three body forces. It is shown the interplay among the various two body channels in terms of isospin singlet and triplet components as well as spin singlet and triplet ones. The broad range of baryon densities enables to study the effects of three body force moving from low to high densities.
The isospin dependence of the nucleon effective mass is investigated in the framework of the Dirac Brueckner-Hartree-Fock (DBHF) approach. The definition of nucleon scalar and vector effective masses in the relativistic approach is clarified. Only the vector effective mass is the quantity related to the empirical value extracted from the analysis in the nonrelatiistic shell and optical potentials. In the relativistic mean field theory, where the nucleon scalar and vector potentials are both energy independent, the neutron vector potential is stronger than that of proton in the neutron rich nuclear matter, which produces a smaller neutron vector effective mass than that of proton. It is pointed out that the energy dependence of nucleon potentials has to be considered in the analysis of the isospin dependence of the nucleon effective mass. In the DBHF the neutron vector effective mass is larger than that of proton once the energy dependence of nucleon potentials is considered. The results are consistent with the analysis of phenomenological isospin dependent optical potentials.
A three parameter scaling relationship between isotopic distributions for elements with Z$leq 8$ has been observed that allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling law (termed iso-scaling) applies for a variety of reaction mechanisms that are dominated by phase space, including evaporation, multifragmentation and deeply inelastic scattering. The origins of this scaling behavior for the various reaction mechanisms are explained. For multifragmentation processes, the systematics is influenced by the density dependence of the asymmetry term of the equation of state.
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