119210704
Improved single particle potential for transport model simulations of nuclear reactions induced by rare isotope beams
Taking into account more accurately the isospin dependence of nucleon-nucleon interactions in the in-medium many-body force term of the Gogny effective interaction, new expressions for the single-nucleon potential and the symmetry energy are derived. Effects of both the spin (isospin) and the density dependence of nuclear effective interactions on the symmetry potential and the symmetry energy are examined. It is shown that they both play a crucial role in determining the symmetry potential and the symmetry energy at suprasaturation densities. The improved single-nucleon potential will be useful for more accurate simulation of nuclear reactions induced by rare-isotope beams within transport models.
118330249
Symmetry energy, its density slope, and neutron-proton effective mass splitting at normal density extracted from global nucleon optical potentials
Based on the Hugenholtz-Van Hove theorem, it is shown that both the symmetry energy E{sub sym}({rho}) and its density slope L({rho}) at normal density {rho}{sub 0} are completely determined by the nucleon global optical potentials. The latter can be extracted directly from nucleon-nucleus scatterings, (p,n) charge-exchange reactions, and single-particle energy levels of bound states. Averaging all phenomenological isovector nucleon potentials constrained by world data available in the literature since 1969, the best estimates of E{sub sym}({rho}{sub 0})=31.3 MeV and L({rho}{sub 0})=52.7 MeV are simultaneously obtained. Moreover, the corresponding neutron-proton effective mass splitting in neutron-rich matter of isospin asymmetry {delta} is estimated to be (m{sub n}{sup *}-m{sub p}{sup *})/m=0.32{delta}.
119233306
Single-nucleon potential decomposition of the nuclear symmetry energy
The nuclear symmetry energy $E_{sym}(\rho)$ and its density slope $L(\rho)$ can be decomposed analytically in terms of the single-nucleon potential in isospin asymmetric nuclear matter. Using three popular nuclear effective interaction models which have been extensively used in nuclear structure and reaction studies, namely, the isospin and momentum dependent MDI interaction model, the Skyrme Hartree-Fock approach and the Gogny Hartree-Fock approach, we analyze the contribution of different terms in the single-nucleon potential to the $E_{sym}(\rho)$ and $L(\rho)$. Our results show that the observed different density behaviors of $E_{sym}(\rho)$ for different interactions are essentially due to the variation of the symmetry potential $U_{sym,1}(\rho,k)$. Furthermore, we find that the contribution of the second-order symmetry potential $U_{sym,2}(\rho,k)$ to the $L(\rho)$ generally cannot be neglected. Moreover, our results demonstrate that the magnitude of the $U_{sym,2}(\rho,k)$ is generally comparable with that of $U_{sym,1}(\rho,k)$, indicating the second-order symmetry potential $U_{sym,2}(\rho,k)$ may have significant corrections to the widely used Lane approximation to the single-nucleon potential in extremely neutron(proton)-rich nuclear matter.
120276588
Recent Progress in Constraining the Equation of State of Dense Neutron-Rich Nuclear Matter with Heavy-Ion Reactions
Abstract The nuclear symmetry energy E s y m ( ρ ) is the most uncertain part of the Equation of State (EOS) of dense neutron-rich nuclear matter. In this talk, we discuss the underlying physics responsible for the uncertain E s y m ( ρ ) especially at supra-saturation densities, the circumstantial evidence for a super-soft E s y m ( ρ ) from analyzing π − / π + ratio in relativistic heavy-ion collisions and its impacts on astrophysics and cosmology.
119311326
Analytical relations between nuclear symmetry energy and single-nucleon potentials in isospin asymmetric nuclear matter
Abstract Using the Hugenholtz–Van Hove theorem, we derive general expressions for the quadratic and quartic symmetry energies in terms of the isoscalar and isovector parts of single-nucleon potentials in isospin asymmetric nuclear matter. These expressions are useful for gaining deeper insights into the microscopic origins of the uncertainties in our knowledge on nuclear symmetry energies especially at supra-saturation densities. As examples, the formalism is applied to two model single-nucleon potentials that are widely used in transport model simulations of heavy-ion reactions.
119614096
Vertex representations of toroidal special linear Lie superalgebras
Based on the loop-algebraic presentation of 2-toroidal Lie superalgebras, a free field representation of toroidal Lie superalgebras of type A(m, n) is constructed using both vertex operators and bosonic fields.
119630115
Lie Superalgebras Arising from Bosonic Representation
A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains osp(1 | 2n)(1) as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type B(0, n). Furthermore, this algebra is a central extension of the algebra osp(1 | 2n) ⊗ ℂ[s, s −1, t, t −1].
118383314
The Dirac Conjecture and the Non-uniqueness of Lagrangian
By adding the total time derivatives of all the constraints to the Lagrangian step by step, we achieve the further work of the Dirac conjecture left by Dirac. Hitherto, the Dirac conjecture is proved completely. It is worth noticing that the addition of the total time derivatives to the Lagrangian can turn up some constraints hiding in the original Lagrangian. For a constrained system, the extended Hamiltonian $H_E$ considers more constraints, and shows symmetries more obviously than the total Hamiltonian $H_T$. In the Lagrangian formalism, we reconsider the Cawley counterexample, and offer an example in which in accordance with its original Lagrangian its extended Hamiltonian is better than its total Hamiltonian.
55059613
Reconstruction of IceCube coincident events and study of composition-sensitive observables using both the surface and deep detector
The combined information from cosmic ray air showers that trigger both the surface and underground parts of the IceCube Neutrino Observa- tory allows the reconstruction of both the energy and mass of the primary particle through the knee region of the energy spectrum and above. The properties of high-energy muon bundles, created early in the formation of extensive air showers and capable of penetrating deep into the ice, are related to the primary energy and composition. New methods for reconstructing the direction and composition-sensitive properties of muon bundles are shown. Based on a likelihood minimization pro- cedure using IceCube signals, and accounting for photon propagation, ice properties, and the energy loss processes of muons in ice, the muon bundle energy loss is reconstructed. The results of the high- energy muon bundle reconstruction in the deep ice and the reconstruction of the lateral distribution of low energy particles in the surface detector can be combined to study primary composition and energy. The performance and composition sensitivity for both simulated and experimental data are discussed. Keywords: Cosmic ray composition, IceTop/IceCube, high-energy muon bundles
119126370
Toroidal Lie superalgebras and free field representations
A loop-algebraic presentation is given for toroidal Lie superalgebras of classical types. Based on the loop superalgebra presentation free field realizations of toroidal Lie superalgebras are constructed for types $A(m,n)$, $B(m,n)$, C(n) and $D(m,n)$.