118473009
Probing Nuclear Symmetry Energy and its Imprints on Properties of Nuclei, Nuclear Reactions, Neutron Stars and Gravitational Waves
Significant progress has been made in recent years in constraining nuclear symmetry energy at and below the saturation density of nuclear matter using data from both terrestrial nuclear experiments and astrophysical observations. However, many interesting questions remain to be studied especially at supra-saturation densities. In this lecture note, after a brief summary of the currently available constraints on nuclear symmetry energy near the saturation density we first discuss the relationship between the symmetry energy and the isopin and momentum dependence of the single-nucleon potential in isospin-asymmetric nuclear medium. We then discuss several open issues regarding effects of the tensor force induced neutron-proton short-range correlation (SRC) on nuclear symmetry energy. Finally, as an example of the impacts of nuclear symmetry energy on properties of neutron stars and gravitational waves, we illustrate effects of the high-density symmetry energy on the tidal polarizability of neutron stars in coalescing binaries.
118586397
Relationship between the symmetry energy and the single-nucleon potential in isospin-asymmetric nucleonic matter
In this contribution, we review the most important physics presented originally in our recent publications. Some new analyses, insights and perspectives are also provided. We showed recently that the symmetry energy Esym(ρ) and its density slope L(ρ) at an arbitrary density ρ can be expressed analytically in terms of the magnitude and momentum dependence of the single-nucleon potentials using the Hugenholtz-Van Hove (HVH) theorem. These relationships provide new insights about the fundamental physics governing the density dependence of nuclear symmetry energy. Using the isospin and momentum (k dependent MDI interaction as an example, the contribution of different terms in the single-nucleon potential to the Esym(ρ) and L(ρ) are analyzed in detail at different densities. It is shown that the behavior of Esym is mainly determined by the first-order symmetry potential Usym,1(ρ, k) of the single-nucleon potential. The density slope L(ρ) depends not only on the first-order symmetry potential Usym,1(ρ, k) but also on the second-order one Usym,2(ρ, k). Both the Usym,1(ρ, k) and Usym,2(ρ, k) at normal density ρ0 are constrained by the isospin- and momentum-dependent nucleon optical potential extracted from the available nucleon-nucleus scattering data. The Usym,2(ρ, k) especially at high density and momentum affects significantly the L(ρ), but it is theoretically poorly understood and currently there is almost no experimental constraints known.
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.
118442016
Extracting the nuclear symmetry potential and energy from neutron-nucleus scattering data
Abstract According to the Hugenholtz–Van Hove theorem, the symmetry energy and its density slope can be decomposed uniquely in terms of the single-nucleon potential in asymmetric nuclear matter which, at normal density, can be constrained by the nucleon optical model potential extracted from analyzing the nucleon–nucleus scattering data. To more accurately extract information on the symmetry energy and its density slope at normal density from neutron–nucleus scattering data, going beyond the well-known Lane potential, we include consistently the second-order terms in isospin asymmetry in both the optical model potential and the symmetry energy decomposition. We find that the strength of the second-order symmetry potential U sym , 2 in asymmetric nuclear matter is significant compared to the first-order one U sym , 1 , especially at high nucleon momentum. While the U sym , 1 at normal density decreases with nucleon momentum, the U sym , 2 is found to have the opposite behavior. Moreover, we discuss effects of the U sym , 1 and U sym , 2 on determining the density dependence of the symmetry energy, and we find that the available neutron–nucleus scattering data favor a softer density dependence of the symmetry energy at normal density with a negligible contribution from the U sym , 2 .
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.
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.
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].
121199327
Dirac Canonical Quantization of Composite Fermions QED
Composite Fermions QED is quantized by using the Dirac’s canonical formalism for constrained systems. As a strategy, we first work out the constraints (including primary and secondary constraints), combine two first-class constraints, introduce Coulomb gauge and its stationary as gauge conditions, and then quantize, replacing the Dirac brackets with quantum commutators.
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 $D(m,n)$.
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.
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.