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 $E_{sym}(\rho)$ and its density slope $L(\rho)$ at an arbitrary density $\rho$ 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 $E_{sym}(\rho)$ and $L(\rho)$ are analyzed in detail at different densities. It is shown that the behavior of $E_{sym}(\rho)$ is mainly determined by the first-order symmetry potential $U_{sym,1}(\rho,k)$ of the single-nucleon potential. The density slope $L(\rho)$ depends not only on the first-order symmetry potential $U_{sym,1}(\rho,k)$ but also the second-order one $U_{sym,2}(\rho,k)$. Both the $U_{sym,1}(\rho,k)$ and $U_{sym,2}(\rho,k)$ at normal density $\rho_0$ are constrained by the isospin and momentum dependent nucleon optical potential extracted from the available nucleon-nucleus scattering data. The $U_{sym,2}(\rho,k)$ especially at high density and momentum affects significantly the $L(\rho)$, but it is theoretically poorly understood and currently there is almost no experimental constraints known.Comment: 9 pages, 6 figures, Review paper, Contribution to the "Topical Issue" on "Nuclear Symmetry Energy" in European Physical Journal

Delineating effects of tensor force on the density dependence of nuclear symmetry energy

In this talk, we report results of our recent studies to delineate effects of the tensor force on the density dependence of nuclear symmetry energy within phenomenological models. The tensor force active in the isosinglet neutron-proton interaction channel leads to appreciable depletion/population of nucleons below/above the Fermi surface in the single-nucleon momentum distribution in cold symmetric nuclear matter (SNM). We found that as a consequence of the high momentum tail in SNM the kinetic part of the symmetry energy $E^{kin}_{sym}(\rho)$ is significantly below the well-known Fermi gas model prediction of approximately $12.5 (\rho/\rho_0)^{2/3}$. With about 15% nucleons in the high momentum tail as indicated by the recent experiments at J-Lab by the CLAS Collaboration, the $E^{kin}_{sym}(\rho)$ is negligibly small. It even becomes negative when more nucleons are in the high momentum tail in SNM. These features have recently been confirmed by three independent studies based on the state-of-the-art microscopic nuclear many-body theories. In addition, we also estimate the second-order tensor force contribution to the potential part of the symmetry energy. Implications of these findings in extracting information about nuclear symmetry energy from nuclear reactions are discussed briefly.Comment: Talk given by Chang Xu at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS

Why is the nuclear symmetry energy so uncertain at supra-saturation densities?

Within the interacting Fermi gas model for isospin asymmetric nuclear matter, effects of the in-medium three-body interaction and the two-body short-range tensor force due to the $\rho$ meson exchange as well as the short-range nucleon correlation on the high-density behavior of the nuclear symmetry energy are demonstrated respectively in a transparent way. Possible physics origins of the extremely uncertain nuclear symmetry energy at supra-saturation densities are discussed.Comment: Added discussions and revised format. Version to appear in Phys. Rev. C (2010

Probing isospin- and momentum-dependent nuclear effective interactions in neutron-rich matter

The single-particle potentials for nucleons and hyperons in neutron-rich matter generally depends on the density and isospin asymmetry of the medium as well as the momentum and isospin of the particle. It further depends on the temperature of the matter if the latter is in thermal equilibrium. We review here the extension of a Gogny-type isospin- and momentum-dependent interaction in several aspects made in recent years and their applications in studying intermediate-energy heavy ion collisions, thermal properties of asymmetric nuclear matter and properties of neutron stars. The importance of the isospin- and momentum-dependence of the single-particle potential, especially the momentum dependence of the isovector potential, is clearly revealed throughout these studies.Comment: 27 pages, 19 figures, 1 table, accepted version to appear in EPJA special volume on Nuclear Symmetry Energ

An 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 supra-saturation densities. The improved single nucleon potential will be useful for simulating more accurately nuclear reactions induced by rare isotope beams within transport models.Comment: 6 pages including 6 figures

Do environmental regulations cause enterprises to exit from market? Quasi-natural experiments based on China’s Cleaner Production Standards

Taking the implementation of Cleaner Production Standards at the industry level in China as a quasi-natural experiment, the impact of these standards on enterprises’ exit behavior was empirically analyzed by using the Difference-in-Differences method. Results suggested that the implementation of Cleaner Production Standards reduced the probability of enterprises exiting the market. A parallel trend test, Propensity Score Matching (PSM), and the exclusion of other policy factors were then used to verify the robustness of this finding. The impact mechanism test showed that implementation of the standards reduced the probability of enterprises exiting the market through improving total factor productivity and promoting enterprise product innovation. The heterogeneity test revealed that, on the one hand, the implementation of Cleaner Production Standards can reduce the probability of R&D intensive industries and medium-sized enterprises exiting the market, and protect innovative and moderately sized enterprises. On the other hand, the implementation of Cleaner Production Standards can increase the probability of state-owned enterprises and small-scale enterprises exiting the market and optimize the allocation of resources among enterprises. This paper has important implications for China’s future approach to environmental policy formulation as well as the optimization of domestic enterprise structur

A Leaf Recognition Algorithm for Plant Classification Using Probabilistic Neural Network

In this paper, we employ Probabilistic Neural Network (PNN) with image and data processing techniques to implement a general purpose automated leaf recognition algorithm. 12 leaf features are extracted and orthogonalized into 5 principal variables which consist the input vector of the PNN. The PNN is trained by 1800 leaves to classify 32 kinds of plants with an accuracy greater than 90%. Compared with other approaches, our algorithm is an accurate artificial intelligence approach which is fast in execution and easy in implementation.Comment: 6 pages, 3 figures, 2 table