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

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