Low-momentum interactions with Brown-Rho-Ericson scalings and the density dependence of the nuclear symmetry energy

Abstract

We have calculated the nuclear symmetry energy $E_{sym}(\rho )$ up to densities of $4\sim 5{\rho }_0$ with the effects from the Brown-Rho (BR) and Ericson scalings for the in-medium mesons included. Using the $V_{low-k}$ low-momentum interaction with and without such scalings, the equations of state (EOS) of symmetric and asymmetric nuclear matter have been calculated using a ring-diagarm formalism where the particle-particle-hole-hole ring diagrams are included to all orders. The EOS for symmetric nuclear matter and neutron matter obtained with linear BR scaling are both overly stiff compared with the empirical constraints of Danielewicz {\it et al.} \cite{daniel02}. In contrast, satisfactory results are obtained by either using the nonlinear Ericson scaling or by adding a Skyrme-type three-nucleon force (TNF) to the unscaled $V_{low-k}$ interaction. Our results for $E_{sym}(\rho )$ obtained with the nonlinear Ericson scaling are in good agreement with the empirical values of Tsang {\it et al.} \cite{tsang09} and Li {\it et al.} \cite{li05}, while those with TNF are slightly below these values. For densities below the nuclear saturation density ${\rho }_0$, the results of the above calculations are nearly equivalent to each other and all in satisfactory agreement with the empirical values.

arXiv comment7 pages, 6 figures

References in corpus (38)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Determination of the Equation of State of Dense Matter
• Neutron Star Observations: Prognosis for Equation of State Constraints
• Construction of high-quality Nucleon-Nucleon potential models
• Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions
• Isospin Asymmetry in Nuclei and Neutron Stars
• Reaction Dynamics with Exotic Beams
• Constraints on the density dependence of the symmetry energy
• Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition
• Model-independent low momentum nucleon interaction from phase shift equivalence
• Determination of the stiffness of the nuclear symmetry energy from isospin diffusion
• Circumstantial evidence for a soft nuclear symmetry energy at supra-saturation densities
• Current correlation functions, QCD sum rules and vector mesons in baryonic matter
• Nucleon-nucleon cross sections in neutron-rich matter and isospin transport in heavy-ion reactions at intermediate energies
• Hadron properties in the nuclear medium
• Low momentum nucleon-nucleon potential and shell model effective interactions
• Low momentum nucleon-nucleon potential and shell model effective interactions
• Is nuclear matter perturbative with low-momentum interactions?
• First observation of in-medium modifications of the omega meson
• Experimental Signature of Medium Modifications for rho and omega Mesons in the 12 GeV p + A Reactions
• Isospin-dependent properties of asymmetric nuclear matter in relativistic mean-field models
• Microscopic calculations in asymmetric nuclear matter
• Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction
• Low momentum nucleon-nucleon potentials with half-on-shell T-matrix equivalence
• Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes
• Neutron star properties and the equation of state of neutron-rich matter
• Shell model description of the 14C dating beta decay with Brown-Rho-scaled NN interactions
• The Microscopic Approach to Nuclear Matter and Neutron Star Matter
• Family of Hermitian Low-Momentum Nucleon Interactions with Phase Shift Equivalence
• Nuclear matter with Brown-Rho-scaled Fermi liquid interactions
• Low-momentum NN interactions and all-order summation of ring diagrams of symmetric nuclear matter
• Isospin Dynamics in Heavy Ion Collisions: from Coulomb Barrier to Quark Gluon Plasma
• Nuclear Saturation with in-Medium Meson Exchange Interactions
• Neutron star, $\beta$-stable ring-diagram equation of state and Brown-Rho scaling
• Low-momentum ring diagrams of neutron matter at and near the unitary limit
• Unitarity potentials and neutron matter at the unitary limit
• Light Vector Mesons

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