Low-momentum NN interactions and all-order summation of ring diagrams of symmetric nuclear matter

Abstract

We study the equation of state for symmetric nuclear matter using a ring-diagram approach in which the particle-particle hole-hole ($pphh$) ring diagrams within a momentum model space of decimation scale $\Lambda$ are summed to all orders. The calculation is carried out using the renormalized low-momentum nucleon-nucleon (NN) interaction $V_{low-k}$, which is obtained from a bare NN potential by integrating out the high-momentum components beyond $\Lambda$. The bare NN potentials of CD-Bonn, Nijmegen and Idaho have been employed. The choice of $\Lambda$ and its influence on the single particle spectrum are discussed. Ring-diagram correlations at intermediate momenta ($k\simeq$ 2 fm${}^{-1}$) are found to be particularly important for nuclear saturation, suggesting the necessity of using a sufficiently large decimation scale so that the above momentum region is not integrated out. Using $V_{low-k}$ with $\Lambda \sim 3$ fm${}^{-1}$, we perform a ring-diagram computation with the above potentials, which all yield saturation energies $E/A$ and Fermi momenta $k_F^{(0)}$ considerably larger than the empirical values. On the other hand, similar computations with the medium-dependent Brown-Rho scaled NN potentials give satisfactory results of $E/A\simeq -15$ MeV and $k_F^{(0)}\simeq 1.4$ fm${}^{-1}$. The effect of this medium dependence is well reproduced by an empirical 3-body force of the Skyrme type.

arXiv comment8 pages, 7 figures

References in corpus (25)

• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Construction of high-quality Nucleon-Nucleon potential models
• 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
• Current correlation functions, QCD sum rules and vector mesons in baryonic matter
• 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?
• Shell-model calculations and realistic effective interactions
• Renormalization group approach to neutron matter: quasiparticle interactions, superfluid gaps and the equation of state
• 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
• Low momentum nucleon-nucleon potentials with half-on-shell T-matrix equivalence
• Double Decimation and Sliding Vacua in the Nuclear Many-Body System
• Low Momentum Nucleon-Nucleon Interaction and Fermi Liquid Theory
• Pairing properties of nucleonic matter employing dressed nucleons
• Dependence of the BCS 1S0 superfluid pairing gap on nuclear interactions
• The structure of nuclear systems derived from low momentum nucleon-nucleon potentials
• Family of Hermitian Low-Momentum Nucleon Interactions with Phase Shift Equivalence
• Nuclear matter with Brown-Rho-scaled Fermi liquid interactions
• Nuclear Saturation with in-Medium Meson Exchange Interactions
• Microscopic Nuclear Structure Based upon a Chiral NN Potential
• Low-momentum ring diagrams of neutron matter at and near the unitary limit
• Hans Bethe: The Nuclear Many Body Problem

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