Stability of relativistic nuclear matter against pion condensation

Birbrair, B.L.; Fomenko, V. N.; Savushkin, L. N.

doi:10.1088/0305-4616/8/11/006

Cited by 13 publications

(12 citation statements)

References 18 publications

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“…An accurate description of pion interactions with few-body systems and nuclei requires that the ∆ resonance be included. This can be done most efficiently by introducing the ∆ as another effective degree of freedom [Pe68,Bi82,De92a,We93,Ta96]. For simplicity, and because we are concerned primarily with bulk and isoscalar properties of nuclei, we will omit ∆ interactions in the models discussed below.…”

Section: Effective Field Theory (Eft)mentioning

confidence: 99%

Recent Progress in Quantum Hadrodynamics

Serot

Walecka

1997

Int. J. Mod. Phys. E

987

1,511

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Quantum hadrodynamics (QHD) is a framework for describing the nuclear many-body problem as a relativistic system of baryons and mesons. Motivation is given for the utility of such an approach and for the importance of basing it on a local, Lorentz-invariant lagrangian density. Calculations of nuclear matter and finite nuclei in both renormalizable and nonrenormalizable, effective QHD models are discussed. Connections are made between the effective and renormalizable models, as well as between relativistic mean-field theory and more sophisticated treatments. Recent work in QHD involving nuclear structure, electroweak interactions in nuclei, relativistic transport theory, nuclear matter under extreme conditions, and the evaluation of loop diagrams is reviewed.

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Section: Effective Field Theory (Eft)mentioning

confidence: 99%

Recent Progress in Quantum Hadrodynamics

Serot

Walecka

1997

Int. J. Mod. Phys. E

987

1,511

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“…In the nuclear ground state A nucleons occupy the lowest single-nucleon orbitals, determined self-consistently by the iterative solution of the Dirac equation (2). Expressing the single-nucleon energy as E i = m + ε i , where m is the nucleon mass, and rewriting the Dirac equation as a system of two equations for φ i and χ i , then, noticing that for bound states ε i << m, the equation for the upper component φ i of the Dirac spinor reduces to the Schrödinger-like form [18,19,21] …”

Section: Spin-orbit Term In Relativistic Effective Interactionsmentioning

confidence: 99%

Spin-orbit interaction in relativistic nuclear structure models

et al. 2016

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Relativistic self-consistent mean-field (SCMF) models naturally account for the coupling of the nucleon spin to its orbital motion, whereas non-relativistic SCMF methods necessitate a phenomenological ansatz for the effective spin-orbit potential. Recent experimental studies aim to explore the isospin properties of the effective spin-orbit interaction in nuclei. SCMF models are very useful in the interpretation of the corresponding data, however standard relativistic mean-field and nonrelativistic Hartree-Fock models use effective spin-orbit potentials with different isovector properties, mainly because exchange contributions are not treated explicitly in the former. The impact of exchange terms on the effective spin-orbit potential in relativistic mean-field models is analysed, and it is shown that it leads to an isovector structure similar to the one used in standard non-relativistic Hartree-Fock. Data on the isospin dependence of spin-orbit splittings in spherical nuclei could be used to constrain the isovector-scalar channel of relativistic mean-field models. The reproduction of the empirical kink in the isotope shifts of even Pb nuclei by relativistic effective interactions points to the occurrence of pseudospin symmetry in the single-neutron spectra in these nuclei.

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“…2 This last point has important implications for an alternative class of RMF investigations, which are not based on EFT but are defined by some specific underlying physics. Examples include models that contain different degrees of freedom (quarks) [47,48], or different types of meson-baryon couplings (derivative couplings) [49,50], or explicit inclusion of chiral symmetry [51][52][53][54][55][56]. (The chronology for this development can be gleaned from some recent review articles [2][3][4], the papers cited above, and references therein.)…”

Section: Implications and Summarymentioning

confidence: 99%

Parameter counting in relativistic mean-field models

2000

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Power counting is applied to relativistic mean-field energy functionals to estimate contributions to the energy from individual terms. New estimates for isovector, tensor, and gradient terms in finite nuclei are shown to be consistent with direct, high-quality fits. The estimates establish a hierarchy of model parameters and identify how many parameters are well constrained by bulk nuclear observables. We conclude that four (possibly five) isoscalar, nongradient parameters, one gradient parameter, and one isovector parameter are well determined by the usual bulk nuclear observables.Relativistic mean-field (RMF) descriptions of the nuclear many-body problem have existed for nearly fifty years [1]. An extensive body of work [2][3][4] has shown that RMF theories can realistically reproduce the bulk and single-particle properties of medium to heavy nuclei. Successful RMF theories are characterized by large, neutral, Lorentz scalar and vector potentials (roughly several hundred MeV at nuclear equilibrium density), a new saturation mechanism for nuclear matter that arises from relativistic (i.e., velocity-dependent) interaction effects from the scalar potential, and a nuclear spin-orbit force that is determined by this velocity dependence. The vector potential provides an efficient representation of the short-range nucleon-nucleon (NN) repulsion, while the scalar potential provides the midrange NN attraction by simulating correlated, scalar-isoscalar two-pion exchange, which is the most important pionic contribution for describing the bulk properties of nuclear matter.For many years, RMF model parameters were determined by fitting them to the properties of nuclei or nuclear matter using various "black-box" fitting schemes [5][6][7]. Direct connections between the RMF parameters and the systematics of nuclear observables have begun to emerge only recently [8][9][10][11]. The modern theoretical viewpoint underlying the RMF, which relies on the ideas of Effective Field Theory (EFT) and of Density Functional Theory (DFT) [11,4,12], provides a systematic truncation procedure for the RMF energy functional. However, it introduces more parameters than can be unambiguously determined by the relevant data. The present work uses EFT power counting to examine the quantity of information contained in the bulk and single-particle input data, and to identify how many parameters can be reliably determined by these data.The original Walecka model [13] (without nonlinear field interactions), contained two free isoscalar parameters in nuclear matter, which were used to fit the equilibrium density and binding energy. An isovector coupling was added [14] to reproduce the bulk symmetry energy, and for finite nuclei, a single scale parameter (the scalar "meson" mass) was chosen to reproduce the rms charge radius of 40 Ca. These procedures yielded reasonable results for charge-density distributions of spherical nuclei and for single-particle spectra, revealing that the nuclear shell model was obtained automatically without any specific adjust...

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Stability of relativistic nuclear matter against pion condensation

Cited by 13 publications

References 18 publications

Recent Progress in Quantum Hadrodynamics

Recent Progress in Quantum Hadrodynamics

Spin-orbit interaction in relativistic nuclear structure models

Parameter counting in relativistic mean-field models

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