Normal Nuclear Matter Research Articles

Nonquenching of gA in nuclei, Landau-Migdal fixed-point theory, and emergence of scale symmetry in dense baryonic matter

How the axial coupling constant $g_A$ in nuclear Gamow-Teller transitions described in shell model gets "quenched" to a universal constant close to 1 can be explained by nuclear correlations in Fermi-liquid fixed point theory using a scale-symmetric chiral Lagrangian supplemented with hidden local symmetric vector mesons. Contrary to what one might naively suspect -- and has been discussed in some circles, there is no fundamental quenching at nuclear matter density due to QCD condensates. When the density of many-body systems treated with the same Lagrangian increases beyond the density $n=n_{1/2}\gsim 2n_0$ (where $n_0$ is the normal nuclear matter density) at which skyrmions representing baryons fractionize to half-skyrmions, with the $\rho$ meson driven toward the vector manifestation fixed point and a scalar meson $\sigma$ driven to the dilaton-limit fixed point with the nucleons parity-doubled, the dense matter supports the "pseudo-conformal" sound velocity for $n\gsim n_{1/2}$ while the trace of the energy momentum tensor remains non-vanishing. A plausible interpretation is that this signals the emergence of scale symmetry not explicitly present or hidden in QCD in the vacuum. The fundamental constant $g_A$, unaffected by QCD condensates for $n< n_{1/2}$, does go to 1 as the dilaton-limit fixed point is approached before arriving at chiral restoration, but it is not directly related to the "quenched $g_A$" in nuclei which can be explained as a Fermi-liquid fixed point quantity. The mechanism that produces a precocious pseudo-conformal sound velocity is expected to impact on the tidal deformability $\Lambda$ in gravity waves from coalescing neutron stars.

Impact of medium modifications of the nucleon weak and electromagnetic form factors on the neutrino mean free path in dense matter

Impact of the in-medium modified nucleon weak and electromagnetic form factors on the neutrino mean free path in dense matter is studied by considering both the weak and electromagnetic interactions of neutrinos with the constituents of the matter. A relativistic mean field model and the quark-meson coupling model are respectively adopted for the in-medium effective nucleon mass and nucleon form factors. We find that the cross sections of neutrino scattering in cold nuclear medium decreases when the in-medium modification of the nucleon weak and electromagnetic form factors are taken into account. This reduction results in the enhancement of the neutrino mean free path, in particular at the baryon density of around a few times of the normal nuclear matter density. The enhancement of the neutrino mean free path is estimated to be about 10--40\% compared with the values obtained without the medium modification of the nucleon form factors, and the enhancement is expected to accelerate the cooling of neutron stars.

Influence of flow constraints on the properties of the critical endpoint of symmetric nuclear matter

We propose a novel family of equations of state for symmetric nuclear matter based on the induced surface tension concept for the hard-core repulsion. It is shown that having only four adjustable parameters the suggested equations of state can, simultaneously, reproduce not only the main properties of the nuclear matter ground state, but the proton flow constraint up its maximal particle number densities. Varying the model parameters we carefully examine the range of values of incompressibility constant of normal nuclear matter and its critical temperature which are consistent with the proton flow constraint. This analysis allows us to show that the physically most justified value of nuclear matter critical temperature is 15.5-18 MeV, the incompressibility constant is 270-315 MeV and the hard-core radius of nucleons is less than 0.4 fm.

Catalysis of partial chiral symmetry restoration by Δ matter

We study the phase structure of dense hadronic matter including $\Delta(1232)$ as well as N(939) based on the parity partner structure, where the baryons have their chiral partners with a certain amount of chiral invariant masses. We show that, in symmetric matter, $\Delta$ enters into matter in the density region of about one to four times of normal nuclear matter density, $\rho_B \sim 1 - 4\rho_0$. The onset density of $\Delta$ matter depends on the chiral invariant mass of $\Delta$, $m_{\Delta0}$: The lager $m_{\Delta0}$, the bigger the onset density. The $\Delta$ matter of $\rho_B \sim 1 - 4\rho_0$ is unstable due to the existence of $\Delta$, and the stable $\Delta$-nucleon matter is realized at about $\rho_B \sim 4\rho_0$, i.e., the phase transition from nuclear matter to $\Delta$-nucleon matter is of first order for small $m_{\Delta0}$, and it is of second order for large $m_{\Delta0}$. We find that, associated with the phase transition, the chiral condensate changes very rapidly, i.e., the chiral symmetry restoration is accelerated by \Delta matter. As a result of the accelerations, there appear $N^*$(1535) and $\Delta$(1700), which are the chiral partners to N(939) and ${\Delta}$(1232), in high density matter, signaling the partial chiral symmetry restoration. Furthermore, we find that complete chiral symmetry restoration itself is delayed by $\Delta$ matter. We also calculate the effective masses, pressure and symmetry energy to study how the transition to $\Delta$ matter affects such physical quantities. We observe that the physical quantities change drastically at the transition density.

The d⁎(2380) in Neutron Stars — A New Degree of Freedom?

Elucidating the appropriate microscopic degrees of freedom within neutron stars remains an open question which impacts nuclear physics, particle physics and astrophysics. The recent discovery of the first non-trivial dibaryon, the d⁎(2380), provides a new candidate for an exotic degree of freedom in the nuclear equation of state at high matter densities. In this paper a first calculation of the role of the d⁎(2380) in neutron stars is performed based on a relativistic mean field description of the nucleonic degrees of freedom supplemented by a free boson gas of d⁎(2380). The calculations indicate that the d⁎(2380) would appear at densities around three times normal nuclear matter saturation density and comprise around 20% of the matter in the centre of heavy stars with higher fractions possible in the higher densities of merger processes. The d⁎(2380) would also reduce the maximum star mass by around 15% and have significant influence on the fractional proton/neutron composition. New possibilities for neutron star cooling mechanisms arising from the d⁎(2380) are also predicted.

Partial restoration of chiral symmetry in cold nuclear matter: the ϕ-meson case

The work presented at this workshop is divided into two parts. In the first part, the mass and decay width of the ϕ-meson in cold nuclear matter are computed in an effective Lagrangian approach. The medium dependence of these properties are obtained by evaluating kaon-antikaon loop contributions to the ϕ-meson self-energy, employing medium-modified kaon masses calculated using the quark-meson coupling model. The loop integral is regularized with a dipole form factor, and the sensitivity of the results to the choice of cutoff mass in the form factor is investigated. At normal nuclear matter density, we find a downward shift of the ϕ mass by a few percent, while the decay width is enhanced by an order of magnitude. Our results support the literature which suggest that one should observe a small downward mass shift and a large broadening of the decay width. In the second part, we present ϕ-meson-nucleus bound state energies and absorption widths for four selected nuclei, calculated by solving the KleinGordon equation with complex optical potentials. The attractive potential for the ϕ-meson in the nuclear medium originates from the in-medium enhanced loop in the ϕ-meson self-energy. The results suggest that the ϕ-meson should form bound states with all the nuclei considered. However, the identification of the signal for these predicted bound states will need careful investigation because of their sizable absorption widths.

Lambda-nuclear interactions and hyperon puzzle in neutron stars

Brueckner theory is used to investigate the in-medium properties of a $\Lambda$-hyperon in nuclear and neutron matter, based on hyperon-nucleon interactions derived within SU(3) chiral effective field theory (EFT). It is shown that the resulting $\Lambda$ single-particle potential $U_\Lambda(p_\Lambda =0,\rho)$ becomes strongly repulsive for densities $\rho$ of two-to-three times that of normal nuclear matter. Adding a density-dependent effective $\Lambda N$-interaction constructed from chiral $\Lambda NN$ three-body forces increases the repulsion further. Consequences of these findings for neutron stars are discussed. It is argued that for hyperon-nuclear interactions with properties such as those deduced from the SU(3) EFT potentials, the onset for hyperon formation in the core of neutron stars is expected to be shifted to extremely high baryon density, thus potentially resolving the so-called hyperon puzzle.

ϕ meson mass and decay width in nuclear matter and nuclei

The mass and decay width of the ϕ meson in cold nuclear matter are computed in an effective Lagrangian approach. The medium dependence of these properties are obtained by evaluating kaon–antikaon loop contributions to the ϕ self-energy, employing the medium-modified kaon masses, calculated using the quark-meson coupling model. The loop integral is regularized with a dipole form factor, and the sensitivity of the results to the choice of cutoff mass in the form factor is investigated. At normal nuclear matter density we find a downward shift of the ϕ mass by a few percent, while the decay width is enhanced by an order of magnitude. For a large variation of the cutoff mass parameter, the results for the ϕ mass and the decay width turn out to vary very little. Our results support results in the literature which suggest that one should observe a small downward mass shift and a large broadening of the decay width. In order to explore the possibility of studying the binding and absorption of ϕ mesons in nuclei, we also present the single-particle binding energies and half-widths of ϕ-nucleus bound states for some selected nuclei.

In-Medium Pion Valence Distribution Amplitude

After a brief review of the quark-based model for nuclear matter, and some pion properties in medium presented in our previous works, we report new results for the pion valence wave function as well as the valence distribution amplitude in medium, which are presented in our recent article. We find that both the in-medium pion valence distribution and the in-medium pion valence wave function, are substantially modified at normal nuclear matter density, due to the reduction in the pion decay constant.

In-medium pion valence distributions in a light-front model

Pion valence distributions in nuclear medium and vacuum are studied in a light-front constituent quark model. The in-medium input for studying the pion properties is calculated by the quark-meson coupling model. We find that the in-medium pion valence distribution, as well as the in-medium pion valence wave function, are substantially modified at normal nuclear matter density, due to the reduction in the pion decay constant.

In-medium properties of mesons

In the project B.4 , the modification of meson properties (mass, width) in a nuclear medium has been studied in photoproduction of mesons off nuclear targets. This work has been motivated by theoretical expectations of in-medium modifications of hadrons based on the conjecture of a partial restoration of chiral symmetry in a strongly interacting medium. It has been shown that these in-medium changes can be discussed in a compact form in terms of an optical potential describing the meson-nucleus interaction. Experimental approaches to determine the real and imaginary part of the meson-nucleus potential have been developed. The experiments have been performed with the Crystal Barrel/TAPS detector at the electron accelerator ELSA (Bonn) and the Crystal Ball/TAPS detector at MAMI (Mainz). Measuring the excitation function and momentum distribution for photo production of ω and η′ mesons, the real parts of the ω and η′ -nucleus potential, given by the in-medium mass shift, have been determined. For the η′ meson a lowering of the mass at normal nuclear matter density by -(39±7(stat)±15(syst)) MeV is observed, while for the ω meson a slightly smaller mass shift is found, however, with much larger uncertainties, not excluding a zero mass shift. The imaginary part of the potentials has been extracted from the measurement of the transparency ratio which compares the meson production cross section per nucleon within a nucleus to the production cross section off the free proton. For the η′ meson the imaginary part of the potential is found to be smaller than the real part. In case of the ω meson the opposite is observed. This makes the η′ meson a good candidate for the search for meson-nucleus bound states while no resolved ω mesic states can be expected. The results are compared with theoretical predictions. An outlook on future experiments is given.

Negative-parity nucleon excited state in nuclear matter

Spectral functions of the nucleon and its negative parity excited state in nuclear matter are studied using QCD sum rules and the maximum entropy method (MEM). It is found that in-medium modifications of the spectral functions are attributed mainly to density dependencies of the $\langle \bar{q}q \rangle $ and $\langle q^{\dagger}q \rangle $ condensates. The MEM reproduces the lowest-energy peaks of both the positive and negative parity nucleon states at finite density up to $\rho \sim \rho_N$ (normal nuclear matter density). As the density grows, the residue of the nucleon ground state decreases gradually while the residue of the lowest negative parity excited state increases slightly. On the other hand, the positions of the peaks, which correspond to the total energies of these states, are almost density independent for both parity states. The density dependencies of the effective masses and vector self-energies are also extracted by assuming the mean-field green functions for the peak states. We find that, as the density increases, the nucleon effective mass decreases while the vector self-energy increases. The density dependence of these quantities for the negative parity state on the other hand turns out to be relatively weak.

Determination of the real part of theη′-Nb optical potential

The excitation function and momentum distribution of η′ mesons have been measured in photoproduction off Nb93 in the energy range of 1.2–2.9 GeV. The experiment has been performed with the combined Crystal Barrel and MiniTAPS detector system, using tagged photon beams from the ELSA electron accelerator. Information on the sign and magnitude of the real part of the η′-Nb potential has been extracted from a comparison of the data with model calculations. An attractive potential of −(41±10(stat)±15(syst)) MeV depth at normal nuclear matter density is deduced within model uncertainties. This value is consistent with the potential depth of −(37±10(stat)±10(syst)) MeV obtained in an earlier measurement for a light nucleus (carbon). This relatively shallow η′-nucleus potential will make the search for η′-nucleus bound states more difficult.Received 12 May 2016DOI:https://doi.org/10.1103/PhysRevC.94.025205©2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear forcesNuclear matterNucleon-nucleon interactionsPhotonuclear reactionsPhysical SystemsLight mesonsNuclear PhysicsParticles & Fields

Scale-invariant hidden local symmetry, topology change, and dense baryonic matter

When scale symmetry is implemented into hidden local symmetry in low-energy strong interactions to arrive at a scale-invariant hidden local symmetric (HLS) theory, the scalar $f_0(500)$ may be interpreted as pseudo-Nambu-Goldstone (pNG) boson, i.e., dilaton, of spontaneously broken scale invariance, joining the pseudo-scalar pNG bosons $\pi$ and the matter fields $V=(\rho,\omega)$ as relevant degrees of freedom. Implementing the skyrmion-half-skyrmion transition predicted at large $N_c$ in QCD at a density roughly twice the nuclear matter density found in the crystal simulation of dense skyrmion matter, we determine the intrinsically density-dependent (IDD) "bare parameters" of the scale-invariant HLS Lagrangian matched to QCD at a matching scale $\Lambda_M$. The resulting effective Lagrangian, with the parameters scaling with the density of the system, is applied to nuclear matter and dense baryonic matter relevant to massive compact stars by means of the double-decimation renormalization-group $V_{lowk}$ formalism. We satisfactorily post-dict the properties of normal nuclear matter and more significantly {\it predict} the EoS of dense compact-star matter that quantitatively accounts for the presently available data coming from both the terrestrial and space laboratories. We interpret the resulting structure of compact-star matter as revealing how the combination of hidden-scale symmetry and hidden local symmetry manifests itself in compressed baryonic matter.

Maximum pulsar mass, equation of state and structure of neutron-star cores

The structure of neutron stars is determined by the equation of state of dense matter in their interiors. Brief review of the equation of state from neutron star surface to its center is presented. Recent discovery of two two-solar-mass pulsars puts interesting constraints on the poorly known equation of state of neutron-star cores for densities greater than normal nuclear matter density. Namely, this equation of state has to be stiff enough to yield maximum allowable mass of neutron stars greater than two solar masses. There are many models of neutron stars cores involving exclusively nucleons that satisfy this constraint. However, for neutron-star models based on recent realistic baryon interaction, and allowing for the presence of hyperons, the hyperon softening of the equation of state yields maximum masses significantly lower than two solar masses. Proposed ways out from this ”hyperon puzzle” are presented. They require a very fine tuning of parameters of dense hadronic matter and quark matter models. Consequences for the mass-radius relation for neutron stars are illustrated. A summary of the present situation and possible perspectives/challenges, as well as possible observational tests, are given.

Three-body force effect on the properties of neutron-rich nuclear matter

We review our research work on the single-particle properties and the equation of state (EOS) of isospin asymmetric nuclear matter within the framework of the Brueckner-Hartree-Fock (BHF) approach extended by including a microscopic three-body force (TBF). The TBF is shown to affect significantly the nuclear matter EOS and the density dependence of nuclear symmetry energy at high densities above the normal nuclear matter density, and it is necessary for reproducing the empirical saturation property of symmetric nuclear matter in a nonrelativistic microscopic framework. The TBF-induced rearrangement effect and the ground state (g.s.) correlation effect on the s.p. properties in neutron-rich nuclear matter are investigated. Both effects turn out to be crucial for predicting reliably the s.p. properties within the Brueckner framework. The TBF effect on nucleon superfluidity in neutron star matter and neutron stars has also been discussed.

Study of in-medium properties in the (γ, ) reaction on nuclei

We study the near-threshold photoproduction of mesons from nuclei in coincidence with forward going protons in the kinematical conditions of the Crystal Barrel/TAPS experiment, recently performed at ELSA. The calculations have been performed within a collision model based on the nuclear spectral function. The model accounts for both the primary process and the two-step intermediate nucleon rescattering processes as well as the effect of the nuclear mean-field potential. We calculate the exclusive kinetic energy distributions for the 12C(γ, ) reaction for different scenarios of in-medium modification. We find that the considered two-step rescattering mechanism plays an insignificant role in photoproduction off the carbon target. We also demonstrate that the calculated kinetic energy distributions in primary photon–proton production reveal strong sensitivity to the depth of the real potential at normal nuclear matter density (or to the in-medium mass shift) in the studied incident photon energy regime. Therefore, such observables may be useful to help determine the above in-medium renormalization from the comparison of the results of our calculations with the data from the CBELSA/TAPS experiment. In addition, we show that these distributions are also strongly influenced by the momentum-dependent optical potential, which the outgoing participant proton feels inside the carbon nucleus. This potential should be taken into account in the analysis of these data with the aim to obtain information on the modification in cold nuclear matter.

Kaon pair production in proton-nucleus collisions at 2.83 GeV kinetic energy

The production of non-ϕK+K− pairs by protons at 2.83 GeV kinetic energy on C, Cu, Ag, and Au targets has been investigated by using the COSY-ANKE magnetic spectrometer. The K− momentum dependence of the differential cross section has been measured for laboratory polar angles θK±≤12∘ over the 0.2–0.9 GeV/c range. The comparison of the data with detailed model calculations indicates an attractive K−-nucleus potential of about −60 MeV at normal nuclear matter density at a mean momentum of 0.5 GeV/c. However, this approach has difficulty in reproducing the smallness of the observed cross sections at low-K− momenta.Received 9 September 2015DOI:https://doi.org/10.1103/PhysRevC.92.065201©2015 American Physical Society

K + mesons, a robust probe to measure the hadronic equation of state?

We demonstrate that the K+ mesons are sensitive to nuclear matter properties, especially to the hadronic equation of state (EoS). Once one has understood how K+ behave in hadronic matter we can use these mesons to study the hadronic EoS. Several observables point towards a rather soft EoS at densities around three times the normal nuclear matter density ρ0.

Asymmetric nuclear matter in a parity doublet model with hidden local symmetry

We construct a model to describe dense hadronic matter at zero and finite temperature, based on the parity doublet model of DeTar and Kunihiro, with including the iso-singlet scalar meson $\sigma$ as well as $\rho$ and $\omega$ mesons. We show that, by including a six-point interaction of $\sigma$ meson, the model reasonably reproduces the properties of the normal nuclear matter with the chiral invariant nucleon mass $m_0$ in the range from $500~{\rm MeV}$ to $900~{\rm MeV}$. Furthermore, we study the phase diagram based on the model, which shows that the value of the chiral condensate drops at the liquid-gas phase transition point and at the chiral phase transition point. We also study asymmetric nuclear matter and find that the first order phase transition for the liquid-gas phase transition disappears in asymmetric matter and that the critical density for the chiral phase transition at non-zero density becomes smaller for larger asymmetry.