Potential In Nuclear Matter Research Articles

Differential rotation in compact objects with hyperons and delta isobars

AbstractNeutron stars may experience differential rotation on short, dynamical timescales following extreme astrophysical events like binary neutron star mergers. In this work, the masses and radii of differentially rotating neutron star models are computed. We employ a set of equations of states for dense hypernuclear and ‐admixed‐hypernuclear matter obtained within the framework of CDF theory in the relativistic Hartree‐Fock (RHF) approximation. Results are shown for varying meson‐ couplings, or equivalently the ‐potential in nuclear matter. A comparison of our results with those obtained for nonrotating stars shows that the maximum mass difference between differentially rotating and static stars is independent of the underlying particle composition of the star. We further find that the decrease in the radii and increase in the maximum masses of stellar models when ‐isobars are added to hyperonuclear matter (as initially observed for static and uniformly rotating stars) persist also in the case of differentially rotating neutron stars.

Rapidly rotating Δ-resonance-admixed hypernuclear compact stars

We use a set of hadronic equations of state derived from covariant density functional theory to study the impact of their high-density behavior on the properties of rapidly rotating Δ-resonance-admixed hyperonic compact stars. In particular, we explore systematically the effects of variations of the bulk energy isoscalar skewness, Qsat, and the symmetry energy slope, Lsym, on the masses of rapidly rotating compact stars. With models for equation of state satisfying all the modern astrophysical constraints, excessively large gravitational masses of around 2.5M⊙ are only obtained under three conditions: (a) strongly attractive Δ-resonance potential in nuclear matter, (b) maximally fast (Keplerian) rotation, and (c) parameter ranges Qsat≳500 MeV and Lsym≲50 MeV. These values of Qsat and Lsym have a rather small overlap with a large sample (total of about 260) parametrizations of covariant nucleonic density functionals. The extreme nature of requirements (a)-(c) reinforces the theoretical expectation that the secondary object involved in the GW190814 event is likely to be a low-mass black hole rather than a supramassive neutron star.

Implementing Chiral Three-Body Forces in Terms of Medium-Dependent Two-Body Forces

Three-nucleon (3N) forces are an indispensable ingredient for accurate few-body and many-body nuclear structure and reaction theory calculations. While the direct implementation of chiral 3N forces can be technically very challenging, a simpler approach is given by employing instead a medium-dependent NN interaction V_med that reflects the physics of three-body forces at the two-body normal-ordered approximation. We review the derivation and construction of V_med from the chiral 3N interaction at next-to-next-to-leading order (N2LO), consisting of a long-range $2\pi$-exchange term, a mid-range $1\pi$-exchange component and a short-range contact term. Several applications of V_med to the equation of state of cold nuclear and neutron matter, the nucleon single-particle potential in nuclear matter, and the nuclear quasiparticle interaction are discussed. We also explore differences in using local vs. nonlocal regulating functions on 3N forces and make direct comparisons to exact results at low order in perturbation theory expansions for the equation of state and single-particle potential. We end with a discussion and numerical calculation of the in-medium NN potential V_med from the next-to-next-to-next-to-leading order (N3LO) chiral 3N force, which consists of a series of long-range and short-range terms.

Extended Skyrme interactions for transport model simulations of heavy-ion collisions

Based on an extended Skyrme interaction that includes the terms in relative momenta up to sixth order, corresponding to the so-called Skyrme pseudopotential up to next-to-next-to-next-to leading order (N3LO), we derive the expressions of Hamiltonian density and single nucleon potential under general non-equilibrium conditions which can be applied in transport model simulations of heavy-ion collisions induced by neutron-rich nuclei. While the conventional Skyrme interactions, which include the terms in relative momenta up to second order, predict an incorrect behavior as a function of energy for nucleon optical potential in nuclear matter, the present extended N3LO Skyrme interaction can give a nice description for the empirical nucleon optical potential. We also construct three interaction sets with different high-density behaviors of the symmetry energy, by fitting both the empirical nucleon optical potential up to energy of $1$ GeV and the empirical properties of isospin asymmetric nuclear matter. These extended N3LO Skyrme interactions will be useful in transport model simulations of heavy-ion collisions induced by neutron-rich nuclei at intermediate and high energies, and they can also be useful in nuclear structure studies within the mean-field model.

Hypernuclear stars from relativistic Hartree-Fock density functional theory

The hypernuclear matter is studied within the relativistic Hartree-Fock theory employing several parametrizations of the hypernuclear density functional with density-dependent couplings. The equations of state and compositions of hypernuclear matter are determined for each parametrization and compact stars are constructed by solving their structure equations in spherical symmetry. We quantify the softening effect of Fock terms on the equation of state, as well as discuss the impact of tensor interactions, which are absent in the Hartree theories. Starting from models of density functionals which are fixed in the nuclear sector to the nuclear phenomenology, we vary the couplings in the hyperonic sector around the central values which are fitted to the hyperon potentials in nuclear matter. We use the SU(6) spin-flavor and SU(3) flavor symmetric quark models to relate the hyperonic couplings to the nucleonic ones. We find, consistent with previous Hartree studies, that for the SU(6) model the maximal masses of compact stars are below the two-solar mass limit. In the SU(3) model we find sufficiently massive compact stars with cores composed predominantly of $\Lambda$ and $\Xi$ hyperons and a low fraction of leptons (mostly electrons). The parameter space of the SU(3) model is identified where simultaneously hypernuclear compact stars obey the astrophysical limits on pulsar masses and the empirical hypernuclear potentials in nuclear matter are reproduced.

Three-baryon interaction generated by determinant interaction of quarks

We discuss the three-baryon interaction generated by the determinant interaction of quarks, known as the Kobayashi-Maskawa-'t Hooft (KMT) interaction. The expectation value of the KMT interaction operator is calculated in fully-antisymmetrized quark-cluster model wave functions for one-, two- and three-octet baryon states. The three-baryon potential from the KMT interaction is found to be repulsive for $NN\Lambda$ and $N\Lambda\Lambda$ systems, while it is zero for the $NNN$ system. The strength and range of the three-baryon potential are found to be comparable to those for the $NNN$ three-body potential obtained in lattice QCD simulations. The contribution to the $\Lambda$ single particle potential in nuclear matter is found to be 0.28 MeV and 0.73 MeV in neutron matter and symmetric nuclear matter at normal nuclear density, respectively. These repulsive forces are not enough to solve the hyperon puzzle, but may be measured in high-precision hyperisotope experiments.

Constraining the density dependence of the symmetry energy using the multiplicity and average pT ratios of charged pions

The charged pion multiplicity ratio in intermediate-energy heavy-ion collisions, a probe of the density dependence of symmetry energy above the saturation point, has been proven in a previous study to be extremely sensitive to the strength of the isovector $\mathrm{\ensuremath{\Delta}}(1232)$ potential in nuclear matter. As there is no knowledge, either from theory or experiment, about the magnitude of this quantity, the extraction of constraints on the slope of the symmetry energy at saturation by using exclusively the mentioned observable is hindered at present. It is shown that, by including the ratio of average ${p}_{T}$ of charged pions $\ensuremath{\langle}{p}_{T}^{({\ensuremath{\pi}}^{+})}\ensuremath{\rangle}/\ensuremath{\langle}{p}_{T}^{({\ensuremath{\pi}}^{\ensuremath{-}})}\ensuremath{\rangle}$ in the list of fitted observables, the noted problem can be circumvented. A realistic description of this observable requires accounting for the interaction of pions with the dense nuclear matter environment by the incorporation of the so-called $S$-wave and $P$-wave pion optical potentials. This is performed within the framework of a quantum molecular dynamics transport model that enforces the conservation of the total energy of the system. It is shown that constraints on the slope of the symmetry energy at saturation density and the strength of the $\mathrm{\ensuremath{\Delta}}$(1232) potential can be simultaneously extracted. A symmetry energy with a value of the slope parameter $L>50$ MeV is favored, at $1\ensuremath{\sigma}$ confidence level, from a comparison with published FOPI experimental data. A precise constraint will require experimental data more accurate than presently available, particularly for the charged pion multiplicity ratio, and better knowledge of the density and momentum dependence of the pion potential for the whole range of these two variables probed in intermediate-energy heavy-ion collisions.

Neutron star equations of state with optical potential constraint

Nuclear matter and neutron stars are studied in the framework of an extended relativistic mean-field (RMF) model with higher-order derivative and density dependent couplings of nucleons to the meson fields. The derivative couplings lead to an energy dependence of the scalar and vector self-energies of the nucleons. It can be adjusted to be consistent with experimental results for the optical potential in nuclear matter. Several parametrization, which give identical predictions for the saturation properties of nuclear matter, are presented for different forms of the derivative coupling functions. The stellar structure of spherical, non-rotating stars is calculated for these new equations of state (EoS). A substantial softening of the EoS and a reduction of the maximum mass of neutron stars is found if the optical potential constraint is satisfied.

Roles of chiral three-nucleon forces in nucleon–nucleus scattering

We investigate the effects of chiral three-nucleon force (3NF) at NNLO level on nucleon–nucleus (NA) elastic scattering, using the standard framework based on the Brueckner–Hartree–Fock method for nuclear matter and the g-matrix folding model for NA elastic scattering. The optical potential in nuclear matter calculated from chiral two-nucleon force (2NF) at N3LO level is found to be close to that from Bonn-B 2NF, whereas the Melbourne g-matrix is known as a practical effective nucleon–nucleon interaction constructed by localizing the g-matrices calculated from Bonn-B 2NF. As the first attempt to estimate chiral-3NF effects on NA scattering, the effects are simply introduced by multiplying the local Melbourne g-matrix by the ratio of the optical potential in nuclear matter calculated from chiral 2NF+3NF to that from chiral 2NF. For NA elastic scattering on various targets at 65 MeV, chiral 3NF makes the folding potential less attractive and more absorptive. The novel property for the imaginary part is originated in the enhancement of tensor correlations due to chiral 3NF (mainly the 2π-exchange diagram). The two effects are small for differential cross sections and vector analyzing powers at the forward and middle angles where the experimental data are available. If backward measurements are made, the data will reveal the effects of chiral 3NF.

Comparative study of three-nucleon potentials in nuclear matter

A new generation of local three-body potentials providing an excellent description of the properties of light nuclei, as well as of the neutron-deuteron doublet scattering length, has been recently derived. We have performed a comparative analysis of the equations of state of both pure neutron matter (PNM) and symmetric nuclear matter (SNM) at zero temperature obtained using these models of three-nucleon forces. In particular, we have carried out both variational and auxiliary field diffusion Monte Carlo calculations of the equation of state of PNM, while in the case of SNM we have only the variational approach has been considered. None of the considered potentials simultaneously explains the empirical equilibrium density and binding energy of symmetric nuclear matter. However, two of them provide reasonable values of the saturation density. The ambiguity concerning the treatment of the contact term of the chiral inspired potentials is discussed.

Formula omitted]-Nucleus optical potential and possible [formula omitted] bound states

Starting from a recent model of the η′N interaction, we evaluate the η′-nucleus optical potential, including the contribution of lowest order in density, tρ/2mη′, together with the second-order terms accounting for η′ absorption by two nucleons. We also calculate the formation cross section of the η′ bound states from (π+,p) reactions on nuclei. The η′-nucleus potential suffers from uncertainties tied to the poorly known η′N interaction, which can be partially constrained by the experimental modulus of the η′N scattering length and/or the recently measured transparency ratios in η′ nuclear photoproduction. Assuming an attractive interaction and taking the claimed experimental value |aη′N|=0.1 fm, we obtain an η′ optical potential in nuclear matter at saturation density of Vη′=−(8.7+1.8i) MeV, not attractive enough to produce η′ bound states in light nuclei. Larger values of the scattering length give rise to deeper optical potentials, with moderate enough imaginary parts. For a value |aη′N|=0.3 fm, which can still be considered to lie within the uncertainties of the experimental constraints, the spectra of light and medium nuclei show clear structures associated to η′-nuclear bound states and to threshold enhancements in the unbound region.

ρ-ω mixing and density dependent CSV potential

We construct the charge symmetry violating (CSV) nucleon-nucleon potential in nuclear matter induced by the p-ω mixing due to the neutron-proton mass difference driven by the NN loop. Analytical expression for for the two-body CSV potential is presented.

Comparative study of hyperon-nucleon interactions in a quark model and in chiral effective field theory by low-momentum equivalent interactions andGmatrices

Hyperon-nucleons interactions constructed by two frameworks, the Kyoto-Niigata SU$_6$ quark model and the chiral effective field theory, are compared by investigating equivalent interactions in a low-momentum space and in addition by calculating hyperon single-particle potentials in the lowest-order Brueckner theory in symmetric nuclear matter. Two descriptions are shown to give similar matrix elements in most channels after renormalizing high momentum components. Although the range of the $\Lambda N$ interaction is different in two potentials, the $\Lambda$ single-particle potential in nuclear matter is very similar. The $\Sigma$-nucleus and $\Xi$-nucleus potentials are also found to be similar. These predictions are to be confronted with forthcoming experimental data.

THE CJT CALCULATION IN STUDYING NUCLEAR MATTER BEYOND MEAN FIELD APPROXIMATION

We have introduced the Cornwall–Jackiw–Tomboulis (CJT) resummation scheme in studying nuclear matter. Based on the CJT formalism and using Walecka model, we have derived a set of coupled Dyson equations of nucleons and mesons. Neglecting the medium effects of the mesons, the usual mean field theory (MFT) results can be obtained. The beyond MFT calculations have been performed by thermodynamic consistently determining the meson effective masses and solving the coupled gap equations for nucleons and mesons together. The numerical results for the nucleon and meson effective masses at finite temperature and chemical potential in nuclear matter are discussed.

The σK coupling in the chiral unitary approach and the isoscalar ¯N , ¯A interaction

We evaluate the “σ exchange contribution to the ¯N → ¯N scattering within a chiral unitary approach. We show that the chiral transition potentials for ππ → K¯ in the t -channel lead to a “σ contribution that vanishes in the ¯ forward direction and, hence, would produce a null “σ exchange contribution to the K- optical potential in nuclear matter in a simple impulse approximation. This is a consequence of the fact that the leading-order chiral Lagrangian gives an I = 0 ππ → K¯ amplitude proportional to the squared momentum transfer, q2. This finding poses questions on the meaning or the origin of “σ exchange potentials used in relativistic mean-field approaches to the K- nuclear self-energy. This elementary “σ ” exchange potential in ¯N → ¯N is compared to the Weinberg-Tomozawa term and is found to be smaller than the present theoretical uncertainties but will be relevant in the future when aiming at fitting increasingly more accurate data.

Elastic proton–nucleus scattering and the optical potential in a relativistic mean field model

We describe elastic proton–nucleus scattering in a relativistic approach with optical potentials deduced from self-energies in a relativistic mean field description for the target nucleus. The energy-dependence of vector and scalar potentials is parametrized by fitting observables for elastic p–208Pb scattering to results from Dirac phenomenology. This energy dependence is then applied to elastic proton scattering on various other targets with energies between 200 MeV and 1 GeV. The energy and density dependence of the Schrödinger equivalent potential in nuclear matter and the total in-medium cross section is deduced and compared to other models.

Partial wave contributions to the antikaon potential at finite momentum

The momentum dependence of the antikaon optical potential in nuclear matter is obtained from a microscopic and self-consistent calculation using the meson-exchange Jülich KN interaction. Two self-consistent schemes are discussed, which would lead to substantially different predictions for the width of K nuclear bound states. The effect of higher partial waves of the KN interaction, beyond the L=0 component, is studied and found to have moderate but nonnegligible effects on the K nuclear potential at zero momentum. At momenta as large as 500 MeV /c, relevant in the analysis of heavy-ion collisions, the higher partial partial waves modify the K optical potential by nearly a factor of two.

Microscopic calculation of a pairing gap in semi-infinite nuclear matter

The pairing gap in semi-infinite nuclear matter has been calculated microscopically by solving the gap equation for a nonlocal interaction with the aid of the method proposed by V.A. Khodel, A.V. Khodel, and J.W. Clark [Nucl. Phys. A 598, 390 (1996)] for the case of infinite nuclear matter. The calculation employs the effective pairing interaction obtained previously for semi-infinite geometry on the basis of the separable 3×3 representation of the Paris nucleon-nucleon potential. The gap found in this way changes sharply in the surface region, where it has a pronounced maximum. The dependence of the surface effect on the chemical potential of nuclear matter has been investigated.

Role of the Coulomb interaction in the flow and the azimuthal distribution of kaons from heavy ion reactions

Coulomb final-state interaction of positive charged kaons in heavy ion reactions and its impact on the kaon transverse flow and the kaon azimuthal distribution are investigated within the framework of QMD (quantum molecular dynamics) model. The Coulomb interaction is found to tend to draw the flow of kaons away from that of nucleons and lead to a more isotropic azimuthal distribution of kaons in the target rapidity region. The recent FOPI data have been analyzed by taking into account both the Coulomb interaction and a kaon in-medium potential of the strong interaction. Although the effect of the kaon Coulomb potential on the kaon flow and azimuthal distribution is much smaller than that of the strong potential, it is found to be visible, and therefore, should be taken into account if one wants to extract unambiguous information about the kaon strong potential in nuclear matter from the kaon flow and azimuthal distribution data.

The two-pion exchange NN potential in nuclear matter and nuclear stability

A meson exchange model of the ππ interaction which fits free ππ scattering data is used to calculate the interactions of pions in nuclear matter as a function of nuclear density. Polarization of the nuclear medium by the pions results in a marked increase in the s-wave ππ attraction at low energy. The influence of this effect on the nucleon-nucleon interaction is a corresponding increase with density of the NN central potential due to the exchange of two correlated pions, resulting in an NN interaction which fails to saturate. A possible mechanism for restoring the theoretical stability of nuclear matter is explored and found to be effective.