Nucleon Effective Mass Research Articles

Pauli nonlocality and the nucleon effective mass

Pauli nonlocality and the nucleon effective mass

Cost of Inferred Nuclear Parameters toward the f-mode Dynamical Tide in Binary Neutron Stars

Gravitational-wave (GW) observations from neutron stars (NSs) in a binary system provide an excellent scenario to constrain the nuclear parameters. The investigation of Pratten et al. has shown that the ignorance of f-mode dynamical tidal correction in the GW waveform model of the binary NS system can lead to substantial bias in the measurement of NS properties and NS equations of state. In this work, we investigate the bias in the nuclear parameters resulting from the ignorance of dynamical tidal correction. In addition, this work demonstrates the sensitivity of the nuclear parameters and the estimated constraints on nuclear parameters and NS properties from future GW observations. We infer the nuclear parameters from GW observations by describing the NS matter within the relativistic mean field model. For a population of GW events, we notice that the ignorance of dynamical tide predicts a lower median for nucleon effective mass (m*) by ∼6% compared to the scenario when dynamical tidal correction is considered. Whereas, at a 90% credible interval, m* gets constrained up to ∼5% and ∼3% in A+ (the LIGO-Virgo detectors with a sensitivity of the fifth observing run) and Cosmic Explorer, respectively. We also discuss the resulting constraints on all other nuclear parameters, including compressibility, symmetry energy, and slope of symmetry energy, considering an ensemble of GW events. We do not notice any significant impact in analyzing nuclear parameters other than m* due to the ignorance of f-mode dynamical tides.

Constraining nucleon effective masses with flow and stopping observables from the SπRIT experiment

Properties of the nuclear equation of state (EoS) can be probed by measuring the dynamical properties of nucleus-nucleus collisions. In this study, we present the directed flow (v1), elliptic flow (v2) and stopping (VarXZ) measured in fixed target Sn + Sn collisions at ▪ with the SπRIT Time Projection Chamber. We perform Bayesian analyses in which EoS parameters are varied simultaneously within the Improved Quantum Molecular Dynamics-Skyrme (ImQMD-Sky) transport code to obtain a multivariate correlated constraint. The varied parameters include symmetry energy, S0, and slope of the symmetry energy, L, at saturation density, isoscalar effective mass, ms⁎/mN, isovector effective mass, mv⁎/mN and the in-medium cross-section enhancement factor η. We find that the flow and VarXZ observables are sensitive to the splitting of proton and neutron effective masses and the in-medium cross-section. Comparisons of ImQMD-Sky predictions to the SπRIT data suggest a narrow range of preferred values for ms⁎/mN, mv⁎/mN and η.

Effects of nuclear matter properties in neutron star mergers

ABSTRACT The dynamics in mergers of binary neutron star (BNS) systems depend sensitively on the equation of state (EOS) of dense matter. This has profound implications on the emission of gravitational waves (GWs) and the ejection of matter in the merger and post-merger phases and is thus of high interest for multimessenger astronomy. Today, a variety of nuclear EOSs are available with various underlying microphysical models. This calls for a study to focus on EOS effects from different physical nuclear matter properties and their influence on BNS mergers. We perform simulations of equal-mass BNS mergers with a set of nine different EOSs based on Skyrme density functionals. In the models, we systematically vary the effective nucleon mass, incompressibility, and symmetry energy at saturation density. This allows us to investigate the influence of specific nuclear matter properties on the dynamics of BNS mergers. We analyse the impact of these properties on the merger dynamics, the fate of the remnant, disc formation, ejection of matter, and GW emission. Our results indicate that some aspects of the merger, such as the frequencies of the post-merger GW spectrum and the shock-heated ejecta mass, are sensitive to the EOS around saturation density while others, such as the contraction of the remnant and the tidal ejecta mass, are sensitive to the behaviour towards higher densities, e.g. characterized by the slope of the pressure versus density. The detailed density dependence of the EOS thus needs to be taken into account to describe its influence on BNS mergers.

Impact of different components of the Skyrme nucleon–nucleon effective interaction on the nuclear density distribution

We systematically investigate the impact of the different terms of the Skyrme energy density functional of the effective nucleon-nucleon interaction, and of its associated nuclear matter (NM) properties, on the density distributions of spherical nuclei. Twenty five Skyrme force parameterizations are examined simultaneously, covering a broad range of each characteristic parameter and NM property. The diffuseness and the neutron-skin thickness are found to be the most sensitive density quantities to the force parameterization. The diffuseness is indicated to decrease with increasing the central zero-range and the effective mass terms of the effective force, and the power σ of its density dependent term, as well as with the coefficient of the NM symmetry energy (asym) and its density slope (L) at saturation density, and the incompressibility (Ko). In contrast, the proton and neutron diffuseness tend to increase with increasing the spin–orbit force and the isoscalar effective nucleon-mass (m*), and to increases slightly with the density dependence parameters other than the power σ. Opposite impacts are pointed out for the different parts of the finite-range, and J2 tensor terms on the proton and neutron density. While the neutron-skin thickness tends to increase significantly upon increasing the central zero-range and spin–orbit force terms, asym, L, and Ko, and to increase slightly with the finite-range and J2 tensor terms, and σ, it decreases with the effective-mass term, the density-dependence exchange parameter, and with the indicated isoscalar effective mass. The proton and neutron radii exhibit decreasing behavior with the central zero-range and the spin–orbit terms, and with Ko, and m*. Increasing asym and L indicate slightly less (larger) proton (neutron) radius.

Constraining Nuclear Parameters Using Gravitational Waves from f-mode Oscillations in Neutron Stars

Gravitational waves (GWs) emanating from unstable quasi-normal modes in neutron stars (NSs) could be accessible with the improved sensitivity of the current GW detectors or with the next-generation GW detectors and, therefore, can be employed to study the NS interior. Assuming f-mode excitation in isolated pulsars with typical energy of pulsar glitches and considering potential f-mode GW candidates for A+ (upgraded LIGO detectors operating at fifth observing run design sensitivity) and Einstein Telescope (ET), we demonstrate the inverse problem of NS asteroseismology within a Bayesian formalism to constrain the nuclear parameters and NS equation of state (EOS). We describe the NS interior within relativistic mean-field formalism. Taking the example of glitching pulsars, we find that for a single event in A+ and ET, among the nuclear parameters, the nucleon effective mass (m*) within 90% credible interval can be restricted within 10% and 5%, respectively. At the same time, the incompressibility (K) and the slope of the symmetry energy (L) are only loosely constrained. Considering multiple (10) events in A+ and ET, all the nuclear parameters are well constrained, especially m*, which can be constrained to 3% and 2% in A+ and ET, respectively. Uncertainty in the observables of a 1.4 M ⊙ NS such as radius (), f-mode frequency (), damping time (), and a few EOS properties including squared speed of sound (c s 2) are also estimated.

Thermal Effects in Binary Neutron Star Mergers

We study the impact of finite-temperature effects in numerical-relativity simulations of binary neutron star mergers with microphysical equations of state and neutrino transport in which we vary the effective nucleon masses in a controlled way. We find that, as the specific heat is increased, the merger remnants become colder and more compact due to the reduced thermal pressure support. Using a full Bayesian analysis, we demonstrate that this effect will be measurable in the postmerger gravitational wave signal with next-generation observatories at signal-to-noise ratios of 15.

Probing nucleon effective mass splitting with light particle emission

Probing nucleon effective mass splitting with light particle emission

Secondary particle predictions in quasifree proton scattering reactions in the 100–250 MeV energy range

Results for observables related to the secondary particle production process in proton-nucleus spallation reactions at low beam incident energy (100--250 MeV) are shown. The energy and angular distributions of the residual nucleus are determined in the context of our multicollisional Monte Carlo intranuclear cascade model. The mechanism of proton-nucleus reactions is conventionally described as a sequence of two stages: the rapid intranuclear cascade phase and the slow particle evaporation step. In this work we focus on the rapid phase considering the nucleon effective mass as an effect of the many-body nuclear interactions and the intranuclear mean field. This procedure represents a more realistic scenario to obtain the particles' multiplicity generated in spallation reactions with light-mass target nuclei in a low-energy range. We focused our attention on target nuclei of macro elements, such as carbon, oxygen, phosphorus, sulfur, sodium, potassium, chlorine, and calcium, and trace elements such as iron, copper, zinc, bromine and selenium, which are the most frequent compounds of the organic material. The choice of these target nuclei is due to our expectancy that our results can work as a preliminary insight for further theoretical approaches, specially taking into account nuclear effects due to the interaction of the particles of the beam with the organic tissue.

A Bayesian Inference of a Relativistic Mean-field Model of Neutron Star Matter from Observations of NICER and GW170817/AT2017gfo

Observations of optical and near-infrared counterparts of binary neutron star mergers not only enrich our knowledge about the abundance of heavy elements in the universe and help reveal the remnant object just after the merger, which is generally known, but can also effectively constrain the dense properties of the nuclear matter and the equation of state (EOS) in the interior of the merging stars. Following the relativistic mean-field description of nuclear matter, we perform a Bayesian inference of the EOS and the properties of the nuclear matter using the first multi-messenger event GW170817/AT2017gfo, together with the NICER mass–radius measurements of pulsars. The kilonova is described by a radiation-transfer model with the dynamical ejecta, and light curves connect with the EOS through the quasi-universal relations between the properties of the ejecta (the ejected mass, velocity, opacity, or electron fraction) and binary parameters (the mass ratio and reduced tidal deformability). It is found that the posterior distributions of the reduced tidal deformability from the AT2017gfo analysis display a bimodal structure, with the first peak enhanced by the GW170817 data, leading to slightly softened posterior EOSs, while the second peak cannot be achieved by a nuclear EOS with saturation properties in their empirical ranges. The inclusion of NICER data results in a stiffened EOS posterior because of the massive pulsar PSR J0740+6620. We provide the results at nuclear saturation density for the nuclear incompressibility, the symmetry energy, and its slope, as well as the nucleon effective mass, from our analysis of the observational data.

Uncertainty quantification for neutrino opacities in core-collapse supernovae and neutron star mergers

We perform an extensive study of the correlations between the neutrino-nucleon inverse mean free paths (IMFPs) and the underlying equation of states (EoSs). Strong interaction uncertainties in the neutrino mean free path are investigated in different density regimes. The nucleon effective mass, the nucleon chemical potentials, and the residual interactions in the medium play an important role in determining neutrino-nucleon interactions in a density-dependent manner. We study how the above quantities are constrained by an EoS consistent with (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. We then study the uncertainties of both the charged current and the neutral current neutrino-nucleon inverse mean free paths due to the variation of these quantities, using Hartree-Fock+random phase approximation method. Finally, we calculate the Pearson correlation coefficients between (i) the EoS-based quantities and the EoS-based quantities; (ii) the EoS-based quantities and the IMFPs; (iii) the IMFPs and the IMFPs. We find a strong impact of residual interactions on neutrino opacity in the spin and spin-isospin channels, which are not well constrained by current nuclear modelings.

Δ baryons in neutron stars

By applying a relativistic mean-field description of neutron star matter with density dependent couplings, we analyse the properties of two different matter compositions: nucleonic matter with delta baryons and nucleonic matter with hyperons and delta baryons. The delta-meson couplings are allowed to vary within a wide range of values obtained by experimental data, while the hyperon-meson couplings are fitted to hypernuclear properties. Neutron star properties with no deconfinement phase transition are studied. It is verified that many models are excluded because the effective nucleon mass becomes zero before the maximum mass configuration is attained. Hyperon-free with delta-dominated composition compact stars are possible, the deltic stars. It is found that with a convenient choice of parameters the existence of deltic stars with 80% of delta baryons at the center of the star is possible. However, the presence of hyperons lowers the delta baryon fraction to values below 20% at the center and below 30% at 2-3 saturation densities. It is discussed that in the presence of delta baryons, the hyperon softening is not so drastic because deltas couple more strongly to the $\omega$-meson, and the stiffness of the equation of state is determined by the $\omega$-dominance at high densities. The speed of sound reflects very well this behavior. The compactness of the pulsar RX J0720.4-3125 imposes $x_{\sigma\Delta}>x_{\omega\Delta}>1$ and favors $x_{\rho\Delta}>1$.

Density dependence of the nuclear symmetry energy and neutron skin thickness in the KIDS framework

The KIDS framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore systematically the effect of EoS parameters on predictions for a variety of observables. The EoS parameters can be varied independently of each other and independently of assumptions regarding the in-medium nucleon effective mass. Here I present a pilot study of the neutron skin thickness (NST) in nuclei of current interest. The results indicate that variations of the symmetry energy slope parameter L by roughly 10 MeV and variations of the droplet-model counterpart of the curvature parameter Kτ by roughly 20 MeV affect predictions by comparable amounts. However, structural details may also have sizable effects on predictions, notably in the cases of 68Ni and 208Pb. This work is part of a systematic investigation of the NST within the KIDS framework and of a broader effort to constrain the density dependence of the nuclear symmetry energy.

Nuclear shell structure in a finite-temperature relativistic framework

The shell evolution of neutron-rich nuclei with temperature is studied in a beyond-mean-field framework rooted in the meson-nucleon Lagrangian. The temperature-dependent Dyson equation with the dynamical kernel taking into account the particle-vibration coupling (PVC) is solved for the fermionic propagators in the basis of the thermal relativistic mean-field Dirac spinors. The calculations are performed for $^{68-78}$Ni in a broad range of temperatures $0 \leq T \leq 4$ MeV. The special focus is put on the fragmentation pattern of the single-particle states, which is further investigated within toy models in strongly truncated model spaces. Such models allow for quantifying the sensitivity of the fragmentation to the phonon frequencies, the PVC strength and to the mean-field level density. The model studies provide insights into the temperature evolution of the PVC mechanism in real nuclear systems under the conditions which may occur in astrophysical environments.

Effect of nucleon effective mass and symmetry energy on the neutrino mean free path in a neutron star

The Korea-IBS-Daegu-SKKU energy density functional (KIDS-EDF) models, constructed from the perturbative expansion of the energy density in nuclear matter, have been successfully and widely applied in describing the properties of finite nuclei and infinite nuclear matter. In the present work, we extend the applications of the KIDS-EDF models to investigate the implications of the nucleon effective mass and nuclear symmetry energy for the properties of neutron stars (NSs) and neutrino interaction with the NS constituent matter in the linear response approximation (LRA). At fixed neutrino energy and momentum transfer, we analyze the total differential cross section of neutrinos, the neutrino mean free path (NMFP), and the NS mass-radius (M-R) relations. Remarkable results are given by the KIDS0-m*87 and SLy4 models, in which ${M}_{n}^{*}/M\ensuremath{\lesssim}1$, and their NMFPs are quite higher in comparison with those obtained from the KIDS0, KIDS-A, and KIDS-B models, which result in ${M}_{n}^{*}/M\ensuremath{\gtrsim}1$. For the KIDS0, KIDS-A, and KIDS-B models, we obtain $\ensuremath{\lambda}\ensuremath{\lesssim}{R}_{\text{NS}}$, indicating that these models could predict the slow NS cooling and neutrino trapping in NSs. In contrast, the KIDS0-m*87 and SLy4 models yield $\ensuremath{\lambda}\ensuremath{\gtrsim}{R}_{\text{NS}}$ and thus we expect faster NS cooling and a small possibility of neutrino trapping within NSs. We also calculate the NMFP as a function of the neutrino energy and the nuclear matter density and find that the NMFP decreases as the density and neutrino energy increase, which is consistent with the result obtained in the Brussels-Montreal Skyrme (BSk17 and BSk18) models at saturation density.

General relativistic treatment of f -mode oscillations of hyperonic stars

We present a systematic study of $f$-mode oscillations in neutron stars containing hyperons, extending recent results obtained within the Cowling approximation to linearized general relativity. Employing a relativistic mean-field model, we find that the Cowling approximation can overestimate the quadrupolar $f$-mode frequency of neutron stars by up to 30% compared to the frequency obtained in the linearized general relativistic formalism. Imposing current astrophysical constraints, we derive updated empirical relations for gravitational wave asteroseismology. The frequency and damping time of quadrupole $f$-mode oscillations of hyperonic stars are found to be in the range of 1.47--2.45 kHz and 0.13--0.51 s, respectively. Our correlation studies demonstrate that among the various parameters of the nucleonic and hyperonic sectors of the model, the nucleon effective mass shows the strongest correlation with mode characteristics and neutron star observables. Estimates for the detectability of $f$ modes in a transient burst of gravitational waves from isolated hyperonic stars is also provided.

Van der Waals equation of state for asymmetric nuclear matter

The application of the van der Waals equation of state to the asymmetric nuclear matter is considered in a critical state region. The corrections to the van der Waals pressure and free energy due to the Fermi statistics are obtained starting from the Thomas - Fermi entropy expression which ensures the fulfilment of the Nernst theorem. The derived corrections account for the effective nucleon mass and neutron-proton isotopic asymmetry. The parameters of the van der Waals equation of state are deduced by taking the experimental value of critical temperature for symmetric nuclear matter and testing the model of van der Waals with statistics corrections included against the theory of Skyrme energy density functional. A critical line in pressure-temperature-composition space is considered. The incompressibility coefficient is determined along the critical line as a function of nuclear matter composition. A jump in the value of specific heat upon crossing a critical line is discussed.

Heavy baryons in hot stellar matter with light nuclei and hypernuclei

The production of light nuclei and hypernuclei together with heavy baryons, both hyperons and $\Delta$-baryons, in low density matter as found in stellar environments such as supernova or binary mergers is studied within relativistic mean-field models. Five light nuclei were considered together with three light hypernuclei. The presence of both hyperons and $\Delta$-baryons shift the dissolution of clusters to larger densities and increase the abundance of clusters. This effect is larger the smaller the charge fraction and the higher the temperature. The couplings of the $\Delta$-baryons were chosen imposing that the nucleon effective mass remains finite inside neutron stars.

Inclusive electron scattering in the quasielastic region with the Korea-IBS-Daegu-SKKU density functional

With the framework of KIDS (Korea-IBS-Daegu-SKKU) density functional model, the isoscalar and isovector effective masses of nucleon and the effect of symmetry energy in nuclear medium are investigated in inclusive $(e,e')$ reaction in quasielastic region. The effective masses are varied in the range $(0.7 \sim 1.0)M$ with free nucleon mass $M$, and the symmetry energy is varied within the uncertainty allowed by nuclear data and neutron star observation. The wave functions of nucleons inside target nucleus are generated by solving Hartree-Fock equation with adjusting equation of state, binding energy and radius of various stable nuclei, and effective mass of nucleon in the KIDS model. With the obtained wave functions, we calculate the differential cross section for the inclusive $(e,e')$ reaction and compare the theoretical results with Bates, Saclay, and SLAC experimental data. Our model describes experimental data better at SLAC-type high incident electron energy than those measured from Bates and Saclay. The influence of the effective mass and symmetry energy appears to be precise on the longitudinal cross section.

Slope parameter of the symmetry energy and the structure of three-particle interactions in nuclear matter

In the first part of this paper, we present a study of the symmetry energy ${a}_{s}$ and its slope parameter $L$ for nuclear matter in the framework of the Fermi-liquid theory of Landau and Migdal. We derive an exact relation between ${a}_{s}$ and $L$, which involves the nucleon effective masses and three-particle Landau-Migdal parameters. We present simple estimates which suggest that there are two main mechanisms to explain the empirical values of $L$: The proton-neutron effective-mass difference in isospin asymmetric matter and the $\ensuremath{\ell}=0$ moment of the isovector in-medium three-particle scattering amplitude. In the second part of this paper, we discuss the general structure of three-particle interactions in nuclear matter in the framework of the Fermi-liquid theory. The connections to the Bethe-Brueckner-Goldstone theory and other approaches are also discussed. We show explicitly how the first few terms in the Faddeev series, together with medium-induced three-particle interactions, emerge naturally in the Fermi-liquid theory.