Nucleon Distribution Research Articles

Nuclear medium effects in lepton-nucleus DIS in the region of x≳1

The nuclear medium effects in the nuclear structure functions and differential cross sections in the deep inelastic scattering (DIS) of charged lepton and neutrino from nuclear targets are studied in the region of large $x$ including $x\ge 1$. The nuclear medium effects due to the Fermi motion and the binding energy of nucleons and the nucleon correlations are included using nucleon spectral function calculated in a microscopic field theoretical model. The numerical results for the nuclear structure functions and the cross sections are obtained using the nucleon structure function evaluated at the next-to-next-to-leading order (NNLO) with the Martin-Motylinski-Harland Lang-Thorne (MMHT) parameterization of the nucleonic parton distribution functions (PDFs) and are compared with the available experimental data on electron scattering from the Jefferson Lab (JLab) and SLAC Nuclear Physics Facility (NPAS). In the case of neutrino scattering the results are relevant for understanding the DIS contributions to the recent inclusive cross sections measured by the Main Injector Neutrino ExpeRiment to study v-A interactions (MINERvA) as well as theoretical predictions are made for Deep Underground Neutrino Experiment (DUNE). The importance of isoscalarity corrections in heavier nuclear targets as well as the effect of the kinematic cut on the CM energy $W$ in defining the DIS region have also been discussed.

Relativistic global solutions of neutrino-dominated accretion flows with magnetic coupling

ABSTRACT A Kerr black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) is one of plausible candidates of the central engine in gamma-ray bursts. The accretion material might inherit and restructure strong magnetic fields from the compact object mergers or massive collapsars. The magnetic coupling (MC) process between a rapid rotating BH and an accretion disc is one of possible magnetic configurations that transfers the energy and angular momentum from the BH to the disc. In this paper, we investigate one-dimensional global solutions of NDAFs with MC (MCNDAFs), taking into account general relativistic effects, detailed neutrino physics, different MC geometries, and reasonable nucleosynthesis processes. Six cases with different accretion rates and power-law indices of magnetic fields are presented and compared with NDAFs without MC. Our results indict that the MC process can prominently impact the structure, thermal properties, and microphysics of MCNDAFs, increase luminosities of neutrinos and their annihilations, result in the changing of radial distributions of nucleons, and push the region of heavy nuclei synthesis to a larger radius than counterparts in NDAFs.

Shape of atomic nuclei in heavy ion collisions

In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flow $v_n$ are linearly related to the strength of the multi-pole shape of the distribution of nucleons in the transverse plane $\varepsilon_n$, $v_n\propto \varepsilon_n$. The $\varepsilon_n$, for $n=1,2,3,4$, are sensitive to the shape of the colliding ions, characterized by the quadrupole $\beta_2$, octupole $\beta_3$ and hexadecapole $\beta_4$ deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, $\langle\varepsilon_n^2\rangle = a_n'+b_n'\beta_n^2$, for events in a fixed centrality. The $\langle\varepsilon_1^2\rangle$ has a contribution from $\beta_3$ and $\beta_4$, and $\langle\varepsilon_3^2\rangle$ from $\beta_4$. In the ultra-central collisions, there are little cross contributions between $\beta_2$ and $\varepsilon_3$ and between $\beta_3$ and $\varepsilon_2$, but clear cross contributions are present in non-central collisions. Additionally, $\langle\varepsilon_n^2\rangle$ are insensitive to non-axial shape parameters such as the triaxiality. This is good news because the measurements of $v_2$, $v_3$ and $v_4$ can be used to constrain simultaneously the $\beta_2$, $\beta_3$, and $\beta_4$ values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical $a_n'$, to obtain simple equation that relates the $\beta_n$ of the two species. This opens up the possibility to map the shape of the atomic nuclei at a timescale ($<10^{-24}$s) much shorter than probed by low-energy nuclear structure physics ($<10^{-21}$s), which ultimately may provide information complementary to those obtained in the nuclear structure experiments.

Symmetry Energy and the Pauli Exclusion Principle

In this article we present a classical potential that respects the Pauli exclusion principle and can be used to describe nucleon-nucleon interactions at intermediate energies. The potential depends on the relative momentum of the colliding nucleons and reduces interactions at low momentum transfer mimicking the Pauli exclusion principle. We use the potential with Metropolis Monte Carlo methods and study the formation of finite nuclei and infinite systems. We find good agreement in terms of the binding energies, radii, and internal nucleon distribution of finite nuclei, and the binding energy in nuclear matter and neutron star matter, as well as the formation of nuclear pastas, and the symmetry energy of neutron star matter.

Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii

Background: Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the standard model of particle physics. In particular, such measurements, augmented by atomic and nuclear calculations, will enable extraction of the higher-order radial moments of the charge-density distribution in spherical and deformed nuclei. The new data impose higher precision requirements on a theoretical description.Purpose: The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. Additional corrections come from the effect of center-of-mass projection. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic and center-of-mass motion corrections to the second and fourth charge radial moments. Special attention has been paid to the magnetic spin-orbit density associated with the local variations of the spin-orbit current.Methods: The calculations for semimagic and open-shell nuclei are performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei.Results: We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which can make an appreciable effect when aiming at high-precision predictions of isotopic shifts. The inclusion of relativistic and center-of-mass corrections impacts the quality of energy density functionals optimized to charge radii data.Conclusions: To establish reliable constraints on the existence of new forces from isotope shift measurements, precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends. It is also important when developing high-quality nuclear energy density functionals optimized using heterogeneous datasets involving absolute charge radii, differential charge radii, and charge form factor properties deduced from electron-scattering data.

Nucleon mass radii and distribution: Holographic QCD, lattice QCD, and GlueX data

We briefly review and expand our recent analysis for all three invariant $A$, $B$, $D$ gravitational form factors of the nucleon in holographic QCD. They compare well to the gluonic gravitational form factors recently measured using lattice QCD simulations. The holographic $A$-term is fixed by the tensor $T={2}^{++}$ (graviton) Regge trajectory, and the $D$-term by the difference between the tensor $T={2}^{++}$ (graviton) and scalar $S={0}^{++}$ (dilaton) Regge trajectories. The $B$-term is null in the absence of a tensor coupling to a Dirac fermion in bulk. A first measurement of the tensor form factor $A$-term is already accessible using the current GlueX data, and therefore the tensor gluonic mass radius, pressure, and shear inside the proton, thanks to holography. The holographic $A$-term and $D$-term can be expressed exactly in terms of harmonic numbers. The tensor mass radius from the holographic threshold is found to be $⟨{r}_{GT}^{2}⟩\ensuremath{\approx}(0.57--0.60\text{ }\text{ }\mathrm{fm}{)}^{2}$, in agreement with $⟨{r}_{GT}^{2}⟩\ensuremath{\approx}(0.62\text{ }\text{ }\mathrm{fm}{)}^{2}$ as extracted from the overall numerical lattice data, and empirical GlueX data. The scalar mass radius is found to be slightly larger $⟨{r}_{GS}^{2}⟩\ensuremath{\approx}(0.7\text{ }\text{ }\mathrm{fm}{)}^{2}$.

Self-consistent methods for structure and production of heavy and superheavy nuclei

Self-consistent methods for the structure of heavy and superheavy nuclei are reviewed. The construction and application of energy-density functionals are discussed. The relationship between the self-consistent methods and microscopic-macroscopic approaches is considered on the mean-field level. The extraction of single-particle potentials from the energy-density functional is described. The isotopic dependence of nucleon distributions and its influence on the nucleus–nucleus interaction is analyzed. As a new additional condition we introduce that the energy-density functional must describe the heights of the Coulomb barriers in nucleus–nucleus interaction potentials, thus imposing constraints on the properties of the functional at low matter densities. The self-consistent methods are applied to describe the quasiparticle structure, cluster radioactivity, and fission of the heaviest nuclei. These methods are used to predict the probabilities of \(\beta \)-delayed multi-neutron emission and half-lives of \(\beta \)-decays and electron captures in heavy and superheavy nuclei. The predicted properties of superheavy nuclei are used to estimate the production cross-sections of superheavy nuclei in complete fusion reactions.

Impact of strong magnetic fields on the inner crust of neutron stars

We study the impact of strong magnetic fields on the pasta phases that are expected to exist in the inner crust of neutron stars. We employ the relativistic mean field model to describe the nucleon interaction and use the self-consistent Thomas-Fermi approximation to calculate the nonuniform matter in neutron star crust. The properties of pasta phases and crust-core transition are examined. It is found that as the magnetic field strength $B$ is less than ${10}^{17}$ G, the effects of magnetic field are not evident comparing with the results without magnetic field. As $B$ is stronger than ${10}^{18}$ G, the onset densities of pasta phases and crust-core transition density decrease significantly, and the density distributions of nucleons and electrons are also changed obviously.

Monte Carlo Based Glauber Model in Pb-Pb Collisions at LHC

Glauber model is a model used to describe heavy ion collision process. In this paper, we describe an implementation of a Monte Carlo based Glauber Model calculation used for the PHOBOS experiment, which simulates the collision of two heavy nuclei. The nucleon distribution in two initial Pb nuclei is parameterized with Woods-Saxon. The energy profile is √(S_NN )=5.5TeV and inelastic cross-section area, i.eσ_NN= 72mb. Geometric quantities such as impact parameter(b), the participant elliptical and triangular eccentricities (ε₂, ε₃) are studied and presented graphically and quantitatively in this paper. The results for collisions of Pb-Pb are compared with other Glauber model calculations which agrees with the results from other studies to a great extent. In this simulation, a decline trend of ε₂ and ε₃ is observed with increasing Npart. The centralities of peripheral events (40 to 50 percent centrality) are ε₂ ranging from 0.5 to 0.4 and ε₃ being roughly 0.3. The ratio of ε₃ to ε₂ is roughly 0.5 at Npart=0 and 1 at Npart=416 (a hundred percent centrality), showing the significance of triangular flow of the area of intersection. The model can also be used to predict geometric quantities in the LHC experiments and other collision processes.

Elliptic and triangular flow of (anti)deuterons in Pb-Pb collisions at sNN=5.02 TeV

The measurements of the (anti)deuterons elliptic flow ($v_2$) and the first measurements of triangular flow ($v_3$) in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon collisions $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV are presented. A mass ordering at low transverse momentum ($p_{\rm T}$) is observed when comparing these measurements with those of other identified hadrons, as expected from relativistic hydrodynamics. The measured (anti)deuterons $v_2$ lies between the predictions from the simple coalescence and blast-wave models, which provide a good description of the data only for more peripheral and for more central collisions, respectively. The mass number scaling, which is violated for $v_2$, is approximately valid for the (anti)deuterons $v_3$. The measured $v_2$ and $v_3$ are also compared with the predictions from a coalescence approach with phase-space distributions of nucleons generated by iEBE-VISHNU with AMPT initial conditions coupled with UrQMD, and from a dynamical model based on relativistic hydrodynamics coupled to the hadronic afterburner SMASH. The model predictions are consistent with the data within the uncertainties in mid-central collisions, while a deviation is observed in central centrality intervals.

Near-threshold photoproduction of J/psi in two-gluon exchange model

The near-threshold photoproduction of J/psi is regarded as one golden process to unveil the nucleon mass structure, pentaquark state involving the charm quarks, and the poorly constrained gluon distribution of the nucleon at large x (>0.1). In this paper, we present an analysis of the current experimental data under a two-gluon exchange model, which shows a good consistency. Using a parameterized function form with three free parameters, we have determined the nucleonic gluon distribution at the J/psi mass scale. Moreover, we predict the differential cross-section of the electroproduction of J/psi as a function of the invariant mass of the final hadrons W, at EicC, as a practical application of the model and the obtained gluon distribution. According to our estimation, hundreds of J/psi events can be detected per year on EicC near the threshold. Therefore, the relevant experimental measurements are suggested to be carried out on EicC.

Beam-energy dependence of the production of light nuclei in Au + Au collisions

We study the collision energy dependence of (anti-)deuteron and (anti-)triton production in the most central Au+Au collisions at $\sqrt{s_\mathrm{NN}}=$ 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV, using the nucleon coalescence model. The needed phase-space distribution of nucleons at the kinetic freeze-out is generated from a new 3D hybrid dynamical model (\texttt{iEBE-MUSIC}) by using a smooth crossover equation of state (EoS) without a QCD critical point. Our model calculations predict that the coalescence parameters of (anti-)deuteron ($B_2(d)$ and $B_2(\bar{d})$) decrease monotonically as the collision energy increases, and the light nuclei yield ratio $N_t N_p/N_d^2$ remains approximately a constant with respect to the collision energy. These calculated observables fail to reproduce the non-monotonic behavior of the corresponding data from the STAR Collaboration. Without including any effects of the critical point in our model, our results serve as the baseline predictions for the yields of light nuclei in the search for the possible QCD critical points from the experimental beam energy scan of heavy ion collisions.

Nucleon density distribution in description of nuclear decays

A correlation is demonstrated between the diffuseness of the self-consistent nucleon distribution and the nucleon-nucleon attraction on nuclear surface. The last two values determine the nucleus-nucleus interaction potential. Because the half-lives of alpha-decay, cluster radioactivity, and spontaneous fission are sensitive to the nucleus-nucleus interaction potential, we try to verify the self-consistent nucleon-nucleon attraction on nuclear surface. Based on the dinuclear system model, the unified approach is proposed for calculating half-lives of different nuclear decay modes using the phenomenological and self-consistent nucleon distributions.

Direct photon emission and influence of dynamical wave packets in an extended quantum molecular dynamics model

Direct photon produced from first proton-neutron ($p$-$n$) collision during the early stage of heavy ion reaction is a sensitive probe to reflect energy and momentum distribution of nucleons. In this work, we embedded the hard photon production channel in an extended quantum molecular dynamics (EQMD) model, and took the direct photon as a possible probe to improve namely the Fermi motion in the EQMD model. A possible scheme is offered to handle the dynamical wave packet width within incoherent bremsstrahlung process. Direct photons calculated by our modified EQMD were compared with data of $^{14}$N + $^{12}$C at beam energies $E/A$ = 20, 30 and 40 MeV, and it is found that the yield, inverse slope and angular distribution of direct photons could be reasonably reproduced. In addition, asymmetric reaction systems of $^{4}$He + C and $^{4}$He + Zn at $E/A$ = 53 MeV are also simulated in this work. It is found that the symmetric angular distribution in the nucleon-nucleon ($N$-$N$) center-of-mass (c.m.) frame and the velocity of $ the \gamma$-emission source can be reasonably obtained from our method although there is some quantitative differences.

Efficient method for estimation of fission fragment yields of r -process nuclei

$\textbf{Background}$ More than half of all the elements heavier than iron are made by the rapid neutron capture process (or r process). For very neutron-rich astrophysical conditions, such at those found in the tidal ejecta of neutron stars, nuclear fission determines the r-process endpoint, and the fission fragment yields shape the final abundances of $110\le A \le 170$ nuclei. The knowledge of fission fragment yields of hundreds of nuclei inhabiting very neutron-rich regions of the nuclear landscape is thus crucial for the modeling of heavy-element nucleosynthesis. $\textbf{Purpose}$ In this study, we propose a model for the fast calculation of fission fragment yields based on the concept of shell-stabilized prefragments defined with help of the nucleonic localization functions. $\textbf{Methods}$ To generate realistic potential energy surfaces and nucleonic localizations, we apply Skyrme Density Functional Theory. The distribution of the neck nucleons among the two prefragments is obtained by means of a statistical model. $\textbf{Results}$ We benchmark the method by studying the fission yields of $^{178}$Pt, $^{240}$Pu, $^{254}$Cf, and $^{254,256,258}$Fm and show that it satisfactorily explains the experimental data. We then make predictions for $^{254}$Pu and $^{290}$Fm as two representative cases of fissioning nuclei that are expected to significantly contribute during the r-process nucleosynthesis occurring in neutron star mergers. $\textbf{Conclusions}$ The proposed framework provides an efficient alternative to microscopic approaches based on the evolution of the system in a space of collective coordinates all the way to scission. It can be used to carry out global calculations of fission fragment distributions across the r-process region.

Evolution of clustering structure through the momentum distributions in Be8–10 isotopes

We investigate the evolution of clustering structure through the momentum distributions in the $^{8-10}$Be isotopes. The nucleon dynamics within the inter-cluster antisymmetrization are discussed via the momentum distribution of a Brink type $\alpha$-$\alpha$ wave function. For the state with a small $\alpha$-$\alpha$ distance, we observe a significant depression with a dip structure at zero-momentum and an enhanced tail at relatively higher momentum region. In addition, we find the "cluster structure" in the intrinsic frame of momentum space, which is complementary to its significant $\alpha$-cluster dissolution in the coordinate space because of the strong antisymmetrization. For the physical $^{8-10}$Be isotopes, the Tohsaki-Horiuchi-Schuck-R{\"o}pke (THSR) wave functions are adopted. The evolution from the dilute clustering state to the compact one is demonstrated by a successive depression at the zero-momentum of nucleon distribution for the two $\alpha$-clusters within $^{8-10}$Be isotopes. For the compact $^{10}$Be nucleus, the momentum distribution of all nucleons shows significant depression at zero-momentum with a dip structure, which is found to be contributed by both the inter-cluster antisymmetrization and the $p$-orbit occupation of the valence neutrons. This study proposes a new window for the investigations of the $\alpha$-clustering effects via the low-momentum components of nuclei, which is expected to be extended to the heavier nuclear clustering states.

Extraction of gluon distributions from structure functions at small x in holographic QCD

We investigate the nucleon and pion gluon distribution functions in the framework of holographic QCD, focusing on the small Bjorken x region. Based on an approximate relation, the gluon distributions are extracted from structure functions of the unpolarized deep inelastic scattering which can be calculated with a holographic QCD model, assuming the Pomeron exchange. All the adjustable parameters of the model are determined with the HERA data of the proton structure functions. We explicitly show that the extracted proton gluon distribution is consistent with results of the recent global QCD analysis. The structure functions of the pion can be computed without any additional parameter, which enables us to predict its gluon distribution also. We find that the resulting pion gluon density is smaller than the proton's, and agrees with the recent global QCD analysis result within the uncertainties.

Estimation of varUpsilon hbox {(1S)} production in ep process near threshold

The near-threshold photo-productions of heavy quarkonia are important ways to test the QCD-inspired models and to constrain the gluon distribution of nucleon in the large x region. Investigating the various models, we choose a photon–gluon fusion model and a pomeron exchange model for hbox {J}/varPsi photo-production near threshold, emphasising on the explanation of the recent experimental measurement by GlueX at JLab. We find that these two models are not only valid in a wide range of the center-of-mass energy of gamma and proton, but also can be generalized to describe the varUpsilon hbox {(1S)} photo-production. Using these two models, we predict the electro-production cross-sections of varUpsilon hbox {(1S)} at EicC to be 48 fb to 85 fb at the center-of-mass energy of 16.75 GeV.

Theory and applications of parton pseudodistributions

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator [Formula: see text] of the parton fields is a function [Formula: see text] of Lorentz invariants [Formula: see text], the Ioffe time, and the invariant interval [Formula: see text]. This observation allows to extract the Ioffe-time distribution [Formula: see text] from Euclidean separations [Formula: see text] accessible on the lattice. Another basic feature is the use of the ratio [Formula: see text], that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining [Formula: see text]-dependence of the reduced Ioffe-time distribution [Formula: see text] corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions [Formula: see text] using matching relations. The [Formula: see text]-dependence of [Formula: see text] governs the [Formula: see text]-dependence of parton densities [Formula: see text]. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.

Clustering structure effect on Hanbury-Brown–Twiss correlation in $$^{12}\hbox {C} {+^{197}}\hbox {Au}$$ collisions at 200 GeV

Through $$^{12}\hbox {C} {+^{197}}\hbox {Au}$$ collisions at $$\sqrt{s_{NN}} = 200\,\hbox {GeV}$$ using a multiphase transport (AMPT) model, the azimuthal angle dependences of the Hanbury Brown–Twiss (HBT) radii relative to the second- and third-order participant plane from $$\pi $$–$$\pi $$ correlations are discussed. Three initial geometric configurations of $$^{12}\hbox {C}$$, namely three-$$\alpha $$-cluster triangle, three-$$\alpha $$-cluster chain and Woods–Saxon distribution of nucleons, are taken into account, and their effects on the correlations are investigated. The ratio of the third- to the second-order HBT radii $$R_{o(s),3}^2/R_{o(s),2}^2$$ is shown to be a clear probe for three configurations. In addition, this work presents the hadronic rescattering time evolution of the azimuthally dependent HBT radii. From the present study, one can learn that the HBT correlation from identical particles at freeze-out is able to provide the information of different initial configurations as collective flow proposed before.