Glauber Model Research Articles

Charge radii of 11−16C, 13−17N and 15−18O determined from their charge-changing cross-sections and the mirror-difference charge radii

Charge-changing cross-sections (CCCSs) of 11−16C, 13−17N and 15−18O on a carbon target have been determined at energies around 300 MeV/nucleon. A nucleon separation energy-dependent correction factor has been introduced to the Glauber model calculation for extracting the nuclear charge radii from the experimental CCCSs. The charge radii of 11C, 13,16N and 15O thus were determined for the first time. With the new radii, we studied the experimental mirror-difference charge radii (ΔRchmirror) of 11B-11C, 13C-13N, 15N-15O, 17N-17Ne pairs for the first time. We find that the ΔRchmirror values of 13C-13N and 15N-15O pairs follow well the empirical relation to the isospin asymmetry predicted by the abinitio calculations, while ΔRchmirror of 11B-11C and 17N-17Ne pairs deviate from such relation by more than two standard deviations.

Jet Quenching for Hadron-Tagged Jets in pA Collisions

We calculate the medium modification factor \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{I}_{{pA}}}$$\\end{document} for 5.02 TeV \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document} + Pb collisions. We use the Monte Carlo Glauber model to determine the parameters of the quark–gluon plasma fireball in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$pA$$\\end{document} jet events. Our calculations show that the jet quenching effect for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{I}_{{pA}}}$$\\end{document} turns out to be rather small. We have found that the theoretical \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{I}_{{pA}}}$$\\end{document} as a function of the underlying event charged multiplicity density, within errors, agrees with data from ALICE [1] for 5.02 TeV \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document} + Pb collisions. However, the experimental errors are too large to draw a firm conclusion on the possible presence of jet quenching.

Neutron radius determination of 133Cs and its impact on the interpretation of CEνNS-CsI measurement

Proton-133Cs elastic scattering at low momentum transfer is performed using an in-ring reaction technique at the Cooler Storage Ring at the Heavy Ion Research Facility in Lanzhou. Recoil protons from the elastic collisions between the internal H2-gas target and the circulating 133Cs ions at 199.4 MeV/u are detected by a silicon-strip detector. The matter radius of 133Cs is deduced by describing the measured differential cross sections using the Glauber model. Employing the adopted proton distribution radius, a point-neutron radius of 4.86(21) fm for 133Cs is obtained. With the newly determined neutron radius, the weak mixing angle sinθW2 is independently extracted to be 0.227(28) by fitting the coherent elastic neutrino-nucleus scattering data. Our work limits the sinθW2 value in a range smaller than the ones proposed by the previous independent approaches, and would play an important role in searching new physics via the high precision CEνNS-CsI cross section data in the future.

Analysis of Glauber model Monte Carlo simulation of Pb+Pb collisions

This review delves into the theoretical foundations, experimental methodologies, and observational aspects of the Glauber Model in the realm of relativistic heavy-ion physics. Our investigation utilizes Glauber Monte Carlo simulations to anticipate and evaluate the anticipated outcomes of an upcoming ultra-relativistic Pb+Pb collision study. Our primary focus centers on analyzing the initial geometric characteristics of these collisions, particularly with respect to the impact parameter. We also examine critical parameters such as the count of participating nucleons to gain insights into the collision dynamics. This comprehensive exploration provides a valuable perspective on the intricacies of heavy-ion interactions, shedding light on the underlying mechanisms and offering predictive power for future experiments in the field of relativistic heavy-ion physics.

Measurement of nuclear interaction cross sections towards neutron-skin thickness determination

The accuracy of reaction theories used to extract properties of exotic nuclei from scattering experiments is often unknown or not quantified, but of utmost importance when, e.g., constraining the equation of state of asymmetric nuclear matter from observables as the neutron-skin thickness. In order to test the Glauber multiple-scattering model, the total interaction cross section of ▪ on carbon targets was measured at initial beam energies of 400, 550, 650, 800, and 1000 MeV/nucleon. The measurements were performed during the first experiment of the newly constructed R3B (Reaction with Relativistic Radioactive Beams) experiment after the start of FAIR Phase-0 at the GSI/FAIR facility with beam energies of 400, 550, 650, 800, and 1000 MeV/nucleon. The combination of the large-acceptance dipole magnet GLAD and a newly designed and highly efficient Time-of-Flight detector enabled a precise transmission measurement with several target thicknesses for each initial beam energy with an experimental uncertainty of ±0.4%. A comparison with the Glauber model revealed a discrepancy of around 3.1% at higher beam energies, which will serve as a crucial baseline for the model-dependent uncertainty in future fragmentation experiments.

Prediction of two-neutron halos in the N = 28 isotones 40Mg and 39Na

The ground states of the nuclei Mg40 and Na39 are investigated using the hyperspherical formalism. Since they are located at the edge of the “big island of inversion”, we concentrate on whether we are likely to find two-neutron Borromean halos in these nuclei. A three-body model with effective n-n and Mg38+n interactions is built for Mg40 based on the available data. We also give predictions for the low-lying spectrum of Na38=37Na+n and two-neutron separation energy of the Na39 nucleus. Depending on parameter choice, we report an increase in the matter radii in the range 0.1-0.5 fm relative to those of the core nuclei. The results suggest a two-neutron halo structure in Mg40 for a subset of parameters, reinforcing the prediction of a Borromean halo nucleus. The calculations indicate that a two-neutron halo is even more likely for Na39. As expected, the halo is linked to the disappearance of the shell gap in these nuclei due to the inversion of the 2p3/2 and 1f7/2 orbitals. We study the total cross section for scattering of these nuclei from a carbon target using a Glauber model and show that these provide a clear signal to assess the halo structure.

Determination of Nuclear Matter Radii by Means of Microscopic Optical Potentials: The Case of 78\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{78}$$\\end{document}Kr

In this work we use microscopic Nucleon–Nucleus Optical Potentials (OP) to analyze elastic scattering data for the differential cross section of the 78\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{78}$$\\end{document}Kr (p,p) 78\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{78}$$\\end{document}Kr reaction, with the goal of extracting the matter radius and estimating the neutron skin, quantities that are both needed to determine the slope parameter L of the nuclear symmetry energy. Our analysis is performed with the factorized version of the microscopic OP obtained in a previous series of papers within the Watson multiple scattering theory at the first order of the spectator expansion, which is based on the underlying nucleon–nucleon dynamics and is free from phenomenological inputs. Differently from our previous applications, the proton and neutron densities are described with a two-parameter Fermi (2pF) distribution, which makes the extraction of the matter radius easier and allows us to make a meaningful comparison with the original analysis, that was performed with the Glauber model. With standard minimization techniques we performed data analysis and extracted the matter radius and the neutron skin. Our analysis produces a matter radius of Rm(rms)=4.12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_m^{\\mathrm{(rms)}} = 4.12$$\\end{document} fm, in good agreement with previous matter radii extracted from 76\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{76}$$\\end{document}Kr and 80\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{80}$$\\end{document}Kr, and a neutron skin of ΔRnp≃-0.1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta R_{np} \\simeq - 0.1$$\\end{document} fm, compatible with a previous analysis. Our factorized microscopic OP, supplied with 2pF densities, is a valuable tool to perform the analysis of the experimental differential cross section and extract information such as matter radius and neutron skin. Without any free parameters it provides a reasonably good description of the experimental differential cross section for scattering angles up to ≈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\approx $$\\end{document} 40 degrees. Compared to the Glauber model our OP can be applied to a wider range of scattering angles and allows one to probe the nuclear systems in a more internal region.

Pion–nucleus elastic scatterings incorporating medium effects within the Eikonal–Glauber model

Pion–nucleus elastic scatterings incorporating medium effects within the Eikonal–Glauber model

A new approach for deducing rms proton radii from charge-changing reactions of neutron-rich nuclei and the reaction-target dependence

We report the charge-changing cross sections (σcc) of 24 p-shell nuclides on both hydrogen and carbon at about 900A MeV, of which 8,9Li, 10–12Be, 10,14,15B, 14,15,17–22N and 16O on hydrogen and 8,9Li on carbon are for the first time. Benefiting from the data set, we found a new and robust relationship between the scaling factor of the Glauber model calculations and the separation energies of the nuclei of interest on both targets. This allows us to deduce proton radii (Rp) for the first time from the cross sections on hydrogen. Nearly identical Rp values are deduced from both target data for the neutron-rich carbon isotopes; however, the Rp from the hydrogen target is systematically smaller in the neutron-rich nitrogen isotopes. This calls for further experimental and theoretical investigations.

Event shape engineering via Glauber MC model

In our exploration of event shape engineering, the Glauber model served as a foundational tool for under- standing the anisotropic geometry of the Quark-Gluon Plasma (QGP). Utilizing the TGlauberMC-3.2 model within ROOT, we systematically analyzed one million events. From the 2 & Npart plot, our data revealed an average maximum dN value of 12.00 with associated parameters: 2 = 0.91, 2 =2.74, 3 =0.91 and Npart = 14.00. These findings illuminate the distinct configurations that yield the most pronounced anisotropic geometries of the QGP, providing insights into optimizing event shape configurations.

ALICE luminosity determination for Pb–Pb collisions at √s NN = 5.02 TeV

Luminosity determination within the ALICE experiment is based on the measurement, in van der Meer scans, of the cross sections for visible processes involving one or more detectors (visible cross sections). In 2015 and 2018, the Large Hadron Collider provided Pb–Pb collisions at a centre-of-mass energy per nucleon pair of √s NN = 5.02 TeV. Two visible cross sections, associated with particle detection in the Zero Degree Calorimeter (ZDC) and in the V0 detector, were measured in a van der Meer scan.This article describes the experimental set-up and the analysis procedure, and presents the measurement results. The analysis involves a comprehensive study of beam-related effects and an improved fitting procedure, compared to previous ALICE studies, for the extraction of the visible cross section. The resulting uncertainty of both the ZDC-based and the V0-based luminosity measurement for the full sample is 2.5%. The inelastic cross section for hadronic interactions in Pb–Pb collisions at √s NN = 5.02 TeV, obtained by efficiency correction of the V0-based visible cross section, was measured to be 7.67 ± 0.25 b, in agreement with predictions using the Glauber model.

A unified description of the halo nucleus 37Mg from microscopic structure to reaction observables

Based on the structure input directly from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we fully study reaction observables to search for halo evidence of 37Mg with the Glauber model. In this scheme, we evaluate the reaction cross sections of 20–37Mg bombarding a C target at 240 MeV/nucleon and find that most of the results agree well with the experimental data within 1σ uncertainty, especially good for the case of 37Mg. Our predicted doubling of the cross section change from 36Mg to 37Mg over that from 34Mg to 35Mg is consistent with a halo structure in 37Mg. Additionally, our calculated narrow longitudinal momentum distribution of 36Mg residues from 37Mg + 12C breakup agrees well with data and imply a nuclear size much larger than 35Mg. Furthermore, our study shows a dominant p-wave contribution to the longitudinal momentum distribution, supporting the conclusion that 37Mg is a p-wave halo nucleus. Our study provides the first unified description of the halo characteristics of 37Mg from nuclear structure to reaction dynamics.

Optimization of asymmetry of Pb-Pb nucleus collision based on Glauber model simulation

Currently, researchers wanted to optimize the radiation by selecting certain asymmetry to produce high-energy particles in QGP collision. Our research utilized the Glauber-Monto-Carlo Model to simulate the collision and tried to find the domain of different independent variables to maximize the asymmetry of the cross-section. We have conducted relevant analysis and research on the principles of this model and generated relevant images using ROOT. The result shows that at the number level of 106, for the number of bins equals 10, we have (0.4, 0.5) for eccentricity in the second harmonic, (0.9, 1.0) for eccentricity in the third harmonic, (2.51, 3.14) for azimuthal angle difference, and (125, 166) for the number of participants, and, for number of bins equal to 20, (0.45, 0.50) for eccentricity in second harmonic, (0.95, 1.0) for eccentricity in the third harmonic, (2.82, 3.14) for azimuthal angle difference, and (146, 166) for the number of participants.

Exploring Global Polarization Splitting in Au+Au Collisions at sNN=19.6 GeV Using Viscous Hydrodynamic Model CLVisc

We present a systematic study of the global polarization of Λ and Λ¯ hyperons in Au+Au collisions at sNN=19.6 GeV using the viscous hydrodynamic model CCNU-LBNL-Viscous hydrodynamic model (CLVisc) with a modified 3D optical Glauber model initial condition. The global polarization splitting as a function of transverse momentum and rapidity is investigated. It is shown that the magnitude of the net baryon density and its longitudinal titled geometry at the initial stage both have significant effects on the global polarization splitting of Λ and Λ¯ hyperons. Specifically, an increase in the magnitude of the net baryon density leads to a corresponding minor increase in the global polarization splitting. Similarly, alterations in the tilted geometry of net baryon density results in significant changes in the splitting of the global polarization.

Simulation of collision using Glauber model

This article is going to discuss several important characteristics of Glauber model from lead isotopes Pb208-under computational analysis. At the start, this paper will provide data under Wood-Saxon distribution in. Then, there are collisions coded from Python, assuming all collisions have reaction cross section of 72 mb, both participant particles and particles under secondary collisions are collected and plot in scatter graphs under impact parameter from 0 fm to 20 fm. Lastly, within the collision area, this paper is going to find the distribution of path length under various parameters.

The relationship between and eccentricities based on Glauber model

This report aims to determine the probability range of the number of collisions under the optimum collision condition. The optimum condition was obtained by determining the average values of the given variables in the Glauber Model. Graphs of against eccentricity 1, 2, and 3 (Ecc1, 2, and 3) were plotted respectively according to the data generated from the Glauber Model Simulation in CERN ROOT. Then, the optimum average value was plotted as a vertical line on the graph to determine the range of . The probability ratio of an optimum collision versus maximum probability in an event was concluded to fall in a certain range of 0.30 0.07, and this range is verified to be a stable range that could be used for prediction of optimum collision numbers in future nuclei collision experiment. This probability ratio can be used to predict the optimum collision with only provided.

Neutron rearrangement of the magic number 90Zr-core determined by the matter density difference between 90Zr and 92Zr

Matter density distributions and root-mean-square matter radii for 90Zr and 92Zr were determined through fitting the small-angle differential cross sections of proton elastic scattering at 0.8 GeV with the Glauber model. With the obtained neutron densities, a neutron rearrangement beyond the expectation for the magic number 90Zr-core was found from 90Zr to 92Zr by adding two valence neutrons. By considering the surface-peaked term, the rearrangement was reproduced by the shell model calculations with the realistic Woods-Saxon potentials. It indicates that the surface-peaked term related to surface nucleon interactions plays an important role in describing the nucleon rearrangement, since the surface-peaked term would improve the description of the radial wave functions.

Isospin-dependence of the charge-changing cross-section shaped by the charged-particle evaporation process

We present the charge-changing cross sections (CCCS) of 11−15C, 13−17N, and 15,17−18O at around 300 MeV/nucleon on a carbon target, which extends to p-shell isotopes with N<Z for the first time. The Glauber model, which considers only the proton distribution of projectile nuclei, underestimates the cross sections by more than 10%. We show that this discrepancy can be resolved by considering the contribution from the charged-particle evaporation process (CPEP) following projectile neutron removal. Using nucleon densities from the deformed relativistic Hartree-Bogoliubov theory in continuum, we investigate the isospin-dependent CPEP contribution to the CCCS for a wide range of neutron-to-proton separation energy asymmetry. Our calculations, which include the CPEP contribution, agree well with existing systematic data and reveal an “evaporation peak” at the isospin symmetric region where the neutron-to-proton separation energy is close to zero. These results suggest that analysis beyond the Glauber model is crucial for accurately determining nuclear charge radii from CCCSs.

Comparison of Ichimura-Austern-Vincent and Glauber models for the deuteron-induced inclusive breakup reaction in light and medium-mass nuclei

Comparison of Ichimura-Austern-Vincent and Glauber models for the deuteron-induced inclusive breakup reaction in light and medium-mass nuclei

Matter density distributions of Ne20,22 and Mg24,26 extracted through proton elastic scattering at 0.8 GeV

Reported small-angle differential cross sections of proton elastic scattering off $^{20,22}\mathrm{Ne}$ and $^{24,26}\mathrm{Mg}$ at 0.8 GeV were analyzed with the Glauber model. Matter density distributions of $^{20,22}\mathrm{Ne}$ and $^{24,26}\mathrm{Mg}$ were determined based on the two-parameter Fermi density model, and the corresponding root-mean-square point-matter radii are 2.891(52) fm, 2.895(104) fm, 2.935(20) fm, and 2.946(21) fm. The occupation number effects of the $2s$ orbital on inner density were probed by the matter density difference between $^{22}\mathrm{Ne}$ and $^{24}\mathrm{Mg}$. Combined with the experimental occupation numbers, the relativistic Hartree-Bogoliubov calculations with the DD-ME2 and PC-PK1 interactions describe the obtained density difference trend, and indicate that there may be a bubble structure in $^{24}\mathrm{Mg}$.