The differential elastic cross sections of $^{12}$C -- $^{12}$C and $^{11}$Li -- $^{12}$C nuclei are calculated in the complete Glauber theory. The role of the possible correlations connected to the shell effects in $^{11}$Li nucleus is considered.
A new approach to deal with the scattering amplitudes in Glauber theory is proposed. It relies on the use of generating function, that has been explicitly found. The method is applied to the analytical calculation of the nucleus-nucleus elastic scattering amplitudes in the all interaction orders of the Glauber theory.
Previous analytical formulas in the Glauber model for high-energy nucleus-nucleus collisions developed by Wong are utilized and extended to study antiproton-nucleus annihilations for both high and low energies, after taking into account the effects of Coulomb and nuclear interactions, and the change of the antiproton momentum inside a nucleus. The extended analytical formulas capture the main features of the experimental antiproton-nucleus annihilation cross sections for all energies and mass numbers. At high antiproton energies, they exhibit the granular property for the lightest nuclei and t…
A systematic analysis of nucleon-nucleon scattering amplitudes is available up to a laboratory energy of $3$~GeV in case of the $pp$ system and up to $1.2$ GeV for $pn$. At higher energies there is only incomplete experimental information on $pp$ elastic scattering, whereas data for the $pn$ system are very scarce. We apply the spin-dependent Glauber theory to calculate spin observables of $pd$ elastic scattering at $3$-$50$ GeV/c using $pp$ amplitudes available in the literature and parametrized within the Regge formalism. The calculated vector $A_y^p$, $A_y^d$ and tensor $A_{xx}$, $A_{yy}$ a…
A Monte Carlo model, initially developed for soft pp and AA collisions at high energy, is applied for proton-lead interaction at the LHC energy. Elementary collisions are implemented at the partonic level and do not involve the usual Glauber supposition of independent nucleon-nucleon collisions. The average number of participating nucleons and charged multiplicity in p-Pb collisions were calculated and compared with the predictions of Glauber model and experimental data. It was demonstrated that taking into account the energy conservation results in the number of participating nucleons conside…
We perform a parameter-free calculation for the high-energy proton-nucleus scattering based on the Glauber theory. A complete evaluation of the so-called Glauber amplitude is made by using the factorization of the single-particle wave functions. The multiple-scattering or multistep processes are fully taken into account within the Glauber theory. We demonstrate that proton- $^{12}$C, $^{20}$Ne, and $^{28}$Si elastic and inelastic scattering ($J^π=0^+ \to 2^+$ and $0^+ \to 4^+$) processes are very well described in a wide range of the incident energies from $\sim$50 MeV to $\sim$ 1 GeV. We eval…
Basing on the thickness (profile) function, previously obtained for the realistic Fermi type distribution of nucleons in nuclei, calculations are made of the microscopic eikonal phases of the nucleus-nucleus scattering and the total reaction cross- sections. In so doing, the phase is deduced to the one-dimensional integral provided that the Gaussian density distribution for the projectile nucleus and an arbitrary shape of the thickness density for the target nucleus are used. The problems of obtaining parameters of the "point" nucleon density are considered. A possibility of approximating the …
We calculate the proton-nucleus total reaction cross sections at different energies of incident protons within the optical limit approximation of the Glauber theory. The isospin effect has been taken into account. The nucleon distribution is obtained in the framework of macroscopic nuclear models in a way depending on the equation of state of uniform nuclear matter near the saturation density. We find that at an energy of order 40 MeV, the reaction cross section calculated for neutron- rich isotopes significantly increases as the parameter L characterizing the density dependence of the symmetr…
Event-by-event fluctuations of observables are often modeled using the Monte Carlo Glauber model, in which the energy is initially deposited in sources associated with wounded nucleons. In this paper, we analyze in detail the correlations between these sources in proton-nucleus and nucleus-nucleus collisions. There are correlations arising from nucleon-nucleon correlations within each nucleus, and correlations due to the collision mechanism, which we dub twin correlations. We investigate this new phenomenon in detail. At the RHIC and LHC energies, correlations are found to have modest effects …
Reaction and elastic differential cross sections are calculated for light nuclei in the framework of the Glauber theory. The optical phase-shift function is evaluated by Monte Carlo integration. This enables us to use the most accurate wave functions and calculate the phase-shift functions without approximation. Examples of proton nucleus (e.g. p-$^6$He, p-$^6$Li) and nucleus-nucleus (e.g. $^6$He$-^{12}$C) scatterings illustrate the effectiveness of the method. This approach gives us a possibility of a more stringent analysis of the high-energy reactions of halo nuclei.
We systematically calculate the total reaction cross sections of oxygen isotopes, $^{15-24}$O, on a $^{12}$C target at high energies using the Glauber theory. The oxygen isotopes are described with Slater determinants generated from a phenomenological mean-field potential. The agreement between theory and experiment is generally good, but a sharp increase of the reaction cross sections from ^{21}O to ^{23}O remains unresolved. To examine the sensitivity of the diffraction pattern of elastic scattering to the nuclear surface, we study the differential elastic-scattering cross sections of proton…
Glauber theory for nucleus-nucleus scattering at high incident energies is reformulated so as to become applicable also for the scattering at intermediate energies. We test validity of the eikonal and adiabatic approximations used in the formulation, and discuss the relation between the present theory and the conventional Glauber calculations with either the empirical nucleon-nucleon profile function or the modified one including the in-medium effect.
In the framework of the classical Glauber approach the exact analytical expression for the variance of the number of participants (wounded nucleons) for given centrality AA interactions is presented. It's shown, that in the case of nucleus-nucleus collisions along with the optical approximation term the additional "contact" term appears. The numerical calculations for PbPb collisions at SPS energies show that at intermediate values of the impact parameter the "optical" and "contact" terms contributions to the variance of the participants number are of the same order and their sum is in a good …
We revisit the Glauber model to study the heavy ion reaction cross sections and elastic scattering angular distributions at low and intermediate energies. The Glauber model takes nucleon-nucleon cross sections and nuclear densities as inputs and has no free parameter and thus can predict the cross sections for unknown systems. The Glauber model works at low energies down to Coulomb barrier with very simple modifications. We present new parametrization of measured total cross sections as well as ratio of real to imaginary parts of the scattering amplitudes for pp and np collisions as a function…
Calculation of elastic p8Li- and p9Li-scattering differential cross sections, performed at two energies 0.07 and 0.7 GeV/nucleon within Glauber multiple diffraction scattering, are presented and discussed. Three-body wave functions: alpha-t-n (for 8Li) and 7Li-n-n (for 9Li) with realistic potentials of intercluster interactions were used there. Sensitivity of elastic scattering to proton-nucleus interaction and nuclear structure has been studied. In particular, dependence of differential cross section on contribution of higher-order collisions, scattering at core and at periphery nucleons, on …
We study the exotic deformed nucleus $^{31}$Ne using an approach that combines self-consistent structure and reaction theory. We utilize the fully-relativistic, microscopic deformed Hartree-Bogoliubov theory in continuum (DRHBc) to demonstrate that deformation and pairing correlations give rise to a halo structure with large-amplitude $p$-wave configuration in $^{31}$Ne. We then use the valence nucleon wave functions and angle-averaged density distributions of $^{30}$Ne from this model as input for a Glauber reaction model to study the observables of neutron-rich Neon isotopes and search for h…
We study the energy dependence of the cross sections for nucleon removal of 8B projectiles. It is shown that the Glauber model calculations with nucleon-nucleon t-matrix reproduce well the energy dependence of the breakup cross sections of 8B. A DWBA model for the breakup cross section is also proposed and results are compared with those of the Glauber model. We show that to obtain an agreement between the DWBA calculations, the Glauber formalism, and the experimental data, it is necessary to modify the energy behavior of the effective interaction. In particular, the breakup potential has a qu…
The Glauber model is extensively applied to heavy ion collision for describing a number of interaction processes over a wide range of energies from near the Coulomb barrier to higher energies. The model gives the nucleus-nucleus interaction in terms of interaction between the constituent nucleons with a given density distribution. The model is a semiclassical model picturing the nuclear collision in the impact parameter representation where the nuclei move along the collision direction in a straight path. In these lectures we derive this model and discuss its applications in variety of problem…
We present a study of coherent pion production in neutrino-nucleus interactions using the formalism based on partially conserved axial current theorem which connects the neutrino-nucleus cross section to the pion-nucleus elastic scattering cross section. Pion-nucleus elastic scattering cross section is calculated using Glauber model which takes three inputs, nuclear densities, pion-nucleon cross section and $α_{πN}$ which is the ratio of real to imaginary part of $πN$ forward scattering amplitude, for which the parametrizations are obtained from measured data. We calculate the differential and…
We present the first application of a recently-developed effective theory of jet propagation in matter SCETG to inclusive hadron suppression in nucleus-nucleus collisions at the LHC. SCETG-based splitting kernels allow us to go beyond the traditional energy loss approximation and unify the treatment of vacuum and medium-induced parton showers. In the soft gluon emission limit, we establish a simple analytic relation between the QCD evolution and energy loss approaches to jet quenching. We quantify the uncertainties associated with the implementation of the in-medim modification of hadron produ…
This is a review of Glauber's asymptotic diffraction theory, in which diffractive scattering is described in terms of interference between semiclassical amplitudes, resulting from a stationary-phase approximation. Typically two such amplitudes are sufficient to accurately describe elastic scattering, but the stationary points are located at complex values of the impact parameter. Their separation controls the interference pattern, and their offsets from the real axis determine the overall fall-off with momentum transfer. Asymptotically, at large momentum transfers, the stationary points move t…
Glauber-theory analysis of nuclear reactions on 12C target with variational Monte Carlo wave functions
Osaka Metropolitan University(大阪公立大学);Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University(大阪公立大学南部阳一郎理论与实验物理研究所);RIKEN Nishina Center(理化学研究所西村中心);Niigata University(新潟大学);Argonne National Laboratory(阿贡国家实验室)
We analyze the prospect of measuring the neutron form factor of a nucleus through the detection of neutrino-nucleus coherent elastic scattering. We predict numbers of events in a liquid noble nuclear recoil detector at a stopped pion neutrino source. We discuss the precision required to distinguish between different theoretical models for the form factor.
In this article, we present the charged and neutral current coherent pion production in the neutrino-nucleus interaction in the resonance region using the formalism based on the partially conserved axial current (PCAC) theorem which relates the neutrino-nucleus cross section to the pion-nucleus elastic cross section. The pion nucleus elastic cross section is calculated using the Glauber model approach. We calculate the integrated cross sections for neutrino-carbon, neutrino-iron and neutrino-oxygen scattering. The results of integrated cross-section calculations are compared with the measured …
A parameterization of the nucleon-nucleon elastic scattering amplitude is needed for future experiments with nucleon and nuclear beams in the beam momentum range of 2 -- 50 GeV/c/nucleon. There are many parameterizations of the amplitude at $P_{lab} >$ 25--50 GeV/c, and at $P_{lab} \leq$ 5 GeV/c. Our paper is aimed to cover the range between 5 -- 50 GeV/c. The amplitude is used in Glauber calculations of various cross sections and Monte Carlo simulations of nucleon-nucleon scatterings. Usually, the differential nucleon-nucleon elastic scattering cross sections are described by an exponential e…
The series of calculations of differential cross sections and analyzing powers (Ay) of the elastic proton scattering on isotopes 6He and 8He was presented in the framework of the theory of Glauber multiple diffraction scattering. The three-body α-n-n and harmonic oscillator wave functions were used for 6He, for 8He - the function of density distribution in LSSM. For p6He scattering the expansion of the Glauber operator into a series of multiple scattering is written in the form consistent with the picture of weakly bound clusters in halo-nuclei, for p8He scattering the members of single- and d…
In this article, we study the coherent pion production in neutrino-nucleus interaction in the resonance region using the formalism based on partially conserved axial current (PCAC) theorem which relates the neutrino-nucleus cross section to the pion-nucleus elastic cross section. The pion nucleus elastic cross section is calculated using the Glauber model in terms of pion-nucleon cross sections obtained by parameterizing the experimental data. We calculate the differential and integrated cross sections for charged current coherent pion production in neutrino carbon scattering. The results of i…
The cross sections for a variety of channels of proton-nucleus interaction associated with large gaps in rapidity are calculated within the Glauber-Gribov theory. We found inelastic shadowing corrections to be dramatically enhanced for such events. We employ the light-cone dipole formalism which allows to calculate the inelastic corrections to all orders of the multiple interaction. Although Gribov corrections are known to make nuclear matter more transparent, we demonstrate that in some instances they lead to an opaqueness. Numerical calculations are performed for the energies of the HERA-B e…
We study within the Monte Carlo Glauber model the influence of collective quantum effects in the Pb nucleus on the azimuthal anisotropy coefficients $ε_{2,3}$ in Pb+Pb collisions at the LHC energies. To account for the quantum effects, we modify the sampling of the nucleon positions by applying suitable filters that guarantee that the colliding nuclei have the mean squared quadrupole and octupole moments consistent with the ones extracted from the experimental quadrupole and octupole strength functions for the Pb nucleus with the help of the energy weighted sum rule. Our Monte Carlo Glauber mo…
We present quasi-elastic neutrino-nucleus cross sections in the energy range from 150 MeV up to 5 GeV for the target nuclei 12C and 56Fe. A relativistic description of the nuclear dynamics and the neutrino-nucleus coupling is adopted. For the treatment of final-state interactions (FSI) we rely on two frameworks succesfully applied to exclusive electron-nucleus scattering: a relativistic optical potential and a relativistic multiple-scattering Glauber approximation. At lower energies, the optical-potential approach is considered to be the optimum choice, whereas at high energies a Glauber appro…
GLISSANDO is a Glauber Monte-Carlo generator for early-stages of relativistic heavy-ion collisions, written in c++ and interfaced to Root. Several models are implemented: the wounded-nucleon model, the binary collisions model, the mixed model, and the model with hot-spots. Subtleties of the distribution of nucleon in the nucleus are discussed. The original geometric distribution of sources in the transverse plane can be superimposed with a statistical distribution simulating the dispersion in the generated transverse energy in each individual collision. The program generates inter alia the fix…
The excitation of two particle-two hole final states in neutrino-nucleus scattering, not taken into account in Monte Carlo simulations for data analysis, has been advocated by many authors as the source of the excess cross section observed by the MiniBooNE collaboration in the quasi elastic channel. We analyse the mechanisms leading to the appearance of two particle-two hole states, and show that interference between the amplitudes involving one- and two-nucleon currents, not consistently included in existing calculations, plays a major role. A novel approach allowing to treat one- and two-nuc…
Two relativistic approaches to charged-current quasielastic neutrino-nucleus scattering are illustrated and compared: one is phenomenological and based on the superscaling behavior of electron scattering data and the other relies on the microscopic description of nuclear dynamics in relativistic mean field theory. The role of meson exchange currents in the two-particle two-hole sector is explored. The predictions of the models for differential and total cross sections are presented and compared with the MiniBooNE data.
The nuclear transparency of the charged hadron produced in the inclusive $(e,e^\prime)$ reaction on the nucleus has been calculated using Glauber model for the nuclear reaction. The color transparency (CT) of the produced hadron and the short-range correlation (SRC) of the nucleons in the nucleus have been incorporated in the Glauber model to investigate their effects on the nuclear transparency of the hadron. The calculated nuclear transparencies for the proton and pion are compared with the data.
Measured J/Psi production cross sections for 200 and 450 GeV/c protons incident on a variety of nuclear targets are analyzed within a Glauber framework which takes into account energy loss of the beam proton, the time delay of particle production due to quantum coherence, and absorption of the J/Psi on nucleons. The best representation is obtained for a coherence time of 0.5 fm/c, previously determined by Drell-Yan production in proton-nucleus collisions, and an absorption cross section of 3.6 mb, which is consistent with the value deduced from photoproduction of the J/Psi on nuclear targets.
Quasielastic double differential neutrino cross sections can be obtained in a phenomenological model based on the superscaling behavior of electron scattering data. In this talk the superscaling approach (SuSA) is reviewed and its validity is tested in a relativistic shell model. Results including meson exchange currents for the kinematics of the MiniBoone experiment are presented.
We develop the Glauber theory description of final-state interaction (FSI) in quasielastic $A(e,e'p)$ scattering. The important new effect is an interaction between the two trajectories which enter the calculation of FSI-distorted one-body density matrix and are connected with incoherent elastic rescatterings of the struck proton on spectator nucleons. We demonstrate that FSI distortions of the missing momentum distribution are large over the whole range of missing momenta. Important finding is that incoherent elastic rescatterings of the ejected proton lead to a strong quantum mechanical dist…
A systematic analysis is made on the total reaction cross sections for Ne, Mg, Si, and S isotopes. The high-energy nucleus-nucleus collision is described based on the Glauber model. Using the Skyrme-Hartree-Fock method in the three-dimensional grid-space representation, we determine the nuclear density distribution for a wide range of nuclei self-consistently without assuming any spatial symmetry. The calculated total reaction cross sections consistently agree with the recent cross section data on Ne$+^{12}$C collision at 240$A$\,MeV, which makes it possible to discuss the radius and deformati…
We present an extended version of GLISSANDO, a Monte-Carlo generator for Glauber-like models of the initial stage of relativistic heavy-ion collisions. The increased functionality of the code incorporates a parametrization of shape of nuclei, including light nuclei needed in the NA61 experiment, the nuclear deformation, a possibility of using correlated distributions of nucleons in nuclei read from external files, an option of overlaying distributions of produced particles dependent on the space-time rapidity, the inclusion of the core-corona effect, or the output of the source distributions t…
Recent data on the nuclear modification of W and Z boson production measured by the ATLAS collaboration in PbPb collisions at $\sqrt{s_{\rm nn}}=5.02$ TeV show an enhancement in peripheral collisions, seemingly contradicting predictions of the Glauber model. The data were previously explained by arguing that the nucleon-nucleon cross section may be shadowed in nucleus-nucleus collisions, and hence suppressed compared to the proton-proton cross section at the same collision energy. This interpretation has quite significant consequences for the understanding of heavy-ion data, in particular in t…
The transparency of the hadrons produced in the $γ(n,p) π^-$ reaction in nuclei is calculated using the Glauber model modified by including the Fermi motion of the nucleon in the nucleus. Since the calculated results underestimates the measured transparency for $^4$He nucleus, the Glauber model is further modified by incorporating the short-range correlation of the nucleon and the color transparency of the hadron in the nucleus. The nuclear transparency of the $γ(n,p) π^-$ reaction is calculated for $θ_{π^-}$(c.m.) = 50$^{\circ}$, 70$^{\circ}$ and 90$^{\circ}$. The calculated results are compa…
We re-evaluate the nuclear suppression of forward $J/ψ$ production at high energy in the Color Glass Condensate framework. We use the collinear approximation for the projectile proton probed at large $x$ and an up to date dipole cross section fitted to HERA data to describe the target in proton-proton collisions. We show that using the Glauber approach to generalize the proton dipole cross section to the case of a nucleus target leads to a nuclear modification factor much closer to LHC data than previous estimates using the same framework.
A parton picture of inclusive quasi-elastic electron-nucleus scattering, where individual nucleons are treated as (non point-like) partons of the nucleus, is presented. All the necessary target-mass corrections to asymptotic scaling are evaluated and a new scaling variable is obtained. Recent inclusive data from Jefferson Lab are analyzed and shown to scale in terms of the new variable. The new approach allows to extract in a model-independent way the nucleon light-cone momentum distribution in the nucleus.
We consider T-violating P-conserving proton-deuteron forward elastic scattering amplitude in a frame of the Glauber multiscattering theory, proceeding from T-odd, P-even N-N interaction.
We construct a microscopic optical potential including breakup effects for elastic scattering of weakly-binding projectiles within the Glauber model, in which a nucleon-nucleus potential is derived by the $g$-matrix folding model. The derived microscopic optical potential is referred to as the eikonal potential. For $d$ scattering, the calculation with the eikonal potential reasonably reproduces the result with an exact calculation estimated by the continuum-discretized coupled-channels method. As the properties of the eikonal potential, the inaccuracy of the eikonal approximation used in the …
The effects of charge symmetry breaking in nucleon electromagnetic form factors on parity- violating elastic electron-12C scattering is studied, and found to be much smaller than other known effects. The analysis of a planned experiment is discussed.
In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions of exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the $^6$He and $^{11}$Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in $^6$He and $^{11}$Li.
Introduction Theory of electromagnetic excitation and dissociation (Inelastic scattering at high energies: one-photon exchange, semiclassical approach and Glauber theory; Higher order electromagnetic effects, small xi-approximation) Discussion of experimental results for nuclear structure Coulomb dissociation as a tool to measure radiative capture processes relevant to nuclear astrophysics Antihydrogen production and electromagnetic processes at relativistic heavy ion colliders Conclusions
At sufficiently large proton energies, Glauber multiple-scattering theory offers good opportunities for describing the final state interactions in electro-induced proton emission off nuclear targets. A fully unfactorized relativistic formulation of Glauber multiple-scattering theory is presented. The effect of truncating the Glauber multiple-scattering series is discussed. Relativistic effects in the description of the final-state interactions are found not to exceed the few percent level. Also the frequently adopted approximation of replacing the wave functions for the individual scattering n…
In order to clear up the sensitivity of the nucleus--nucleus reaction cross sections $σ_R$ to the nuclear matter distributions in exotic halo nuclei, we have calculated the values of $σ_R$ for scattering of $^6$He, $^{11}$Li, and $^{19}$C nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon. The calculations were performed in the "rigid target" approximation to the Glauber theory, different shapes of the nuclear density distributions in $^6$He, $^{11}$Li, and $^{19}$C being assumed.
We perform Glauber model calculations of the antiproton-nucleus elastic and quasielastic scattering and absorption in the beam momentum range $\sim 0.5\div10$ GeV/c. A good agreement of our calculations with available LEAR data and with earlier Glauber model studies of the $\bar p A$ elastic scattering allows us to make predictions at the beam momenta of $\sim 10$ GeV/c, i.e. at the regime of the PANDA experiment at FAIR. The comparison with the proton-nucleus elastic scattering cross sections shows that the diffractive minima are much deeper in the $\bar p A$ case due to smaller absolute valu…
We investigate the sensitivity of the medium effect in the high-density region on the nucleus-nucleus elastic scattering in the framework of the double-folding (DF) model with the complex $G$-matrix interaction. The medium effect including three-body-force (TBF) effect is investigated with two methods. In the both methods, the medium effect is clearly seen on the potential and the elastic cross section. Finally, we make clear the crucial role of the TBF effect up to $k_F =$ 1.6 fm$^{-1}$ in the nucleus-nucleus elastic scattering.
The quasi-elastic neutrino-nucleus cross section has been calculated by using a Fermi gas model corrected to consider the re-scattering between the emitted nucleon and the rest nucleus. As an example of the relevance of this effect we show results for the muon production cross section on 16O target.
Obtaining cross sections for nuclear reactions at intermediate energies based on the Glauber formulation has a long tradition. Only recently the energy regime of a few hundred MeV has become accessible to ab-initio Faddeev calculations of three-body scattering. In order to go to higher energies, the Faddeev equation for three-body scattering is formulated and directly solved without employing a partial wave decomposition. In the simplest form the Faddeev equation for interacting scalar particles is a three-dimensional integral equation in five variables, from which the total cross section, the…
The proposed hadronic and string cascade model, JPCIAE, for ultrarelativistic nucleus - nucleus collisions based on the LUND model and the PYTHIA event generator especially, is used to investigate the $J/ψ$ suppression due to the nuclear absorption of a $J/ψ$ in minimum bias pA and BA collisions at 200 A GeV energy. With the different sets of reasonable formation time for hadron and $J/ψ$ the results of $J/ψ$ suppression factor from both the usual scenario and the Glauber - like simulations are comparable with all the NA38 pA and BA data, except the NA50 data of Pb + Pb collisions. However, th…
In the presented review we discuss the problem of extraction the parameters of nuclear matter and charge distribution in stable and unstable isotopes. A substantial amount of information on the nuclear radii and other distribution parameters in light exotic nuclei has been obtained from experiments on intermediate-energy nucleus-nucleus collisions. The analyses of these experiments is usually performed with the help of the Glauber Theory. We review the main assumptions the Glauber Theory and show how this theoretical approach is used to calculate reaction and interaction cross sections. We als…