Glauber Approximation Research Articles

Nuclear C(e, e′p) Transparencies in a Relativistic Glauber Model

In light of the recent Jefferson Laboratory (JLab) data for the nuclear 12C(e,e′p) transparencies, calculations, obtained in a relativistic multiple scattering Glauber approximation, are discussed. The shell-separated 12C transparencies are shown and it is concluded that the p-shell nucleons are 75% more transparent than the s-shell ones. The presented comparisons between the calculations made here and the current 12C(e,e′p) data show no clear indication for the onset of color transparency when implemented within the color diffusion model with standard parameters.

Radon-to-Helmholtz mappings and nonlinear diffraction tomography.

This paper addresses a number of approximate, analytically invertible solutions of the scalar Helmholtz equation. Primary attention is devoted to the Glauber approximation (GA) derived for the far-field pattern. It is shown that the GA has the form of a nonlinear Radon-to-Helmholtz (RtH) mapping, which transforms a sinogram of the scattering potential into an approximate solution of the Helmholtz equation. A proposal of how to construct a position space counterpart of the GA is formulated. Also, it is established that a paraxial version of the Glauber model coincides, up to an inessential constant factor, with a momentum-space representation of the Mazar-Felsen propagator, which describes forward-scattered waves. For weakly scattering objects, these solutions are reduced to the conventional Born/Rytov approximations, which may, however, preserve the parametrization and sampling formats of the original nonlinear models. Since all RtH mappings are analytically invertible, they can be applied to the (nonlinear) diffraction tomography of penetrable objects. In particular, the Glauber model, which has been largely ignored for years, is shown to provide efficient inversion of synthetic data. The resulting tomograms clearly outperform the Born inversions, even for moderately scattering potentials.

EMC effect, few-nucleon systems and Poincaré covariance

An approach for a Poincaré covariant description of nuclear structure and of lepton scattering off nuclei is proposed within the relativistic Hamiltonian dynamics in the light-front form. Indeed a high level of accuracy is needed for a comparison with the increasingly precise present and future experimental data at high momentum transfer. Therefore, to distinguish genuine QCD effects or effects of medium modified nucleon structure functions from conventional nuclear structure effects, the commutation rules between the Poincaré generators should be satisfied. For the first time in this paper a proper hadronic tensor for inclusive deep inelastic scattering of electrons off nuclei is derived in the impulse approximation in terms of the single nucleon hadronic tensor. Our approach is based : i) on a light-front spectral function for nuclei, obtained taking advantage of the successful non-relativistic knowledge of nuclear interaction, and ii) on the free current operator that, if defined in the Breit reference frame with the momentum transfer, , parallel to the z axis, fulfills Poincaré covariance and current conservation. Our results can be generalized : i) to exclusive processes or to semi-inclusive deep inelastic scattering processes; ii) to the case where the final state interaction is considered through a Glauber approximation; iii) to finite momentum transfer kinematics. As a first test, the hadronic tensor is applied to obtain the nuclear structure function and to evaluate the EMC effect for 3He in the Bjorken limit. Encouraging results including only the two-body part of the light-front spectral function are presented.

Dimesoatom breakup in the Coulomb field

Momentum and angular distributions of charged meson pairs $h^+h^-$ ($h=\pi, K$) from elementary atoms (EA) breakup (ionization) in the Coulomb field of a target atom is considered in the Born and Glauber approximations. Exploiting the fact that the atomic screening of the target Coulomb potential is important at small transfer momenta, while multi-photon exchanges are essential at large transfer momenta we express the cross sections of EA breakup as a sum of two terms. In the region of modest transfer momenta the cross section is determined by the single-photon exchange (first Born approximation) accounting for the target atoms screening, whereas at large transfer momenta using the unscreened potential allows to take into account all multi-photon exchanges and obtain the cross section of EA breakup in the close analytical form.

Measurement of nuclear transparency ratios for protons and neutrons

This paper presents, for the first time, measurements of neutron transparency ratios for nuclei relative to C measured using the (e,e′n) reaction, spanning measured neutron momenta of 1.4 to 2.4 GeV/c. The transparency ratios were extracted in two kinematical regions, corresponding to knockout of mean-field nucleons and to the breakup of Short-Range Correlated nucleon pairs. The extracted neutron transparency ratios are consistent with each other for the two measured kinematical regions and agree with the proton transparencies extracted from new and previous (e,e′p) measurements, including those from neutron-rich nuclei such as lead. The data also agree with and confirm the Glauber approximation that is commonly used to interpret experimental data. The nuclear-mass-dependence of the extracted transparencies scales as Aα with α=−0.289±0.007, which is consistent with nuclear-surface dominance of the reactions.

Parameter-free calculation of charge-changing cross sections at high energy

Charge-changing cross sections at high energies are expected to provide useful information on nuclear charge radii. No reliable theory to calculate the cross section has yet been available. We develop a formula using Glauber and eikonal approximations and test its validity with recent new data on carbon isotopes measured at around $900A$ MeV. We first confirm that our theory reproduces the cross sections of $^{12,13,14}\mathrm{C}+^{12}\mathrm{C}$ consistently with the known charge radii. Next we show that the cross sections of $^{12\ensuremath{-}19}\mathrm{C}$ on a proton target are all well reproduced provided the role of neutrons is accounted for. We also discuss the energy dependence of the charge-changing cross sections.

Evidence forx-dependent proton color fluctuations inpAcollisions at the CERN Large Hadron Collider

We argue that the pattern of the deviation from the Glauber approximation prediction for the centrality dependence of the rate of forward jet production observed in pA collisions at the LHC provides the first experimental evidence that parton configurations in the projectile proton containing a parton with large $x$ interact with a nuclear target with a significantly smaller than average cross section and have smaller than average size. We implement the effects of fluctuations of the interaction strength and, using the ATLAS analysis of how hadron production at backward rapidities depends on the number of wounded nucleons, make quantitative predictions for the centrality dependence of the jet production rate as a function of the $x$-dependent interaction strength $\sigma(x)$. We find that \sigma(x)\sim 0.6 ~\sigma_{tot}(pp) gives a good description of the x=0.6 data and may shed a light on the origin of the EMC effect.

Nuclear shadowing in photoproduction of ρ mesons in ultraperipheral nucleus collisions at RHIC and the LHC

We argue that with an increase of the collision energy, elastic photoproduction of ρ mesons on nuclei becomes affected by the significant cross section of photon inelastic diffraction into large masses, which results in the sizable inelastic nuclear shadowing correction to σγA→ρA and the reduced effective ρ-nucleon cross section. We take these effects into account by combining the vector meson dominance model, which we upgrade to include the contribution of high-mass fluctuations of the photon according to QCD constraints, and the Gribov–Glauber approximation for nuclear shadowing, where the inelastic nuclear shadowing is included by means of cross section fluctuations. The resulting approach allows us to successfully describe the data on elastic ρ photoproduction on nuclei in heavy ion UPCs in the 7 GeV<Wγp<46 GeV energy range and to predict the value of the cross section of coherent ρ photoproduction in Pb–Pb UPCs at sNN=5.02 TeV in Run 2 at the LHC, dσPbPb→ρPbPb(y=0)/dy=560±25 mb.

Strong interaction of hadrons in quark cluster model

The theoretical information on the hadrons interactions according to the basis investigation of the multiple scattering process theory is described. As we know multi-particle reactions on the hadrons targets are attracting a great attention nowadays. To survey strong interaction of jet particles with quarks that are inside hadrons ( Baryons,mesons, exotic baryons(Penta-quarks), exotic mesons(Tetra-quarks) , we can use the estimate called high energy approximation ( Eikonal or Glauber approximation) theory that known very well in nuclear physics. This estimate describes collision and interactions of jet particles with quarks and scattering from multi-focus hadrons like diffraction phenomenon in optics. Glauber multiple scattering process theory may apply in analyzing elastic and inelastic collision of hadrons in a range of high energy levels. In elastic collision, scattering amplitude is equal to total ranges of multiple collisions inside the hadrons. It’s possible to express Glauber multiple scattering factor in a form of mathematic series. So that each elements shows the number of occurred scattering inside the hadrons. Determination of scattering amplitude by the high energy approximation depends on elected primary coming wave function of the shot particle and function of out coming wave from the target nucleus. Therefore it’s not so hard to determine scattering amplitude. The main purpose of this paper is to show how to determine mathematical formula for differential cross section of jet particles in high energy levels with a hadrons in cluster model ( qq, qq ) ( Quarkonium-Quarkonium cluster) .

The3He(e,e′p)2Hand4He(e,e′p)3Hreactions at high momentum transfer

We present updated calculations for observables in the processes ${}^{3}\text{He}$($e,{e}^{\ensuremath{'}}p$)${}^{2}\text{H}$, ${}^{4}\text{He}$($e,{e}^{\ensuremath{'}}p$)${}^{3}\text{H}$, and ${}^{4}\text{He}$($\stackrel{P\vec}{e},{e}^{\ensuremath{'}}\stackrel{P\vec}{p}\phantom{\rule{0.16em}{0ex}}$)${}^{3}\text{H}$. This update entails the implementation of improved nucleon-nucleon ($NN$) amplitudes to describe final-state interactions (FSI) within a Glauber approximation and includes full spin-isospin dependence in the profile operator. In addition, an optical potential, which has also been updated since previous work, is utilized to treat FSI for the ${}^{4}\text{He}$($e,{e}^{\ensuremath{'}}p$)${}^{3}\text{H}$ and ${}^{4}\text{He}$($\stackrel{P\vec}{e},{e}^{\ensuremath{'}}\stackrel{P\vec}{p}\phantom{\rule{0.16em}{0ex}}$)${}^{3}\text{H}$ reactions. The calculations are compared with experimental data and show good agreement between theory and experiment. Comparisons are made between the various approximations in the Glauber treatment, including model dependence owing to the $NN$ scattering amplitudes, rescattering contributions, and spin dependence. We also analyze the validity of the Glauber approximation at the kinematics the data is available by comparing to the results obtained with the optical potential.

Probing nuclei by deeply penetrating and peripherally interacting Hadron: Bridging low and high-energy processes

The search for signals of new phenomenon is an important trend in the contemporary strong interaction physics. The nuclear J/ψ suppressions are considered as like candidates for the signals of unusual events, e.g. quark-gluon plasma. They were explained in the framework of Glauber approximation. On the contrary, we show that new experimental data on the total cross section of K+-nucleus interaction at intermediate energies cannot be described by the novel well-elaborated Glauber model. This may indicate a unique event in ground state nuclei (in-medium effect).

Modeling neutrino-nucleus interactions in the few-GeV regime

Detecting neutrinos and extracting the information they bring along is an ambitious task that requires a detailed understanding of neutrino-nucleus interactions over a broad energy range. We present calculations for quasi-elastic neutrino-induced nucleon knockout reactions on atomic nuclei and neutrino-induced pion production reactions. In our models, final-state interactions are introduced using a relativistic multiple-scattering Glauber approximation (RMSGA) approach. For interactions at low incoming neutrino energies, long-range correlations are implemented by means of a continuum random phase approximation (CRPA) approach. As neutrinos are the only particles interacting solely by means of the weak interaction, they can reveal information about e.g. the structure of nuclei or the strange quark content of the nucleon that is difficult to obtain otherwise. We investigated these effects and present results for the sensitivity of neutrino interactions to the influence of the nucleon's strange quark sea.

Non-statistical population distributions for hydrogen beams in fusion plasmas

Most atomic models for neutral hydrogen beams in fusion plasmas assume a statistical (Boltzmann) distribution of populations for excited states with the same principal quantum number n. Here we analyze population distributions for the excited magnetic sublevels of a beam under typical conditions of existing and future fusion devices. The collisional–radiative model NOMAD based on completely m-resolved parabolic states up to n = 10 is used to study this problem. The model utilizes new proton-impact excitation data calculated with the atomic-orbital close-coupling method and the Glauber approximation and takes into account electric-field-induced ionization from highly excited states. Our simulations show that the statistical assumption for a specific n is generally not valid for typical fusion conditions due to radiative processes and strong field ionization. The deviation increases considerably for higher beam energies and stronger magnetic fields. The calculated line intensities of σ and π components and beam-emission parameters are discussed in detail.

A non-statistical atomic model for beam emission and motional Stark effect diagnostics in fusion plasmas

In this work we analyze magnetic sublevel populations in a neutral beam penetrating a fusion plasma. The collisional-radiative model NOMAD was extended to include magnetic parabolic sublevels with principal quantum numbers n ≤ 10. The collisional parameters were calculated with the advanced atomic-orbital close coupling method and the Glauber approximation. The ionization by the induced electric field was also included in the model. The results of our calculations show significant deviations of the sublevel populations and, accordingly, line intensities of the σ and π components, from the statistical approximation. It is shown, for instance, that for a number of experimental conditions the total intensity of σ components is not equal to the total intensity of π components, which has a strong effect on determination of magnetic field and pitch angle in fusion devices. The results are presented for a wide range of plasma and beam parameters. The most significant deviations are observed for strong magnetic fields and high beam energies typical for the ITER plasma, where component intensity ratios may deviate by more than 20% from the statistical values.

Fivefold differential cross sections for the ionization of aligned hydrogen molecule by electron and positron impact

We report fivefold differential cross section (5DCS) for the ionization of aligned hydrogen molecule by electron and positron impact in coplanar geometry. The calculations have been performed for an incident energy of 200 eV and ejection energies of (3.5 ± 2.5) and (16 ± 4) eV. The present calculations are based on the eikonal approximation due to Glauber, and the BBK approximation. We have included the effect of post collision interaction (PCI) in the Glauber approximation classically. A comparison is made of the present calculations with the results of other theoretical methods and the recent experiment of Senftleben et al. [ 28]. The present theoretical models predict that the 5DCS is maximum when the intermolecular axis is aligned along the incident beam direction. The binary to recoil peak ratios predicted by the Glauber approximation with PCI (GA-PCI) are in reasonably good agreement with the experiment. The positions of the binary peaks predicted by the BBK approximation are also in good agreement with the experiment. The positron-impact ionization cross sections obtained in the BBK and GA-PCI methods are found to be higher than the electron-impact cross sections in the binary region while the converse is true for the recoil regime. In case of positron impact, the binary peaks predicted by both the GA-PCI and BBK models shifted away from the direction of momentum transfer, and showed a trend which is opposite to the case of electron impact ionization.

Antinucleus–nucleus cross sections implemented in Geant4

Cross sections of antinucleus (p¯, d¯, t¯, He¯3, He¯4) interactions with nuclei in the energy range 100 MeV/c to 1000 GeV/c per antinucleon are calculated in the Glauber approximation which provides good description of all known p¯A cross sections. The results were obtained using a new parameterization of the total and elastic p¯p cross sections. Simple parameterizations of the antinucleus–nucleus cross sections are proposed for use in estimating the efficiency of antinucleus detection and tracking in cosmic rays and accelerator experiments. These parameterizations are implemented in the Geant4 toolkit.

The role of projectile interactions in triply differential cross sections for excitation–ionization of helium

We report triply differential cross section (TDCS) for the simultaneous excitation–ionization of helium by electron impact for both coplanar and non-coplanar geometry. In the coplanar case, calculations have been performed for an incident energy of 500 eV and low ejection energies (3 and 10 eV), whereas in the noncoplanar case we have considered impact energies in the range 1240–4260 eV for a symmetric geometry. The present calculation is based on the eikonal approximation due to Glauber. We have incorporated the effect of post-collision interaction in the Glauber approximation. A comparison is made of the present calculations with the results of other theoretical methods and recent experiments. The Glauber results are in reasonably good agreement with the experiment for small scattering angles.

TOTAL REACTION CROSS SECTIONS OF LIGHT NEUTRON-RICH NUCLEI IN THE GLAUBER APPROXIMATION

We report our recent numerical results of total reaction cross sections of light neutron-rich nuclei, such as carbons and oxygens, in the Glauber approximation to study the exotic structure of neutron-rich unstable nuclei.

Non-statistical populations of magnetic sublevels of hydrogen beam atoms in fusion plasmas

Emission of spectral lines from the excited states of neutral beam atoms in fusion plasmas is the basis of beam emission spectroscopy and motional Stark effect diagnostics. It is well known that the measured intensities of Stark multiplet lines between the n=3 and 2 excited states of hydrogen systematically deviate from the full statistical model. Here we study the H α Stark component intensities using a newly developed collisional-radiative model that is based on the description of magnetic sublevels in a parabolic basis. Proton excitation cross-sections between the parabolic states are calculated in the Glauber (eikonal) approximation. The model incorporates various collisional processes between the hydrogen beam atoms and plasma particles (protons, impurity ions and electrons) as well as the radiative processes. The simulated line component ratios σ 1 / σ 0 , π 2 / π 3 and π 4 / π 3 are found to agree with the measured ratios from JET plasmas within the experimental uncertainties.

Medium effects on intermediate-energy one-nucleon removal cross sections

The influence of Pauli-blocking medium effects on intermediate-energy one-nucleon removal cross sections for $\mathit{sd}$-shell nuclei have been investigated using density-dependent nucleon-nucleon interaction cross sections within the $S$-matrix formalism under the Glauber approximation. All considered prescriptions for the density dependence result in a reduction of the one-nucleon removal cross sections. The effect is smaller than 20% for incident energies between 50 and 100 MeV/nucleon, and smaller than a few percent above 200 MeV/nucleon.