Eikonal expansion in electron scattering

We extend a previously developed eikonal expansion method to the case of high-energy electron scattering from dynamic nuclei. Nuclear degrees of freedom can be included either by a DWBA-like expansion or by neglecting the nuclear excitation energies. The latter approach is considered in detail and applied to the elastic and inelastic scattering from deformed nuclei. The impact parameterT-matrix is calculated by diagonalizing the inelastic zeroth-order and first-order eikonal phases in the subspace of the nuclear rotational levels; static eikonal phases are included up to second order. For¹⁵²Sm,¹⁵⁴Sm coupled-channel calculations including three and four rotational states show large multi-step effects for the 0⁺→4⁺ and the 0⁺→6⁺ excitations compared to DWBA results.     

Multi-step processes in high-energy elastic and inelastic nuclear scattering

Multi-step processes in elastic and inelastic nuclear scattering at intermediate and high energies are investigated using a formulation whereby a finite number of channels are explicitly treated while all the other channels are approximately accounted for through a “second-order potential matrix”. Within the framework of the eikonal approximation the problem reduces to a finite system of first-order coupled integro-differential equations with non-local potentials which depend on the two-body density matrix of the target nucleus. The relationship of the above formulation to the DWIA, the close-coupling method, and the Glauber multiple scattering model is examined. This approach is applied to the elastic and inelastic (2⁺, 4.43 MeV) scattering of 1 GeV nucleons by ¹²C. The corrections to the DWIA are sizeable, and the inelastic scattering appears to be very sensitive to the multi-step contributions and the nuclear structure.     

Pion-Rotational Nucleus Scattering and the Interacting Boson Model

A procedure of combining the medium energy scattering theory in the eikonal approximation with the interacting boson model (IBM) is proposed to study the pion-rotational nucleus scattering. The channel coupling effects in the excitation of nuclear collective state with π^- and π⁺ elastic and inelastic scattering are analyzed. The calculated cross sections for the excitation of 2₁⁺ state of ¹⁵²Sm agmree with the experimental data quite well.     

Eikonal theory of electron- and positron-atom collisions

We review recent developments in the application of eikonal methods to the field of electron and positron collisions with atoms. The foundations of the eikonal approximation are first analyzed within the framework of potential scattering, with particular attention to those aspects of the theory which can be generalized to atomic collision processes. We next discuss various many-body applications of the eikonal method, namely: the Glauber approximation, the eikonal-Born series method, optical model theories, the eikonal distorted wave method and the multistate eikonal approximation. We also analyze eikonal exchange amplitudes. Applications of these methods are then considered, first for the case of elastic scattering and then for various inelastic processes.     

Eikonal description of quantal scattering

Elastic and inelastic quantal scattering is described by a theory in which the contribution of a range of impact parameters to the scattering amplitude is determined by a phase integral (“eikonal”) which is integrated along a real curved “quantal” trajectory. This amplitude reduces to the Glauber expression in the high-energy, forward-angle limit, and to the usual semiclassical amplitude in the classical limit. The formulation can be applied to the study of heavy-ion scattering. The quantal trajectories are investigated analytically for the case of Coulomb scattering. A numerical analysis of elastic ¹⁶O¹⁶O scattering is carried out. The results show appreciable improvement as compared with the Glauber approximation.     

Long-range Coulomb forces in DIS: missed radiative corrections?

The Born approximation, one photon exchange, used for DIS (deep inelastic scattering) is subject to virtual radiative corrections which are related to the long-range Coulomb forces. They may be sizeable for heavy nuclei since Zα is not a small parameter. So far, these corrections are known only for two processes, elastic scattering and bremsstrahlung on the Coulomb field of a point-like target. While the former amplitude acquires only a phase, in the latter case also the cross-section is modified. Although the problem of Coulomb corrections for DIS on nuclei is extremely difficult, it should be challenged rather than “swept under the carpet”. The importance of these radiative corrections is questioned in the present paper. We show that, in the simplest case of a constant hadronic current, the Coulomb corrections provide a phase to the Born amplitude, therefore the cross-section remains the same. Inclusion of more realistic hadronic dynamics changes this conclusion. The example of coherent production of vector mesons off nuclei reveals large effects. So far a little progress has been made deriving lepton wave functions in the Coulomb field of an extended target. Employing available results based on the first-order approximation in Zα, we conclude that the Coulomb corrections are still important for heavy nuclei. We also consider an alternative approach for extended nuclear targets, the eikonal approximation, which we demonstrate to reproduce the known exact results for Coulomb corrections. Calculating electroproduction of vector mesons, we again arrive at a large deviation from the Born approximation. We conclude that one should accept with caution the experimental results for nuclear effects in DIS based on analyses done in the Born approximation. Received: 16 May 2001 / Accepted: 4 July 2001     

Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of ¹⁷O from a series of nuclei with excitation of the 2⁺ level.     

Heavy-ion inelastic scattering from deformed nuclei

Theoretical and experimental methods for studying heavy-ion inelastic scattering from deformed nuclei are described. The theoretical methods involve classical-limit approximations, while particle- γ-spectroseopy techniques are employed experimentally. With these approaches, heavy-ion excitation in the Coulomb-nuclear interference region acquires a transparent interpretation, despite the apparent complexity of the multistep excitation processes involved. The examples discussed provide a good illustration of the relationship between classical and quantum physics. The sensitivity of the inelastic scattering to details of the surface ion-ion potential due to radial and angular localization is exploited to provide a method of determining the equipotential contours in a direct manner which bypasses particular model-dependent parametrizations. The method is used to construct ion-ion potentials from inelastic scattering data for the systems ⁴⁰Ar + ¹⁶⁰Gd, ¹⁵⁶Gd, ¹⁶²Dy, ¹⁶⁴Dy, and¹⁸⁰Hf. The contribution of adiabatic giant resonance polarization to this potential is discussed. The relation between the deformed ion-ion potential and nuclear shapes is illustrated by comparing the experimental potentials to deformed double-folding and deformed proximity-potential calculations.     

Nuclear shadowing and heavy-ion collisions at high energies

Nuclear shadowing effects for quarks and gluons are calculated using information on diffractive deep inelastic scattering on a nucleon. Role of these effects in interactions of hadrons and nuclei with nuclei at high energies is investigated. A decrease in particle densities for heavy-ion collisions in comparison with the Glauber model is predicted and nuclear modification factors are calculated. Distributions of gluons in nuclei are used to predict suppression of heavy quarkonia. The parameter-free calculation of J/ψ in DAu and AuAu collisions is in a good agreement with recent RHIC data. Predictions for heavy quarkonia suppression in heavy-ion collisions at LHC are formulated.     

Virtual nuclear excitation corrections to elastic electron scattering from 40Ca

The virtual nuclear excitation (dispersion) corrections to elastic electron scattering from ⁴⁰Ca have been calculated in second-order Born approximation. A model that can reproduce the whole inelastic response surface is employed for the nuclear currents that enter. The dispersion correction, expressed relative to the first Born result, is dependent only on the nuclear Fermi momentum. When the intermediate nuclear states are summed (without using closure) through the quasi-elastic scattering region, the corrections are found to be small (about 3%). However, these should be included in analyzing future data with better experimental accuracy. For the first time, the effect of isobar excitation on the dispersion correction has been examined; because of the questionable validity of the approximations in this case, no definite conclusion can be drawn.     

A study of proton-12C inelastic scattering at 1 GeV

The inelastic scattering of protons on ¹²C is investigated on the basis of the first order term of the multiple scattering expansion of Kerman, McManus, and Thaler. The spin degrees of freedom are taken into account. The inelastic transitions to the three lowest excited states of the target are studied within the distorted wave impulse approximation, the distortion being evaluated using an eikonal approximation. The elementary nuleon-nucleon high-energy interaction employed contains a simplified but realistic spin dependence. Special emphasis is placed on the influence of the small-angle approximation, the effect of spin, and the sensitivity to different nuclear transition densities.     

用高能核子非弹性散射研究核力有效势

本文用扭曲波玻恩近似法及多体高能近似法,处理了原子核对高能核子的非弹性散射现象。在具有可靠的靶核激发态波函数的情况下,可利用这些理论处理方法研究核内两核子间的有效势,本文具体就碳核对185MeV入射核子的非弹性散射进行了计算。在计算中利用了粒子-空穴模型核波函数。在采用了具有各种交换性质并包含自旋轨道耦合项的有效势后,用一组合理的位阱参数,由多体高能近似法计算的理论值可与几个微分截面及极化实验曲线同时符合。     

Coulomb scattering in the eikonal approximation

We derive a new expression for the eikonal approximation of the nuclear Coulomb scattering amplitude. Our expression should be particularly useful for the treatment of Coulomb scattering in hadron-nucleus and nucleus-nucleus scattering at high and intermediate energies.     

Role of nuclear couplings in the inelastic excitation of weakly bound neutron-rich nuclei

We study the breakup of weakly bound systems close to the neutron drip line in collisions with heavy-ions. The process is described in terms of inelastic excitations leading to states in the continuum. The nuclear and Coulomb multipole fields induced by the reaction partner are both included in the microscopic construction of the inelastic form factors. A fraction of the dissociation cross sections is triggered by the presence of resonances at high excitation energy. The largest probabilities for breakup result, however, from strongly coupled transitions to low-lying states in the continuum. Nuclear couplings associated with inelastic excitation to these states are found to extend to unusually large distances. As a consequence, the interplay of nuclear and Coulomb excitations differs from the ordinary situation encountered in heavy-ion inelastic processes involving systems close to the stability line.     

Surface green function matching approach to the surface dynamics of ionic crystals: II. Theoretical analysis of the inelastic scattering of He from NaF(001) in the eikonal approximation

A theoretical analysis of recent scattering time of flight (TOF) data for NaF(001)/He is done by means of a new version of the eikonal approximation to the inelastic processes, which allows for the use of atom-surface potentials obtained by summing over two-body potentials. A Morse potential for He-ion interactions is adopted in the present work. A good agreement between theory and experiment is found with the present scheme.     

Excitation of nuclear collective states by heavy ions within the model of semimicroscopic optical potential

The (semi)microscopic double-folding nucleus-nucleus optical potentials are suggested for consideration of inelastic scattering with excitation of collective nuclear states by using the adiabatic approach and the elastic scattering amplitude in the high-energy approximation. The analytical expression for inelastic scattering amplitude is obtained keeping the first-order terms in the deformation parameter of a potential. Calculations of inelastic cross sections for the ¹⁷O heavy ions scattered on different nuclei at about hundred MeV/nucleon are made, and the acceptable qualitative agreement with the experimental data is obtained without introducing free parameters. The prospect of the method for further applications is discussed. The text was submitted by the authors in English.     

Large-angle scattering of heavy ions: (II). General structure of inelastic cross section

Closed-form expressions are derived for the differential cross section of inelastic heavy-ion scattering at large angles. The inelastic transition amplitude given by the distorted-waves theory for excitation of low-lying collective states is evaluated by an extension of analytic methods developed in the preceding paper for elastic large-angle scattering. The very close relation between the inelastic and elastic cross sections is displayed. In particular it is shown that the angular distributions have a universal form, and that the backward-angle inelastic excitation function has, aside from a slowly varying overall energy dependence, an oscillatory gross structure of diffractive origin which is nearly identical to that of the elastic excitation function, irrespective of the physical mechanism involved.