Eikonal and Fresnel corrections to the Glauber theory of nuclear multiple scattering

Starting from a Watson-type multiple scattering series we study first-order corrections to the Glauber high-energy collision model. These are obtained by replacing the free-space Green function between successive scatterings by the second-order eikonal propagator. We distinguish between Fresnel corrections and eikonal-type corrections. Due to large cancellation effects the eikonal contribution is very small compared to the Fresnel contribution. First-order corrections to Glauber theory are calculated explicitly for high-energy elastic scattering of protons from light nuclei (⁴He, ¹²C, ¹⁶O).     

Corrections to Weinberg's pion-pion scattering lengths

We derive twice subtracted dispersion sum rules for theππ scattering lengths. The subtraction constants are the Weinberg values, and the dispersion integrals yield small corrections in good agreement with other authors.     

Glauber exchange amplitudes for electron-helium scattering

An exact closed form expression is obtained for the Glauber-Bonham-Ochkur exchange amplitudes for the electron helium scattering. The results thus obtained are compared with the results from Ochkur approximation and are used further for obtaining closed form expressions for the differential and total exchange cross-sections for the elastic scattering of electrons from the ground state of helium atom.     

Implications of the Glauber model for inelastic hadron-nucleus scattering

The Glauber model for elastic hadron-nucleus scattering is extended to inelastic processes by supplementing it with the Abramovskii, Gribov, Kancheli cutting rules. Inelastic screening due to low mass states is also included. The results can be interpreted in terms of the probabilistic multiple collision model. The mutual relationship of the two approaches is discussed.     

Dispersion relations and Glauber model for pion-deuteron scattering

Forward dispersion relations are used to calculate the real part of the elastic amplitude for forward pion-deuteron scattering. The same real part is also calculated from the Galuber multiple scattering model. The results of the two approaches are critically compared in the light of present experiments. A theoretically deduced value for the pion-deuteron scattering length is also given. A theoretical prediction for the pion-deuteron total cross section for energies below 450 MeV is found to agree rather well with experiments.     

Corrections to angular ordering in multiple hadroproduction

One of the key ideas in describing the multiparticle production at high energies in the perturbative QCD is the angular ordering in successive soft-gluon emission. We analyse the angular distribution of particles in a jet, and investigate the corrections to the angular ordering. At a small angle from the jet direction, the angular ordering is exact at the next-to-leading order. At a large angle, the angular ordering overestimates the angular particle density by a factor (1?γln cos²(γ/2)), whereγ is the anomalous dimension of the multiplicity. TheO(γ) correction restores the boost invariance of the cross section.     

Glauber theory of high-energy p-He scattering with composite nucleons

We analyze some recent experimental data on p-He high energy elastic scattering by means of Glauber's multiple-scattering theory.By taking explicitly into account the composite structure of hadrons, we eliminate some discrepancies between the theory and the data that were recently pointed out.We comment on the consistency of the multiple scattering analysis of elastic and inelastic data with the hypothesis of an increase of size of bound nucleons as compared to free ones.     

Electron-hydrogen scattering in a modified Glauber theory with exchange

We analyze the elastic scattering of e-H with the modified Glauber amplitude recently proposed by us and with the Glauber exchange effect included through the formula by Foster and Williamson [1]. The results are found in very good agreement with experimental data.     

Test of the Glauber formula for nucleon-deuteron scattering at intermediate energies

A high-precision test of the Glauber formula for the amplitude of nucleon-deuteron scattering is performed. Nucleon-nucleon amplitudes used in the calculations depend on the spins of interacting particles, phase shifts, and mixing parameters. These amplitudes were derived by using the Njim I, Njim II, Njim 93, and Reid 93 realistic potentials. The differential cross sections for nucleon-deuteron scattering were calculated for the projectile-nucleon energies of 65, 95, 135, 150, 190, and 250 MeV, and the results of these calculations were compared with experimental data.     

Method for calculating the complete expansion of the Glauber amplitude for nucleus-nucleus scattering

A method for calculating the complete expansion of the Glauber amplitude for nucleus-nucleus scattering processes is proposed. An example of the calculation of the elastic differential cross section is given as an illustration.     

Multiple scattering of heavy ions,Glauber theory,and optical model

An exact multiple-scattering series for the scattering of two heavy ions is derived and compared to the Glauber approximation. An optical model potential operator is indicated which is an accurate approximation to the multiple-scattering formalism.     

Corrections to eikonal models for hadron-nucleus scattering at high and intermediate energies

Corrections to eikonal amplitudes for hadron-nucleus scattering are calculated for realistic optical potentials at medium and high energies. The corrections, involving only one-dimensional integrals, are found to provide rapid convergence towards the exact results. In contrast to the lowest-order eikonal approximation, the corrections lead to a sensitivity of the calculated cross section to the sign of the real part of the optical potential.     

Wave scattering functions and their application to multiple scattering problems

Scattering functions arise naturally in standard treatments of the effects of a material object or surface embedded in a uniform field. The most commonly used scattering function describes the far-field modulation imparted at large distances to a spherical wavefront eminating from the scatterer. The purpose of this is to develop the properties of the spectrum of scattered plane waves as an exact generalized scattering function. The linearity of the wave equations guarantees that such a representation exists; moreover, it is possible to derive the generalized scattering function from the far-field scattering function by analytic continuation. Although these properties are known, recent theoretical developments have motivated us to reexplore the interrelations among the far-field scattering function, the Green's function and various forms of the generalized scattering function as well as the symmetry properties of the generalized scattering function imposed by reciprocity. For multiple-scattering objects that can be separated by parallel planes, a system of difference equations is developed that fully accommodates the mutual interaction among the scatterers. The mutual interaction equations were developed earlier, but we show here that they can be transformed into the form that would be obtained by using the Foldy-Lax-Twersky formalism. This reinforces the equivalence between wave-space and configuration space formulations of the scattering problems.     

Symmetrization of the Glauber amplitude in the rigid nucleus approximation for nucleus-nucleus scattering at high energies

The virtual excitations in the elastic nucleus-nucleus scattering at high energies being taken into the account, a symmetrization of the Glauber amplitude is achieved in the framework of the rigid nucleus approximation. The differential and total cross section obtained at different energies in this symmetric amplitude approximation are compared with experimental data and with results obtained through other models.     

Defect of total nuclear scattering cross sections: Fifty years of the Glauber diffraction theory

In this mini survey, a historical excursus into theoretical investigations on the diffraction theory of fundamental nuclear processes, the origins of which go back to work by Glauber (1955), is presented with an emphasis on recent achievements in the field.     

Deuteron-deuteron scattering at 1.65, 2.00 AND 2.29 GeV: Theoretical interpretation in the Glauber model

An analysis of deuteron-deuteron scattering data at T₀= 1.65, 2.00 and 2.29 GeV is given in the framework of the Glauber NN multiple-scattering model. The model accounts qualitatively well for the larger momentum transfer data. The model cannot reproduce the observed experimental bump at small transfer in the region of missing mass $\text{2 GeV}\text{c}{}^2$, because pionic processes have not been considered. Nevertheless, it shows that the nucleon background is important.