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).     

Scattering from nonoverlapping potentials II. Extension and comparison with glauber multiple scattering theory for deuterium

Scattering on a two-body nuclear target is considered in the nonoverlapping potentials model. The double scattering terms are discussed and it is suggested that their off-shell propagation part is not cancelled by higher-order terms of the multiple scattering series. The effect of reflections is discussed and practical ways to sum up their effect are offered. Finally, spin degrees of freedom are introduced within the nonoverlap formalism.     

Off-shell effects in scattering from the deuteron

A simple model for scattering from a deuteron is studied. Within this model exact coupled channel solutions, including all multiple scattering series terms, are obtained for a fixed separation of the two scattering potentials. These solutions are compared with approximations which involve a spherically averaged or non-overlapping potential. Our results indicate that the non-negligible contributions arising from the overlapping potential region can be adequately reproduced by a combination of simple approximations thereby facilitating calculations of scattering from a more physical deuteron model.     

Higher-order QCD corrections to exclusive processes: The multiple scattering mechanism

The multiple-scattering diagram, calculated to lowest order in QCD, fits well topp elastic scattering data at larget. It is shown that higherorder QCD corrections seem to spoil this agreement: calculated as far as the insertion of two additional gluons, they give an exponential factor. This factor differs in detail from some previous conjectures. For colour-singlet bound states of quarks, the exponential factor is independent of whether or not the gluon mass is zero, unlike the case of simple quark-quark scatterin. Two régimes are considered:t ands of the same order, andt large but much less thans. Exponentiation seems to occur in both cases, but in a non-abelian theory more diagrams are important for the latter case.     

On the theory of multiple scattering

In this paper a kinetic equation is derived for the distribution function in the variable q=2 sin(ϑ/2) for the case of a scattering cross section of general form under the assumption that the region of multiple scattering (the diffusion region) is small. The limits of the kinetic equation are discussed, with no restrictions imposed on the scattering angles. It is found that the equation has a solution in the form of an integral. Finally, it is established that the solution is applicable over the entire range of angles, from 0 to 180°. Zh. éksp. Teor. Fiz. 116, 418–435 (August 1999)     

Radiative corrections to the Bhabha scattering

In this review we consider the high energy processes in QED frames in peripherical kinematics. The key feature of this kinematics is that processes have a large cross section which do not decrease with the increasing of the initial center of mass energy. Two purposes to study peripheral processes are: the background processes with large total cross sections and the structure of jets in the fragmentation region.     

Off-shell πN scattering near the Δ resonance

A parameter-free form factor for virtual πN scattering near the Δ resonance is derived. It depends only on s and m²_N ?P²_N, not on P²_π.     

Two-loop corrections to Bhabha scattering

The two-loop radiative photonic corrections to Bhabha scattering are computed in the leading order of the small electron mass expansion up to the nonlogarithmic term. After including the soft photon bremsstrahlung, we obtain the infrared-finite result for the differential cross section, which can directly be applied to a precise luminosity determination of the present and future e+ e- colliders.     

On the theory of multiple scattering I

A systematic theory of multiple scattering is given for a nonpolar fluid of point dipoles. Local-field correction factors are consistently accounted for to all orders. To first order (single scattering) Einstein's result is obtained; the theory yields, however, automatically to this order the attenuation of the incoming beam before and of the scattered light after scattering. In the usual theories these effects are hidden in secular (shadow) contributions to multiple scattering. The single-triple and double-scattering intensities are briefly discussed.     

On the theory of multiple scattering II. Critical scattering

The systematic theory of multiple scattering which we gave in a previous paper is further elaborated for critical scattering. It is shown that in each order the multiple-scattering intensity near the critical point is in essence a contraction of consecutive uncorrelated single-scattering intensities. The anomaly of the critical depolarization factor is calculated and is found to be in quantitative agreement with recent experimental results. Double scattering corrections to the Ornstein-Zernike plot are discussed.     

The multiple scattering and N-body approaches to nuclear reactions

The relationship between conventional multiple scattering approaches and the recently developed N-body approaches to nuclear reactions is considered with a view towards elastic scattering applications. Connectivity expansions in the N-body approach and multiple scattering expansions in the Watson approach are developed by a common technique so that a comparison of the physical content of each can be made. In the N-body case this leads to a new derivation of the equations of Bencze, Redish, and Sloan in both particle-labelled and partition-labelled form and this yields new insight into the minimal dimensionality of these equations and into the role of channel coupling schemes within this formulation. The relative simplicity and generality with which these results are obtained is designed to be easily understood by those unfamiliar with N-body formalisms. The two approaches are contrasted first for the three-particle problem and subsequently for the many-body problem. We argue that a strict adherence to the connected-kernel property which is advantageous for the three-particle problem may not be so advantageous for the many-body elastic scattering problem. Undesirable physical characteristics of the connectivity expansion for elastic scattering are identified and their rectification is discussed. The off-shell transformation associated with the N-body approach is examined critically. The origin of the multiplicity of N-body coupling schemes is elucidated. It is shown that a modified concept of connectivity, called inclusive connectivity, can be introduced to guide expansions which can be truncated in a physically meaningful way. The inclusive connectivity expansion is seen to be identical to the spectator expansion for an elementary projectile but differs in the case of a composite projectile. Extant elastic scattering optical potential formulations based on the two concepts of connectivity are compared and contrasted. We show that connected kernel integral equations of the few-body type are required for computation of the individual low-order terms of the inclusive connectivity expansion of the optical potential.     

Proton-nucleus elastic scattering at 1 GeV in the glauber model

Differential elastic cross sections and polarizations are calculated in a multiple-scattering formalism for proton-nucleus scattering at 1 GeV incident energy. The calculations include Coulomb and spin effects. Corrections to the Glauber model are studied. It is shown that for momentum transfer up to 2.0–2.5 fm^?1 the reaction mechanism can be taken with confidence. Consequently, fits to the experimental data over this limited range in q can be considered to extract nuclear structure information. In the present case, use has been made of nuclear densities arising from self-consistent calculations. The calculations are compared with experimental data.     

Off-shell states in dual resonance theory

We discuss ooff-shell states guided by an analogue model approach. This leads us to a more complete understanding of a model proposed recently by Schwarz with critical dimension 16. We are led, by algebraic considerations, to off-shell states in the Neveu- Schwarz-Ramond model, which obey the gauge conditions in the same critical dimension as the on-shell theory, the amplitudes factorizing on the usual positive definite states in 10 dimensions. Brief calculations reveal that some of the divergences present in the orbital model disappear in the fermion theory.     

Some corrections to the Thomas-Fermi theory

In the presented model the wave function describing the electron is a superposition of contributions from individual components of the system, in the case of metals - lattice ions and in this sense refers not to a single electron, but rather to the system as a whole. An unconventional approach to the Schro¨dinger equation can provide a simple analytical relationship between the total energy of the electron and the wave number. This expression can directly determine the basic parameters such as Fermi radius, the screening radius or work function and also produce a graphical interpretation of the Fermi surface.     

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.     

Radiative corrections to high-energy neutrino scattering

Motivated by precise neutrino experiments, we reconsider the electromagnetic radiative corrections to the data. We investigate the usefulness and demonstrate the simplicity of the “leading log” approximation: the calculation to order α ln (Q/μ), α ln (Q/m_q). Here Q is an energy scale of the overall process, μ is the lepton mass and m_q is a hadronic mass, the effective quark mass in a parton model. We identify those questions the answers to which do not depend on unknown hadron parameters like quark masses. The leading log radiative corrections to dδ/dy distributions and to suitably interpreted dδ/dx distributions are quark-mass independent. We improve upon the conventional leading log approximation and compute explicitly the largest terms that lie beyond the leading log level. In practice this means that our model-independent formulae, though approximate, are likely to be excellent estimates everywhere except at low energy or very large y. We point out that radiative corrections to measurements of deviations from the Callan-Gross relation and to measurements of the “sea” constituency of nucleons are gigantic. The QCD inspired study of deviations from scaling is of particular interest. We compute, beyond the leading log level, the radiative corrections to the QCD predictions.     

Radiative corrections to pion nucleus scattering

The radiative corrections to elastic pion-nucleus scattering are evaluated for kinematical conditions pertaining to the pion spectrometer facilities at the newer meson factories, and are found to be experimentally relevant. A reasonably simple, experimentally useful approximation to the exact expression for the radiative correction is given.     

Analytical multiple scattering extension of the mie theory

Multiple scattering of light in aerosol is described in a simple picture within the framework of the Mie theory. Our approach leads to an analytical expression of the n-fold scattered electromagnetic field and then to a generalization of the optical parameters. The multiple scattering contributions are calculated avoiding the convergency and stability problems which are often encountered in standard numerical approaches. These problems occur due to the large number of events that have to be taken into account when large optical depths and/or a low signal to noise level exists. Such conditions are frequently encountered in atmospheric measurements.