Multiple scattering with a linearized propagator

Scattering by a many-body system is studied within the framework of the “fixed scatterer” approximation and the eikonal approximation formulated in terms of a linearized propagator. If properly treated, the “fixed scatterer” approximation is able to take into account the center-of-mass motion. We specifically study the linearized propagator proposed by Abarbanel and Itzykson. Although for potential scattering the above approximation is essentially equivalent to the Glauber eikonal approximation, its physical implications are quite different when applied to scattering by a composite system. The multiple-scattering series can generally no longer be simply expressed in terms of the individual on-shell scattering amplitudes, and the additivity of phase shifts is shown to break down for overlapping potentials. The implications for phenomenological calculations are discussed. Finally, the above approximation is explicitly applied to high-energy elastic nucleon-deuteron scattering and the results are compared with several variants of the Glauber multiple-scattering formalism.     

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.     

Correlations in alpha-alpha scattering and semi-classical optical models

We show the equivalence of semi-classical solutions to optical model coupled-channel equations derived from Watson's form of the nucleus-nucleus multiple-scattering series to the Glauber multiple-scattering series. A second-order solution to the semi-classical coupled-channel elastic amplitude is shown to be nearly equivalent to a second-order optical-phase-shift approximation to the Glauber amplitude if the densities of all nuclear excited states are approximated by the ground-state density. Using the Jastrow method to model the two-body density we find an average excited-state density to be of negligible importance in the double-scattering region of alpha-alpha scattering.     

Scattering from non-overlapping potentials. I. General formulation

The problem of scattering from an assembly of non-overlapping spherical potentials is solved in partial-wave basis for each of the constituent potentials. The resulting scattering operator is a quotient of two infinite matrices and depends on “on-shell” partial wave amplitudes of the individual potentials. It suggests in general a truncation scheme which essentially considers only those partial waves effective for each collision at the given energy. The multiple-scattering series is recovered and limiting cases of low energy and high energy are considered. Applications to high-energy scattering of elementary particles on nuclei are briefly discussed.     

Inelastic intermediate states in proton-deuteron and deuteron-deuteron elastic collisions at the ISR

We present experimental results on proton-deuteron and deuteron-deuteron elastic scattering measured at the two highest ISR energies, √s = 53 GeV and √s = 63 GeV. The data cover the single- and multiple-scattering regions over a wide interval of four-momentum transfer t. In both reactions we find clear evidence for a substantial t-dependent contribution of inelastic intermediate states in the multiple-scattering region, as well as in single scattering. In the analysis we use the Glauber multiple-scattering theory extended to include inelastic shadow effects. This extension of the basic theory contains as input a triple-Regge parametrization describing the high-mass inclusive spectrum. The analysis of inelastic corrections to multiple scattering on deuterons at high energies is shown to provide a sensitive test of different parametrization of inclusive production in proton-proton collisions.     

Effect of the shell structure of nuclei on p 15C and p 15N scattering within diffraction theory

The differential cross sections for elastic proton scattering on ¹⁵C and ¹⁵N nuclei at energies of 150 and 800 MeV were calculated within the diffraction theory of Glauber multiple scattering. Shellmodel wave functions were used in these calculations, and particular attention was given to analyzing the sensitivity of the calculated features to distinctions between the shell structure of the ¹⁵C nucleus and the shell structure of the ¹⁵N nucleus. The calculations were performed in the approximation of double scattering. The multiple-scattering operator was written in a form that permits taking into account collisions with nucleons belonging to different shells. It is shown that the difference in structure between the two nuclei in question leads to substantial distinctions between the differential cross sections for scattering at an energy of 800 MeV and scattering angles larger than 25°.     

Comparative analysis of proton and pion scattering on the isotopes <Superscript>6,8</Superscript>Не within Glauber theory

The differential cross sections for p^6,8He and p^6,8He scattering at the RIKEN andGSI energies (0.073 and 0.7 GeV per nucleon) were calculated on the basis of Glauber theory. Pion and proton interaction with a nucleus is determined by the multiple-scattering series (Glauber operator), so that various collision multiplicities and their contributions to the summed cross section can be taken into account. The use of the α-n-n wave function for ⁶He and the wave function on the basis of the large-scale shell model (LSSM) for ⁸He makes it possible to calculate analytically scattering matrix elements.     

Multiple scattering, optical potential, and N-body approaches to elastic two-fragment collisions

Two-fragment elastic scattering problems are often studied using multiple scattering theories such as those due to Watson along with Feshbach-type optical potentials. These conventional methods are re-examined, rephased, and generalized using the language and techniques of contemporary N-particle scattering theory. A special realization of the latter theory is developed which is especially useful for relating the older and newer methods. This is facilitated by maintaining the same off-shell continuations of the scattering operators in both approaches. In particular, a set of connected-kernel scattering integral equations is introduced which provides a consistent N-particle framework for the calculation of that definition of the optical potential possessing the Feshbach off-shell continuation. These equations exhibit a multiple-scattering substructure and therefore allow the systematic generalization of some of the usual low-order approximations.     

The Extraction of Neutron Target Cross Sections from Reactions on Deuterium

The theory of scattering and production reactions on deuterium is developed with a view to the extraction of neutron target amplitudes from analysis of deuterium experiments. Corrections to the spectator model due to the following effects are examined: target particle binding corrections to the Impulse Approximation; (ii) the Pauli principle in charge exchange reactions; (iii) internal or „Fermi”︁ motion of the target particles; (iv) multiple scattering and final state interactions. The closure approximation and the general analysis of single-arm spectrometer experiments are discussed. The connection at high energies and small momentum transfers between the general Watson Theory and the Glauber model is established, and the results of calculations of deuterium corrections for pion and rho photoproduction at high energies are reviewed. “Fresnel” and recoil corrections to Glauber theory are examined. An approximation scheme suitable to the analysis of high energy wide angle coincidence or bubble chamber experiments is developed. A special examination is made of the breakdown of the impulse approximation in the 3-3 resonance region, and of the applicability of lowest order binding and in multiple scattering corrections in this sensitive kinematical region.     

Structure of 6Li from high-energy proton scattering

The elastic and inelastic (2.189 MeV level) scattering of 1 GeV protons from ⁶Li is predicted using Glauber multiple-scattering theory in conjunction with an α-d cluster model capable of fitting quantitatively a large number of measured form factors, in particular the most recent high-momentum-transfer electron scattering data. The predictions, especially in the inelastic channel, are quite sensitive to the parameters of the model. A valuable opportunity is thus provided via experiments well within the capabilities of LAMPF for comparison of structure information obtained from proton scattering with that from other sources in the case of a “test” nucleus whose properties are relatively well determined and unambiguous. Moreover, proton scattering goes beyond electron scattering in possibly providing information about the effective real part of the proton-deuteron cluster amplitude, and thus indirectly about D-state effects in the deuteron cluster.     

Recursion relations and scattering amplitudes in the light-front formalism

The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends–Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.     

Glauber gluon effects in soft collinear factorization

Effects of Glauber gluons, which cause the elastic scattering process between different jets, are studied in the frame of soft-collinear effective theory. Glauber modes are added into the action before being integrated out, which is helpful in studies on the Glauber couplings of collinear and soft particles. It is proved that the final state interactions cancel out for processes inclusive enough. So are interactions with the light cone coordinates x⁺ and x⁻ greater than those of the hard collision. The eikonalization of Glauber couplings of active particles and absorption of these couplings into soft and collinear Wilson lines are discussed, which is related to the loop level definitions of Glauber gluons here. The active-spectator coherence is proved to be harmless to the inclusive summation of spectator-spectator and spectator-soft Glauber exchanges. Based on this result, spectator-spectator and spectator-soft Glauber exchanges cancel out in the processes considered here. Graphic aspects of the cancellation are also discussed to explain relations between the graphic and operator level cancellation of Glauber gluons.     

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).     

随机介质中的矢量辐射传输理论

本文讨论了极化电磁波在随机介质中多次散射,传输和热辐射的斯托克斯矢量的辐射传输理论。其中包括随机分布离散的球形和非球形粒子的矢量辐射传输方程,离散坐标-特征分析法,付利叶变换,迭代法等数值解。讨论了非球形粒子的穆勒矩阵。并研究了密集分布的散射粒子介质的辐射传输理论,考虑了密集粒子散射的相干性,计算了有效传播常数。理论及数值结果与实验作了很好的比较。     

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.     

Theoretical and experimental study of blurring of a femtosecond laser pulse in a turbid medium

We propose an analytical model of the spatio-temporal structure of a short laser pulse transmitted through a layer of an optically inhomogeneous medium with high anisotropy of scattering. The light-field brightness in the medium is represented as a finite series in terms of multiplicities of the small-angle scattering, while the contribution from the higher-order scattering is allowed for as a quasi-diffuse component. The scattered-pulse structure is calculated on the basis of solving the radiative-transfer equation in the small-angle approximation with allowance for the effect of multipath light propagation. Compared with the first approximation of the multiple-scattering theory (attenuated nonscattered light plus the diffuse component), this approach makes it possible to describe more correctly the transformation of the spatio-angular distribution of light in the medium when passing from the single-scattering to multiple-scattering regime, as well as specify the temporal profile of the scattered pulse. The temporal profile of the femtosecond pulse transmitted through a layer of model scattering medium with various concentrations of scatterers is studied experimentally. The blurred-pulse structure is studied with the help of nonlinear optical gating in the case of noncollinear generation of the second harmonic. Good agreement between the theoretical and experimental time profiles of the scattered pulse is shown for the optical-thickness intervals corresponding to both the predominantly low multiplicity scattering and multiple small-angle scattering, which allows us to use the proposed analytical model for solving the inverse problem of the pulse sounding of a homogeneous turbid medium. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 333–348, April 2008.     

Elastic scattering via quark structure of nucleons

In the framework of the Glauber multiple-scattering theory, the elastic collisions of proton-proton (pp) at the center-of-mass energies = 23.5, 30.7, 44.7, and 52.8 GeV and alpha-proton (p) at = 88 and 89 GeV are analyzed by considering the quark structure of their constituents. The differential cross-section containing the full multiple-scattering series between their quarks is calculated using Gaussian forms for the quark density and quark-quark (QQ) scattering amplitudes. The results obtained from the quark model and the conventional nucleon model are compared with the experimental data. The comparison shows that the nucleon model reproduces the experimental data more satisfactorily than the quark model, and both approaches have limited success in describing the data at such energies. The agreement with the experimental data is improved by the inclusion of the phase variation.     

Analysis of <Emphasis Type="Italic">p</Emphasis><Superscript>10</Superscript>B scattering within Glauber theory

The differential cross sections for p ¹⁰B scattering are calculated at the energies of 197, 600, and 1000 MeV within Glauber theory. The contributions of single and double collisions are taken into account in the multiple-scattering operator. The contributions of proton collisions with nucleons belonging to various (1s, 1p) shells are estimated in the single-scattering cross sections. A comparison with experimental data and with the result of calculations in the distorted-wave Born approximation (DWBA) at 197 MeV showed that the differential cross sections for p ¹⁰B scattering are adequately described in the region forward scattering angles.     

Mechanism of elastic and inelastic proton scattering on a 15C nucleus in diffraction theory

The amplitudes for elastic and inelastic proton scattering on the neutron-rich nucleus ¹⁵C (to its J ^?? = 5/2⁺ level in the latter case) in inverse kinematics were calculated within Glauber diffraction theory. First- and second-order terms were taken into account in the multiple-scattering operator. The ¹⁵C wave function in the multiparticle shell model was used. This made it possible to calculate not only respective differential cross sections but also the contribution of proton scattering on nucleons occurring in different shells. The differential cross sections for elastic and inelastic scattering were calculated at the energies of 0.2, 0.6, and 1 GeV per nucleon.