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THE COLOR DIPOLE APPROACH TO THE DRELL-YAN PROCESS IN PA COLLISIONS

Description: In the target rest frame and at high energies, Drell-Yan (DY) dilepton production looks like bremsstrahlung of massive photons, rather than parton annihilation. The projectile quark is decomposed into a series of Fock states. Configurations with fixed transverse separations are interaction eigenstates for pp scattering. The DY cross section can then be expressed in terms of the same color dipole cross section as DIS. This approach is especially suitable to describe nuclear effects, since it allows to apply Glauber multiple scattering theory. We go beyond the Glauber eikonal approximation by taking into account transitions between interaction eigenstates. We calculate nuclear shadowing at large Feynman-x{sub f} for DY in proton-nucleus collisions, compare to existing data from E772 and make predictions for RHIC. Nuclear effects on the transverse momentum distribution are also investigated.
Date: March 1, 2001
Creator: KOPELIOVICH, B. & AL, ET
Partner: UNT Libraries Government Documents Department

Dynamic effects in fragmentation reactions.

Description: Fragmentation reactions offer a useful tool to study the spectroscopy of halo nuclei, but the large extent of the halo wave function makes the reaction theory more difficult. The simple reaction models based on the eikonal approximation for the nuclear interaction or first-order perturbation theory for the Coulomb interaction have systematic errors that they investigate here, comparing to the predictions of complete dynamical calculations. They find that stripping probabilities are underpredicted by the eikonal model, leading to extracted spectroscopy strengths that are two large. In contrast, the Coulomb excitation is overpredicted by the simple theory. They attribute this to a screening effect, as is well known in the Barkas effect on stopping powers. The errors decrease with beam energy as E{sub beam}{sup -1}, and are not significant at beam energies above 50 MeV/u. At lower beam energies, the effects should be taken into account when extracting quantitative spectroscopic strengths.
Date: March 26, 2002
Creator: Bertsch, G. F. & Esbensen, H.
Partner: UNT Libraries Government Documents Department

The high energy behavior of the forward scattering parameters -- {sigma}{sub tot}, {rho}, and B

Description: Utilizing the most recent experimental data, the authors reanalyze high energy {anti p}p and pp data, using, two distinct (and dissimilar) analysis techniques: (1) asymptotic amplitude analysis, under the assumption that they have reached ``asymptopia``, and (2) an eikonal model whose amplitudes are designed to mimic real QCD amplitudes. The former gives strong evidence for a log(s/s{sub o}) dependence at current energies and not log{sup 2}(s/s{sub o}), and demonstrates that odderons are not necessary to explain the experimental data. The latter gives a unitary model for extrapolation into true ``asymptopia`` from current energies, allowing the authors to predict the values of the total cross section at future supercolliders. Using the QCD-model, they obtain {sigma}{sub tot}(16 TeV) = 109 {+-} 4mb and {sigma}{sub tot}(40 TeV) = 124 {+-} 4 mb.
Date: October 1994
Creator: Block, M. M.; Halzen, F.; Margolis, B. & White, A. R.
Partner: UNT Libraries Government Documents Department

The VIIth Blois workshop: Theory summary and factorization issues

Description: Theory presentations at this workshop have covered a wide range of topics. In addition to the traditional topics of elastic and diffractive scattering, the workshop has had a variety of interesting talks coming under the broad umbrella of ``Recent Advances in Hadron Physics.`` These have included review talks on lattice gauge theory, techniques for high-order perturbative QCD calculations, strong interaction effective field theories, the current status of QED and the construction of theories beyond the Standard Model. While the author briefly describes some topics covered, a ``review of reviews`` is in no way a substitute for the original reviews which also appear, of course, in this same volume. Among the more traditional topics covered are: BFKL physics -- higher-order corrections and jet cross-sections; unitarity and eikonal screening -- mainly in deep-inelastic diffraction but also in soft diffraction; elastic scattering phenomenology -- including real parts, the pomeron intercept and small-t oscillations. Also discussed is the role of factorization, i.e. both Regge pole factorization and perturbative QCD factorization theorems in the definition of a pomeron structure function and in the formulation of a parton model description of diffractive hard physics. The author focuses on one gluon versus two gluons as illustrating the issues involved.
Date: September 17, 1997
Creator: White, A.R.
Partner: UNT Libraries Government Documents Department

Variational formulation of eikonal theory for vector waves

Description: The eikonal theory of wave propagation is developed by means of a Lorentz-covariant variational principle, involving functions defined on the natural eight-dimensional phase space of rays. The wave field is a four-vector representing the electromagnetic potential, while the medium is represented by an anisotropic, dispersive nonuniform dielectric tensor D/sup ..mu.. sup ..nu../(k,x). The eikonal expansion yields, to lowest order, the Hamiltonian ray equations, which define the Lagrangian manifold k(x), and the wave action conservation law, which determines the wave amplitude transport along the rays. The first-order contribution to the variational principle yields a concise expression for the transport of the polarization phase. The symmetry between k-space and x-space allows for a simple implementation of the Maslov transform, which avoids the difficulties of caustic singularities.
Date: May 1, 1986
Creator: Kaufman, A.N.; Ye, H. & Hui, Y.
Partner: UNT Libraries Government Documents Department

Congruent reduction and mode conversion in 4-dimensional plasmas

Description: Standard eikonal theory reduces, to N=1, the order of the system of equations underlying wave propagation in inhomogeneous plasmas. The condition for this remarkable reducibility is that only one eigenvalue of the unreduced NxN dispersion matrix D(k,x) vanishes at a time. If, however, two or more eigenvalues of D become simultaneously small, the geometric optics reduction scheme becomes singular. These regions are associated with linear mode conversion, and are described by higher order systems. A new reduction scheme based on congruent transformations of D is developed, and it is shown that, in ''degenerate'' plasma regions, a partial reduction of order is possible. The method comprises a constructive step-by-step procedure, which, in the most frequent (doubly) degenerate case, yields a second order system, describing the pairwise mode conversion problems, the solution of which in general geometry has been found recently.
Date: April 1, 1987
Creator: Friedland, L. & Kaufman, A.N.
Partner: UNT Libraries Government Documents Department

Final-state interactions in semi-inclusive deep inelastic scattering off the Deuteron

Description: Semi-inclusive deep inelastic scattering off the Deuteron with production of a slow nucleon in recoil kinematics is studied in the virtual nucleon approximation, in which the final state interaction (FSI) is calculated within general eikonal approximation. The cross section is derived in a factorized approach, with a factor describing the virtual photon interaction with the off-shell nucleon and a distorted spectral function accounting for the final-state interactions. One of the main goals of the study is to understand how much the general features of the diffractive high energy soft rescattering accounts for the observed features of FSI in deep inelastic scattering (DIS). Comparison with the Jefferson Lab data shows good agreement in the covered range of kinematics. Most importantly, our calculation correctly reproduces the rise of the FSI in the forward direction of the slow nucleon production angle. By fitting our calculation to the data we extracted the W and Q{sup 2} dependences of the total cross section and slope factor of the interaction of DIS products, X, off the spectator nucleon. This analysis shows the XN scattering cross section rising with W and decreasing with an increase of Q{sup 2}. Finally, our analysis points at a largely suppressed off-shell part of the rescattering amplitude.
Date: July 1, 2011
Creator: Wim Cosyn, Misak Sargsian
Partner: UNT Libraries Government Documents Department

Use of the Lorentz-Boosted Frame Transformation to Simulate Free-Electron Laser Amplifier Physics

Description: Recently [1]it has been pointed out that numerical simulation of some systems containing charged particles with highly relativistic directed motion can by speeded up by orders of magnitude by choice of the proper Lorentz boosted frame. A particularly good example is that of short wavelength free-electron lasers (FELs) in which a high energy (E0>_ 250 MeV) electron beam interacts with a static magnetic undulator. In the optimal boost frame with Lorentz factor gamma F, the red-shifted FEL radiation and blue shifted undulator have identical wavelengths and the number of required time-steps (presuming the Courant condition applies) decreases by a factor of g2 F for fullyelectromagnetic simulation. We have adapted the WARP code [2]to apply this method to several FEL problems including coherent spontaneous emission (CSE) from pre-bunched e-beams, and strong exponential gain in a single pass amplifier configuration. We discuss our results and compare with those from the"standard" FEL simulation approach which adopts the eikonal approximation for propagation ofthe radiation field.
Date: July 27, 2008
Creator: Fawley, W.M. & Vay, J.-L.
Partner: UNT Libraries Government Documents Department

Coherence effects in deep inelastic scattering from nuclei

Description: A complete theoretical picture of multiple scattering processes in QCD remains elusive. In deep inelastic scattering experiments (DIS), we hope to find out information about the internal structure of nuclei from inelastically scattering high-energy electrons off them. The electrons interact via virtual photon exchange with the target. In the target rest frame the virtual photon splits into a quark-antiquark pair which is then scattered off the target color field. At high energies, coherent multiple scattering within the nucleus takes place. We develop a model that uses a parameterization of scattering cross section of the quark-antiquark pair off the proton to predict the cross section suppression known as shadowing in larger nuclei. This model takes the possibility of multiple scattering into account using Glauber high-energy collision theory. In large nuclei we must also move beyond the eikonal approximation by correcting for the finite lifetime of the quark-antiquark pair inside the nucleus. Results and implications of this model in relation to available data will be discussed. Finally, application of this type of model to predicting gluon densities will be considered. Understanding this process can give us insights into the more oomplicated scattering taking place in heavy ion colliders such as RHIC and LHC.
Date: January 1, 2001
Creator: Ver Steeg, G. L. (Greg L.) & Raufeisen, J. (Jorg)
Partner: UNT Libraries Government Documents Department

Nuclear effects in the Drell-Yan process.

Description: In the target rest frame and at high energies, Drell-Yan (DY) dilepton production looks like bremsstrahlung of massive photons, rather than parton annihilation. The projectile quark is decomposed into a series of Fock states. Configurations with fixed transverse separations in impact parameter space are interaction eigenstates for p p scattering. The DY cross section can then be expressed in terms of the same color dipole cross section as DIS. We compare calculations in this dipole approach with E772 data and with next-to-leading order parton model calculations. This approach is especially suitable to describe nuclear effects, since it allows one to apply Glauber multiple scattering theory. We go beyond the Glauber eikonal approximation by taking into account transitions between states, which would be eigenstates for a proton target. We calculate nuclear shadowing at large Feynman-x{sub F} for DY in proton-nucleus collisions and compare to E772 data. Nuclear effects on the transverse momentum distribution are also investigated.
Date: January 1, 2002
Creator: Raufeisen, J. (Jorg)
Partner: UNT Libraries Government Documents Department

Factorization and resummation for collinear poles in QCD amplitudes

Description: We study the origin of subleading soft and collinear poles of form factors and amplitudes in dimensionally-regulated massless gauge theories. In the case of form factors of fundamental fields, these poles originate from a single function of the coupling, denoted G({alpha}{sub s}), depending on both the spin and gauge quantum numbers of the field. We relate G({alpha}{sub s}) to gauge-theory matrix elements involving the gluon field strength. We then show that G({alpha}{sub s}) is the sum of three terms: a universal eikonal anomalous dimension, a universal non-eikonal contribution, given by the coefficient B{sub {delta}}({alpha}{sub s}) of {delta}(1-z) in the collinear evolution kernel, and a process-dependent short-distance coefficient function, which does not contribute to infrared poles. Using general results on the factorization of soft and collinear singularities in fixed-angle massless gauge theory amplitudes, we conclude that all such singularities are captured by the eikonal approximation, supplemented only by the knowledge of B{sub {delta}}({alpha}{sub s}). We explore the consequences of our results for conformal gauge theories, where in particular we find a simple exact relation between the form factor and the cusp anomalous dimension.
Date: May 28, 2008
Creator: Dixon, Lance J.; Magnea, Lorenzo & Sterman, George
Partner: UNT Libraries Government Documents Department

Full Electromagnetic Fel Simulation via the Lorentz-Boosted Frame Transformation

Description: Numerical electromagnetic simulation of some systems containing charged particles with highly relativistic directed motion can by speeded up by orders of magnitude by choice of the proper Lorentz-boosted frame. A particularly good application for calculation in a boosted frame isthat of short wavelength free-electron lasers (FELs) where a high energy electron beam with small fractional energy spread interacts with a static magnetic undulator. In the optimal boost frame (i.e., the ponderomotive rest frame), the red-shifted FEL radiation and blue-shifted undulator field have identical wavelengths and the number of required longitudinal grid cells and time-steps for fully electromagnetic simulation (relative to the laboratory frame) decrease by factors of gamma^2 each. In theory, boosted frame EM codes permit direct study of FEL problems for which the eikonal approximation for propagation of the radiation field and wiggler-period-averaging for the particle-field interaction may be suspect. We have adapted the WARP code to apply this method to several electromagnetic FEL problems including spontaneous emission, strong exponential gain in a seeded, single pass amplifier configuration, and emission from e-beams in undulators with multiple harmonic components. WARP has a standard relativistic macroparticle mover and a fully 3-D electromagnetic field solver. We discuss our boosted frame results and compare with those obtained using the ?standard? eikonal FEL simulation approach.
Date: August 16, 2010
Creator: Fawley, William & Vay, Jean-Luc
Partner: UNT Libraries Government Documents Department

Eikonal expansion of the Vlasov-Maxwell equations valid near cyclotron resonance

Description: In the usual formulations of geometrical optics, the physics of the medium enters the equations through a conductivity tensor operator sigma. An essential assumption in the subsequent expansion is that the magnitude of sigma/sup H/, the Hermitian part of sigma, is much smaller than sigma/sup A/, the anti-Hermitian part. In a finite temperature plasma with ..omega../sub pe/ approx. absolute value ..cap omega../sub e/, this condition is always violated sufficiently close to cyclotron resonance, even though in many cases the waves are weakly damped and k is slowly varying. Simultaneously expanding the Vlasov equation and Maxwell equations and taking explicit account of the relative magnitude of the electric field components in the ordering scheme yields a formalism in terms of real rays, real eikonal function, and slowly varying amplitude that is valid at cyclotron resonance. It is assumed that ..omega../sub pe/ approx. absolute value ..cap omega../sub e/ approx. ..omega.. are large, that ..omega.. approx. = absolute value ..cap omega../sub e/, and that v/sub e/k/..omega.. is small. It is shown that when the waves are weakly damped at cyclotron resonance, the ray trajectories are to leading order exactly those of cold plasma theory.
Date: January 1, 1980
Creator: Weitzner, H. & Batchelor, D.B.
Partner: UNT Libraries Government Documents Department

Effects of multiple scattering and target structure on photon emission

Description: The Landau-Pomeranchuk-Migdal effect is the suppression of Bethe-Heitler radiation caused by multiple scattering in the target medium. The quantum treatment given by S.D. Drell and the author for homogeneous targets of finite thickness will be reviewed. It will then be extended to structured targets. In brief, it is shown that radiators composed of separated plates or of a medium with a spatially varying radiation length can exhibit unexpected structure, even coherence maxima and minima, in their photon spectra. Finally, a functional integral method for performing the averaging implicit in multiple scattering will be briefly discussed and the leading corrections to previous results evaluated.
Date: May 1, 1996
Creator: Blankenbecler, R.
Partner: UNT Libraries Government Documents Department

Eikonal theory of the transition to phase incoherence

Description: When a monochromatic electromagnetic wave propagates through a nonuniform plasma (of n dimensions), its refraction may be studied in terms of its family of rays in 2n-dimensional phase space (k,x). These rays generate and n-dimensional surface. Imbedded in the phase space. The wave amplitude and phase are defined on this surface. As the rays twist and separate (from the dynamics of the ray Hamiltonian), the surface develops pleats and becomes convoluted. Projection of the surface onto x-space then yields a multivalued k(x). The local spectral density, as a function of k for given x, exhibits sharp spikes at these k(x), in the ray-optics limit. The next correction yields a finite width to these spikes. As the surface becomes more and more pppleated, these spectral peaks overlap; the spectrum changes qualitatively from a line spectrum to a continuous spectrum. Correspondingly, the two-point spatial correlation function loses its long-range order, as the correlation volume contracts. This phenomenon is what we call the transition to incoherence.
Date: February 1, 1983
Creator: Kaufman, A.N. & Rosengaus, E.
Partner: UNT Libraries Government Documents Department

Wave dynamics of regular and chaotic rays

Description: In order to investigate general relationships between waves and rays in chaotic systems, I study the eigenfunctions and spectrum of a simple model, the two-dimensional Helmholtz equation in a stadium boundary, for which the rays are ergodic. Statistical measurements are performed so that the apparent randomness of the stadium modes can be quantitatively contrasted with the familiar regularities observed for the modes in a circular boundary (with integrable rays). The local spatial autocorrelation of the eigenfunctions is constructed in order to indirectly test theoretical predictions for the nature of the Wigner distribution corresponding to chaotic waves. A portion of the large-eigenvalue spectrum is computed and reported in an appendix; the probability distribution of successive level spacings is analyzed and compared with theoretical predictions. The two principal conclusions are: 1) waves associated with chaotic rays may exhibit randomly situated localized regions of high intensity; 2) the Wigner function for these waves may depart significantly from being uniformly distributed over the surface of constant frequency in the ray phase space.
Date: September 1, 1983
Creator: McDonald, S.W.
Partner: UNT Libraries Government Documents Department

Orbit dynamics in isochronous cyclotrons

Description: Acceleration of heavy ions in an isochronous cyclotron can lead to a ..nu../sub r/-value near unity for many turns. In ORIC, several departures from 3-fold symmetry unfortunately exist, so that a complex resonant behavior may lead to beam loss. To study these questions, a program has been initiated with the aim of devising and using very efficient algorithms for calculating the motion of ions during acceleration. The eikonal function was chosen as the basis for these studies, with methods and some results here described.
Date: January 1, 1981
Creator: Welton, T.A. & Nichols, T.
Partner: UNT Libraries Government Documents Department

Ballooning instabilities in tokamaks with sheared toroidal flows

Description: The stability of ballooning modes in the presence of sheared toroidal flows is investigated. The eigenmodes are shown to be related by a Fourier transformation to the non-exponentially growing Floquet solutions found by Cooper. It is further shown that the problem cannot be reduced further than to a two dimensional partial differential equation. Next, the generalized ballooning equation is solved analytically for a circular tokamak equilibrium with sonic flows, but with a small rotation shear compared to the sound speed. With this ordering, the centrifugal forces are comparable to the pressure gradient forces driving the instability, but coupling of the mode with the sound wave is avoided. A new stability criterion is derived which explicitly demonstrates that flow shear is stabilizing at constant centrifugal force gradient. 34 refs.
Date: November 1, 1990
Creator: Waelbroeck, F.L. & Chen, L.
Partner: UNT Libraries Government Documents Department

Noneikonal effects in the spin-dependent proton--nucleus interactions. [Scattering amplitudes, 800 MeV, Glauber diffraction]

Description: Simple expressions are derived for the noneikonal corrections to the Glauber diffraction approximation for the proton--nucleus scattering amplitudes, with the spin-dependence of the proton--nucleon amplitudes taken into account. As an example, the numerical importance of these corrections is studied for elastic p-/sup 58/Ni scattering at 800 MeV. The polarization and the spin rotation, which are sensitive to the relative phase of the amplitudes, are at small angles changed by typically 5 to 10%. 19 references.
Date: January 1, 1979
Creator: Bleszynski, M. & Osland, P.
Partner: UNT Libraries Government Documents Department

Group representation matrix and scattering from nuclei

Description: It is shown that the transition matrix for elastic and inelastic medium energy protons scattered from nuclei described by the interacting boson model is the SU/sub 6/ group representation matrix. Closed form expressions for this transition matrix are derived for the special cases of a vibrational nucleus, a ..gamma..-unstable rotor nucleus, and an axially symmetric rotor nucleus.
Date: January 1, 1985
Creator: Ginocchio, J.N.
Partner: UNT Libraries Government Documents Department

Theoretical study of electron capture in ion-ion and ion-atom collisions. Progress report, September 1, 1980-April 30, 1981

Description: The eikonal approximation has been recently shown to be of significant utility in the study of electron capture cross sections for energetic ion-atom collisions. The method generally gives much better agreement with available experimental data than does the simple OBK approximation without substantially increasing the difficulty of computation. In the present work, the total cross section is computed for electron capture into an arbitrary nl subshell of H/sup +/, C/sup +6/, O/sup +8/, and Fe/sup +24/ ions from ground state hydrogen atoms, at energies of 40 to 200 keV/nuclear (30 to 100 keV in the H/sup +/ case). These species were selected because of their importance in fusion studies. Interesting variations with l were obtained. Cross sections for capture into an arbitrary final n-shell, or into all final bound states were also obtained. An analytical closed form expression is derived for electron capture from an arbitrary initial nlm state to an arbitrary final n'l'm' state of a hydrogenic target. Numerical results are presented for all n' = 2,3 final states in hydrogen, which may be subjected to experimental test in the near future. Extension of the eikonal method to multielectron targets was studied. There are ambiguities in the method requiring further analysis. Agreement with experimental data is nevertheless satisfactory, but the high energy results are suspect.
Date: April 1, 1981
Creator: Lieber, M. & Chan, F.T.
Partner: UNT Libraries Government Documents Department