Gauge dependence of calculations in relativistic Coulomb excitation

Before a quantum-mechanical calculation involving electromagnetic interactions is performed, a choice must be made of the gauge to be used in expressing the potentials. If the calculation is done exactly, the observable results it predicts will be independent of the choice of gauge. However, in most practical calculations approximations are made, which can destroy the gauge invariance of the predictions. We compare here the results of coupled-channel time-dependent relativistic Coulomb excitation calculations, as performed in either Lorentz or Coulomb gauges. We find significant differences when the bombarding energy per nucleon is $\geq$ 2 GeV, which indicates that the common practice of relying completely on the Lorentz gauge can be dangerous.Comment: 23 pages, 3 figure

Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces

In this work, the scattering of surface plasmons by a finite periodic array of one-dimensional grooves is theoretically analyzed by means of a modal expansion technique. We have found that the geometrical parameters of the array can be properly tuned to achieve optimal performance of the structure either as a Bragg reflector or as a converter of surface plasmons into light. In this last case, the emitted light is collimated within a few degrees cone. Importantly, we also show that a small number of indentations in the array are sufficient to fully achieve its functional capabilities.Comment: 5 pages, 5 figures; changed sign convention in some definition

Quantum derivation of the use of classical electromagnetic potentials in relativistic Coulomb excitation

We prove that a relativistic Coulomb excitation calculation in which the classical electromagnetic field of the projectile is used to induce transitions between target states gives the same target transition amplitudes, to all orders of perturbation theory, as would a calculation in which the interaction between projectile and target is mediated by a quantized electromagnetic field.Comment: 1 .zip file containing LaTex source plus three figures as .eps file

Rutherford scattering with radiation damping

We study the effect of radiation damping on the classical scattering of charged particles. Using a perturbation method based on the Runge-Lenz vector, we calculate radiative corrections to the Rutherford cross section, and the corresponding energy and angular momentum losses.Comment: Latex, 11 pages, 4 eps figure

Generalization of the Schott energy in electrodynamic radiation theory

We discuss the origin of the Schott energy in the Abraham-Lorentz version of electrodynamic radiation theory and how it can be used to explain some apparent paradoxes. We also derive the generalization of this quantity for the Ford-O'Connell equation, which has the merit of being derived exactly from a microscopic Hamiltonian for an electron with structure and has been shown to be free of the problems associated with the Abraham-Lorentz theory. We emphasize that the instantaneous power supplied by the applied force not only gives rise to radiation (acceleration fields), but it can change the kinetic energy of the electron and change the Schott energy of the velocity fields. The important role played by boundary conditions is noted

Helical Symmetry in Linear Systems

We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman--Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.Comment: 11 page

East Africa and Uganda Francolins

Volume:

Higgs boson production with one bottom quark including higher-order soft-gluon corrections

A Higgs boson produced in association with one or more bottom quarks is of great theoretical and experimental interest to the high-energy community. A precise prediction of its total and differential cross-section can have a great impact on the discovery of a Higgs boson with large bottom-quark Yukawa coupling, like the scalar (h^0 and H^0) and pseudoscalar (A^0) Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) in the region of large \tan\beta. In this paper we apply the threshold resummation formalism to determine both differential and total cross-sections for b g \to b\Phi (where \Phi = h^0, H^0), including up to next-to-next-to-next-to-leading order (NNNLO) soft plus virtual QCD corrections at next-to-leading logarithmic (NLL) accuracy. We present results for both the Fermilab Tevatron and the CERN Large Hadron Collider (LHC).Comment: revtex4, 13 pages, 11 figures; new references and additional comment

A simple derivation of the electromagnetic field of an arbitrarily moving charge

The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the Lienard-Wiechert potentials. The derivation uses arguments based on Lorentz invariance and a physically transparent expression originally due to J.J.Thomson for the field of a charge that experiences an impulsive acceleration.Comment: The following article has been accepted by the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp; 12 pages, 1 figur