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

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

Algebraic {qq}-Integration and Fourier Theory on Quantum and Braided Spaces

We introduce an algebraic theory of integration on quantum planes and other braided spaces. In the one dimensional case we obtain a novel picture of the Jackson $q$-integral as indefinite integration on the braided group of functions in one variable $x$. Here $x$ is treated with braid statistics $q$ rather than the usual bosonic or Grassmann ones. We show that the definite integral $\int x$ can also be evaluated algebraically as multiples of the integral of a $q$-Gaussian, with $x$ remaining as a bosonic scaling variable associated with the $q$-deformation. Further composing our algebraic integration with a representation then leads to ordinary numbers for the integral. We also use our integration to develop a full theory of $q$-Fourier transformation $F$. We use the braided addition $\Delta x=x\otimes 1+1\otimes x$ and braided-antipode $S$ to define a convolution product, and prove a convolution theorem. We prove also that $F^2=S$. We prove the analogous results on any braided group, including integration and Fourier transformation on quantum planes associated to general R-matrices, including $q$-Euclidean and $q$-Minkowski spaces.Comment: 50 pages. Minor changes, added 3 reference

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

Coulomb Excitation of Multi-Phonon Levels of the Giant Dipole Resonance

A closed expression is obtained for the cross-section for Coulomb excitation of levels of the giant dipole resonance of given angular momentum and phonon number. Applications are made to the Goldhaber-Teller and Steinwedel-Jensen descriptions of the resonance, at non-relativistic and relativistic bombarding energies.Comment: 16 pages, 5 figure

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

Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances

In this work, a sensitivity of the rate of relaxation of ground-state atomic coherences to magnetic-field inhomogeneities is studied. Such coherences give rise to many interesting phenomena in light-atom interactions, and their lifetimes are a limiting factor for achieving better sensitivity, resolution or contrast in many applications. For atoms contained in a vapor cell, some of the coherence-relaxation mechanisms are related to magnetic-field inhomogeneities. We present a simple model describing relaxation due to such inhomogeneities in a buffer-gas-free anti-relaxation coated cell. A relation is given between relaxation rate and magnetic-field inhomogeneities including the dependence on cell size and atomic spices. Experimental results, which confirm predictions of the model, are presented. Different regimes, in which the relaxation rate is equally sensitive to the gradients in any direction and in which it is insensitive to gradients transverse to the bias magnetic field, are predicted and demonstrated experimentally.Comment: 6 pages, 4 figures, Submitted to Phys. Rev.