No abstract

We derive compact analytical formulae of the Bonneau-Martin type for the reaction e + e − →f f γ with cuts on minimal energy and acollinearity of the fermions, where the photons may be emitted both from the initial or final states. Soft-photon exponentiation is also taken into account.One of the cleanest scattering processes at elementary particle accelerators is fermion-pair production in e + e − annihilation, potentially accompanied by one or few photons:( 1) Initial-state corrections may be written as an integral over the (normalized) invariant mass squared R = s ′ /s of the final-state fermion pair:where σ 0 (s ′ ) is an effective Born cross-section. The radiator function ρ ini T (R) for the initialstate first-order corrections to the total cross-section σ T , with soft-photon exponentiation, is [1]:where h.o. stands for higher orders, and [2]:Experiments at LEP1, SLC, LEP2, and those planned at a linear collider aim at precisions well below a per cent and need theoretical predictions with an accuracy of the order of 0.1 % a Supported by Bulgarian foundation for Scientific Research with grant Φ-620/1996.

The Schrodinger equation for an electron on the surface of an elliptical torus in the presence of a constant azimuthally symmetric magnetic field is developed. The single particle spectrum and eigenfunctions as a function of magnetic flux through the torus are determined and it is shown that inclusion of the geometric potential is necessary to recover the limiting cases of vertical strip and flat ring structures.

The time-dependent Schrödinger equation is developed for a spinless electron which is confined to move on a toroidal surface and curvature effects are taken into account. The electron motion is driven by linearly or circularly polarized microwaves including an interference field. To calculate the magnetic moments which are induced by the electronic surface currents on the torus an eight-state basis set is used. The system is driven at a resonance frequency to allow for transitions between states with opposite θ -parity. Optical transitions into modes of excitation can be observed that correspond to a magnetic dipole term parallel to the toroidal central symmetry axis as well as additional components in radial and azimuthal direction (solenoidal modes). Size and relative magnitude of the different components can be steered by adjusting magnitude, polarization, and phase information of the microwave field. Substantial enhancements of the solenoidal magnetic modes versus the dipole mode can be observed when adding a sufficiently strong static magnetic field parallel to the symmetry axis.

A recursive Green's function method is employed to calculate the density-of-states, transmission function, and current through a 150 layer (3,3) armchair nanotorus (1800 atoms) with laterally attached metallic leads as functions of relative lead angle and magnetic flux. Plateaus in the transmissivity through the torus occur over wide ranges of lead placement, accompanied by enhancements in the transmissivity through the torus as magnetic flux normal to the toroidal plane is varied.