Experimental results on neutrino-electron scattering

A determination of sin² θ _w based on measurements of elastic scattering of muon-neutrinos and muon-anti-neutrinos on atomic electrons is described. These purely leptonic processes were studied using the CHARM calorimeter exposed to neutrino and antineutrino wide-band beams at the CERN super proton synchrotron. A total of 83±16 neutrino-electron and 112±21 antineutrino-electron events have been detected. From the measurement of the ratio of muon-neutrino and muon-antineutrino cross-sections a value of sin² θ _w =0.211±0.037 was obtained.     

Of Ghosts, Gauge Volumes, and Gauss's Law

The relationship between the canonical operator and the path integral formulation of quantum electrodynamics is analyzed with a particular focus on the implementation of gauge constraints in the two approaches. The removal of gauge volumes in the path integral is shown to match with the presence of zero-norm ghost states associated with gauge transformations in the canonical operator approach. The path integrals for QED in both the Feynman and the temporal gauges are examined and several ways of implementing the gauge constraint integrations are demonstrated. The upshot is to show that both the Feynman and the temporal gauge path integrals are equivalent to the Coulomb gauge path integral, matching the results developed by Kurt Haller using the canonical formalism. In addition, the Faddeev–Popov form for the Feynman gauge and temporal gauge Lagrangian path integrals are derived from the Hamiltonian form of the path integral.     

On the mechanism of liquid metal ion sources

We have developed a theoretical model of liquid metal ion source operation which consistently explains the shape and size of the ion emitting region, the mechanism of ion formation and properties of the ion beam. We find that field evaporation is the main current generating mechanism and that field evaporation and subsequent postionization produce the doubly and higher charged ions. Field ionization of thermally evaporated neutrals may make a significant, but not dominant, contribution to the current of singly charged ions. Our model is consistent with experimental results on energy spread, energy deficit and charge state ratios and we are able to explain the stability of the emitted ion current.     

Transport with a Very Low Density Contrast in Hele–Shaw Cell and Porous Medium: Evolution of the Mixing Zone

The optimal concentration of a blue dye solution with 'tracer' properties, enabling a pollutant to be marked was determined by the use of numerical, theoretical and experimental approaches. Experimental investigations were performed on a transparent Hele–Shaw cell and the concentration distribution was analyzed using an optical technique based on dye light absorption properties. The injected optimal concentration was established thanks to a theoretical and experimental study carried out on the output signal dynamics. Using the same experimental conditions, numerical simulations were performed. The very good agreement between the data (experimental and numerical) clarified that: (i) the choice of the blue dye optimal concentration was valid and (ii) the concentration-dependent density should not be neglected in flow and transport equations even if it concerns a so-called 'tracer'. Following this remark, a theoretical aspect was developed in order to determine the analogous conditions between a Hele–Shaw cell and a porous medium for the variable density transport phenomenon. The structure of the concentration-dependent dispersion tensor used in the numerical code was obtained by homogenizing the Stokes flow of a bi-component mixture. The numerical results show that, as long as the tracer density does not exceed a certain value, it is not necessary to take into account a density contrast in terms of the dispersion tensor. The classical form of the Taylor dispersion tensor can be used successfully.     

Beta–neutrino correlation experiments on laser trapped 38mK, 37K

Laser trapping and cooling techniques are now being applied to the study of nuclear β-decay at several labs. A magneto-optical trap (MOT) provides a localized source of atoms suspended in space, so the low-energy recoiling nuclei can freely escape and be detected in coincidence with the β. This allows reconstruction of the neutrino momentum, and the deduction of the β-v correlation in a more direct fashion than previously possible. In addition, the nuclei can be polarized by atomic techniques, opening a new class of spin correlation measurements to test the degree to which parity is maximally violated in the weak interaction. Our present experiment has detected several hundred thousand recoil-β⁺ coincidences from the 0⁺ → 0⁺ pure Fermi decay of ^38mK, produced at the on-line isotope separators TISOL and ISAC at TRIUMF. Our goal is to set constraints on non-Standard Model scalar bosons competitive with high-energy colliders and more conventional β-v correlation experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Truncation rules for modelling discontinuities with Galerkin method in electromagnetic theory

It is well known that apparently similar discretization schemes of Maxwell's equations in Fourier series may provide very different convergence performances because of truncation. We argue that this work performed in grating theory can be applied to other electromagnetic theories relying on expansions over series different from Fourier series. This generalization is supported by an intuitive argument and by a simple numerical example with Hermite–Gauss functions.     

Novel search for heavy nu mixing from the beta+ decay of 38mK confined in an atom trap

A new technique, full neutrino momentum reconstruction, is used to set limits on the admixture of heavy neutrinos into the electron neutrino. We measure coincidences between nuclear recoils and positrons from the beta decay of trapped radioactive atoms and deduce the neutrino momentum. A search for peaks in the reconstructed recoil time-of-flight spectrum as a function of positron energy is performed. The admixture upper limits range from 4 x 10(-3) to 2 x 10(-2) and are the best direct limits for neutrinos (as opposed to antineutrinos) for the mass region of 0.7 to 3.5 MeV.     

Linearly implicit time discretization of non-linear parabolic equations

We give a stability and error analysis of linearly implicitone-step methods for time discretization of non-linear parabolicequations. We derive precise error bounds for Rosenbrock andW-methods, and we explain the error reduction by Richardsonextrapolation of the linearly implicit Euler method which occursin spite of the breakdown of asymptotic expansions. The parabolicequations are studied in a Hilbert space framework that includessemilinear and quasilinear parabolic equations, and also stiffreaction-diffusion equations with reactions at different timescales.