BYU Physics and Astronomy

Abstract: We assess several widely used vector models of a Gaussian laser beam in the context of more accurate vector diffraction integration. For the analysis, we present a streamlined derivation of the vector fields of a uniformly polarized beam reflected from an ideal parabolic mirror, both inside and outside of the resulting focus. This exact solution to Maxwell’s equations, first developed in 1920 by V. S. Ignatovsky, is highly relevant to high-intensity laser experiments since the boundary conditions at a focusing optic dictate the form of the focus in a manner analogous to a physical experiment. In contrast, many models simply assume a field profile near the focus and develop the surrounding vector fields consistent with Maxwell’s equations. In comparing the Ignatovsky result with popular closed-form analytic vector models of a Gaussian beam, we find that the relatively simple model developed by Erikson and Singh in 1994 provides good agreement in the paraxial limit. Models involving a Lax expansion introduce a divergences outside of the focus while providing little if any improvement in the focal region. Extremely tight focusing produces a somewhat complicated structure in the focus, and requires the Ignatovsky model for accurate representation.

Abstract: We report on measurements of relative beta-decay rates of Na-22, Cl-36, Co-60, Sr-90, Cs-137 monitored for more than one year. The radioactive samples are mounted in an automated sample changer that sequentially positions the five samples in turn, with high spatial precision, in front of each of four Geiger–Müller tubes. The sample wheel, detectors, and associated electronics are housed inside a sealed chamber held at constant absolute pressure, humidity, and temperature to isolate the experiment from environmental variations. The statistical uncertainty in the count rate approaches a few times 0.01% with two weeks of averaging. Other sources of error are on a similar scale. The data are analyzed in variety of ways, comparing count rates of the various samples on one or more detectors, and comparing count rates of a particular sample across multiple detectors. We observe no statistically significant variations in the ratios of decay rates, either annual or at higher-frequency, at a level above 0.01%. 

Abstract: We develop a model that reduces quantum electrodynamics (QED) in time plus three spatial dimensions to time plus a single spatial dimension, making it is possible to numerically calculate the dynamic behavior of simple QED systems. The dimensionality is restricted in such a way as to preserve the influence of spin and angular momentum. In contrast to the S -matrix scattering approach, these calculations are not perturbative within the zero- and one-photon sector of the relevant Hilbert space. The model restricts the electron occupation number to one and the photon occupation number to zero or one. We use this model to calculate the dynamics of a so-called bare electron that dresses itself by a photon field.