An elegant but “simple” form for the Dirac hydrogen atom

The operator structures for the constants of the motion of the relativistic hydrogen atom are examined. ThoughJ ³ andJ · J are constants of the motion,J is not. Its replacement, , is shown to emerge rather naturally in transforming the equation to spherical coordinates. The separation of variables is presented in hypercomplex number form. This leads to some interesting suggestions regarding the matter/antimatter operator for the Dirac equation.     

Ultra-Precise Mass Measurements Using the UW-PTMS

Based on the use of a single ion, isolated at the center of a cryogenically cooled Penning trap, an environment is produced which makes this mass spectrometer remarkably free of systematic errors. The most notable developments in our quest for an ultra-high accuracy instrument were (a) the compensation of the trapping potential, (b) the discovery that motional sidebands could manipulate radial energies, (c) the use of multiply-charged ions that could improve signal-to-noise, and (d) the use of an ultra-stable superconducting magnet/cryostat system with drift <0.010 ppb/h. The dominant systematic errors are associated with radial electric fields caused by image charges in the trap electrodes and with the rf-electrical drive field used to determine the harmonic axial resonance. To illustrate the potential of this improved spectrometer, the four-fold improved measurement of the proton's mass and the eight-fold improved measurement of oxygen's atomic mass will be described. This revised version was published online in July 2006 with corrections to the Cover Date.     

Graceful exit from inflation using quantum cosmology

A massless scalar field without self-interaction and string coupled to gravity is quantized in the framework of quantum cosmology using the Bohm–de Broglie interpretation. Gaussian superpositions of the quantum solutions of the corresponding Wheeler–DeWitt equation in minisuperspace are constructed. The Bohmian trajectories obtained exhibit a graceful exit from the inflationary pre-big bang epoch to the decelerated expansion phase.     

Characterizations of taut semi-local rings

Summary It is proved that the following statements are equivalent for semi-local domain R:1) R is taut (i.e., for each non-maximal prime ideal P in R, height P+depth P=altitude R).2) Every integral domain which contains and is integral over R is taut.3) R[1/b]. satisfies the second chain condition for prime ideals (s.c.c.), for each non-zero b in the Jacobson radical J of R.4) R[1/b] satisfies the first chain condition for prime ideals (f.c.c.), for some non-zero b in J.5) For each depth one prime ideal P in R, R_P satisfies the s.c.c. and height P=altitude R−1.6) R(X) is taut, where X is an indeterminate.7) For each pair of analytically independent elements b, c in R, R(c/b) is taut and altitude R(c/b)=altitude R−1.8) Each maximal set of analytically independent elements in R contains either one element or altitude R elements. Much of the theorem is then generalized (with suitable modifications) to rings which contain and are integral over a taut semi-local ring. Entrata in Redazione il 5 dicembre 1975. Research on this paper was supported in part by the National Science Foundation grant NSF GP-28939-1.     

Far-Infrared Laser Stark Spectroscopy of CH3OD

The high resolution Stark spectra of the singly deuterated methanol isotope, CH₃OD, have been studied using the HCN laser with Stark fields up to approximately 60 000 V/cm. Numerous families of absorption lines have been observed in both parallel and perpendicular polarizations, resulting in the following assignments: with the 311 m line – J _K = 18₁ 18₀ E ₂, _t = 1; and with the 337 m line – J _k = 6₄ 5₃ E ₂, _t = 0 and J _K = 14₆ 13₅ A, _t = 1. Zero-field frequencies for the assigned transitions are in agreement with Fourier transform measurements and those calculated from the available molecular constants.     

Residual stress determination in aluminium using electromagnetic acoustic transducers

The residual stresses in a shrink-fit specimen were measured ultrasonically, using shear-horizonal (SH) waves transmitted and received by noncontacting electromagnetic acoustic transducers. The presence of stress induces a small change in the velocity of the SH-waves. The difference in velocities of orthogonally polarized SH-waves (acoustic birefringence) was measured with a simple time-interval averaging system; this velocity difference can be related to the difference of principal stresses. The presence of material anisotropy (texture) in the specimen also causes relative velocity changes comparable to stress-induced changes. A simple method was used to remove the anisotropy-dependent component of the total relative velocity change, thereby allowing a determination of residual stress. This method consisted of measuring the birefringence in unstressed reference specimens and subtracting it from the birefringence measured at stressed locations. For the specimen used here, good agreement between theoretical and experimental values of stress was obtained.     

Design and Analysis of Planar Photonic Band Gap Devices

The need for a highly efficient numerical simulation platform for designing photonic band gap (PBG) structures is outlined in the context of various functional device topologies. In this paper we therefore introduce the Method of Auxiliary Sources (MAS) as a semi-analytical, frequency-domain method for computational optics, which has already proven its accuracy and efficiency in various other fields of electrodynamics. The proposed software package provides an easy-to-handle approach to full-wave analysis of two-dimensional (2D) PBG circuits, PBG-based antennas as well as to dense-integrated optics components that contain optical waveguides, scatterers, resonators and other functional elements. Experimental verifications of the numerical results have been conducted along large-scale prototypes in the microwave frequency range for several device topologies.     

The effect of controlled ion bombardment on the electronic structure of the Si(0 0 1) surface

We have studied the effects of controlled ion bombardment on the electronic structure of the Si(0 0 1) surface. The surface was exposed to various doses of Ar⁺ ions accelerated towards the surface at 500 eV. X-ray photoelectron spectroscopy (XPS) spectra of the irradiated H-terminated Si(0 0 1) surface reveal the appearance of peaks that are associated with the presence of cleaved Si bonds. Ultraviolet photoelectron spectroscopy (UPS) spectra of the irradiated Si(0 0 1)2 × 1 surface show that the dimer dangling-bond surface state decays monotonically with increasing dose. These results, coupled with previous scanning tunneling microscopy (STM) studies, indicate that the breaking of dimers, and possibly the creation of adatom-like defects, during ion irradiation are responsible for the changes in the electronic structure of the valence band for this surface.