Existence theorems for π/n vortex scattering

The analysis of 90° vortex-vortex scattering is extended to /n scattering in all head-on collisions ofn vortices in the Abelian Higgs model. A Cauchy problem with initial data that describe the scattering ofn vortices is formulated. It is shown that this Cauchy problem has a unique global finite-energy solution. The symmetry of the solution and the form of the local analytic solution then show that /n scattering is realized.     

Improved measurement of the hydrogen 1S-2S transition frequency

We have measured the 1S-2S transition frequency in atomic hydrogen via two-photon spectroscopy on a 5.8 K atomic beam. We obtain f(1S-2S) = 2,466,061,413,187,035 (10) Hz for the hyperfine centroid, in agreement with, but 3.3 times better than the previous result [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)]. The improvement to a fractional frequency uncertainty of 4.2 × 10(-15) arises mainly from an improved stability of the spectroscopy laser, and a better determination of the main systematic uncertainties, namely, the second order Doppler and ac and dc Stark shifts. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.     

Analysis of the high-resolution infrared spectrum of cyclopropane

The high-resolution infrared spectrum of cyclopropane (C₃H₆) has been measured from 100 cm⁻¹ to 2200 cm⁻¹. In that region we have identified 24 absorption bands attributed to six fundamental bands, five combination bands, three hot bands and 10 difference bands. Long pathlength spectra, up to 32 m, facilitated the identification and analysis of many previously unstudied infrared inactive, and Raman and infrared inactive vibrational states, including direct access to two forbidden fundamental states, ν₄ and ν₁₄. An improved set of constants for the ground vibrational state as well as for the fundamental vibrations ν₇, ν₉, ν₁₀, ν₁₁ are also reported. The spectral resolution of the measurements varied from 0.002 cm⁻¹ to 0.004 cm⁻¹.     

Direct EPR detection of transient and continuous wave signals at 2.5 GHz

Direct detection of free induction decays and electron spin echoes, and the recording of echo-detected EPR spectra and electron spin echo envelope modulation patterns at a microwave frequency of 2.5 GHz is demonstrated. This corresponds to the measurement of the transverse magnetization in the laboratory frame, rather than in the rotating frame as usually done by down-converting the signal (homodyne detection). An oscilloscope with a 6-GHz analog bandwidth, a sampling rate of 20 GigaSamples per second, and a trigger frequency of 5 GHz for the edge trigger and 750 MHz for the advanced trigger, is used in these experiments. For signal averaging a 3-GHz microwave clock divider has been developed to synchronize the oscilloscope with the frequency of the EPR signal. Moreover, direct detection of continuous wave EPR signals at 2.5 GHz is described.     

Geometric algebra techniques for general relativity

Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the straightforwardness of coordinate methods. We focus our attention on orthonormal frames and the associated connection bivector, using them to find the Schwarzschild and Kerr solutions, along with a detailed exposition of the Petrov types for the Weyl tensor.     

Analysis of some combination-overtone infrared bands of SO3

Several new infrared absorption bands for ³²S¹⁶O₃ have been measured and analyzed. The principal bands observed were ν₁+ν₂ (at 1561 cm⁻¹), ν₁+ν₄ (at 1594 cm⁻¹), ν₃+ν₄ (at 1918 cm⁻¹), and 3ν₃ (at 4136 cm⁻¹). Except for 3ν₃, these bands are very complicated because of (a) the Coriolis coupling between ν₂ and ν₄, (b) the Fermi resonance between ν₁ and 2ν₄, (c) the Fermi resonance between ν₁ and 2ν₂, (d) ordinary l-type resonance that couples levels that differ by 2 in both the k and l quantum numbers, and (e) the vibrational l-type resonance between the A₁^′ and A₂^′ levels of ν₃+ν₄. The unraveling of the complex pattern of these bands was facilitated by a systematic approach to the understanding of the various interactions. Fortunately, previous work on the fundamentals permitted good estimates of many constants necessary to begin the assignments and the fit of the measurements. In addition, the use of hot band transitions accompanying the ν₃ band was an essential aid in fitting the ν₃+ν₄ transitions since these could be directly observed for only one of four interacting states. From the hot band analysis we find that the A₁^′ vibrational level is 3.50 cm⁻¹ above the A₂^′ level, i.e., r₃₄=1.75236(7) cm⁻¹. In the case of the 3ν₃ band, the spectral analysis is straightforward and a weak Δk=±2, Δl₃=±2 interaction between the l₃=1 and l₃=3 substates locates the latter A₁^′ and A₂^′ “ghost” states 22.55(4) cm⁻¹ higher than the infrared accessible l₃=1 E^′ state.     

Giant spin splitting through surface alloying

The long-range ordered surface alloy Bi/Ag(111) is found to exhibit a giant spin splitting of its surface electronic structure due to spin-orbit coupling, as is determined by angle-resolved photoelectron spectroscopy. First-principles electronic structure calculations fully confirm the experimental findings. The effect is brought about by a strong in-plane gradient of the crystal potential in the surface layer, in interplay with the structural asymmetry due to the surface-potential barrier. As a result, the spin polarization of the surface states is considerably rotated out of the surface plane.     

Intensification of oxidation capacity using chloroalkanes as additives in hydrodynamic and acoustic cavitation reactors

The effect of the presence and absence of the chloroalkanes, dichloromethane (CH(2)Cl(2)), chloroform (CHCl(3)) and carbon tetrachloride (CCl(4)) on the extent of oxidation of aqueous I(-) to I(3)(-) has been investigated in (a) a liquid whistle reactor (LWR) generating hydrodynamic cavitation and (b) an ultrasonic probe, which produces acoustic cavitation. The aim has been to examine the intensification achieved in the extent of oxidation due to the generation of additional free radicals/oxidants in the reactor as a result of the presence of chloroalkanes. It has been observed that the extent of increase in the oxidation reaction is strongly dependent on the applied pressure in the case of the LWR. Also, higher volumes of the chloroalkanes favour the intensification and the order of effectiveness is CCl(4)>CHCl(3)>CH(2)Cl(2). However, the results with the ultrasonic probe suggest that an optimum concentration of CH(2)Cl(2) or CHCl(3) exists beyond which there is little increase in the extent of observed intensification. For CCl(4), however, no such optimum concentration was observed and the extent of increase in the rates of oxidation reaction rose with the amount of CCl(4) added. Stage wise addition of the chloroalkanes was found to give marginally better results in the case of the ultrasonic probe as compared to bulk addition at the start of the run. Although CCl(4) is the most effective, its toxicity and carcinogenicity may mean that CH(2)Cl(2) and CHCl(3) offer a safer viable alternative and the present work should be useful in establishing the amount of chloroalkanes required for obtaining a suitable degree of intensification.