Lifetimes of high Rydberg states of methyl halides

The lifetimes of high Rydberg states of the methyl halides CH₃I, CH₃Br and CH₃Cl have been studied. A pulsed dye laser tuned near half the ionization energy was used, with preprogrammed field pulses, and the high Rydberg states of the compounds in selected ranges of n values were ionized after a variable delay. Plots of the electron signal versus delay yielded information about the Rydberg state lifetime. The clearest trend was found for around n = 120–160: the lifetimes of the states decreased by more than an order of magnitude from CH₃I (τ ≈12.3 μs) through CH₃Br to CH₃C1. Within the range studied, the theoretically predicted increase in lifetimes (n ⁵ or n ³) was not found, and in fact the highest group of states studied (with n > 215) exhibited for all three compounds relatively short lifetimes (≈2-3 μs), possibly due to collisional processes.     

Observation of the fast component in the fluorescence of gaseous SO2 excited to the A1A2 state in the presence of a magnetic field

Effects of an external magnetic field (B) on the SO₂ fluorescence have been examined under excitation of the ‘C’ band and the single rotational levels of the ‘B’ and ‘E’ bands of the A(¹A₂) ← X¹A₁ transition. For the ‘C’ band, the total SO₂ fluorescence was studied, while for excitation of the single rotational levels, fluorescence of the single rotational lines of (^rR₅(5) (31711 cm^-1), ^pP₇(7) (31662 cm^-1)) (‘E’ band) and of (^rR₈(8) (31000 cm^-1), ^pP₁₀(10) (30927 cm^-1)) (‘B’ band) was studied. Decay of the SO² fluorescence was studied with nanosecond time resolution in the 1?5–50 mTorr region. In the presence of a magnetic field, decay of the total SO₂ fluorescence and of the fluorescence belonging to the single rotational lines were fitted by the bi-exponential functions. In the case of the total SO₂ fluorescence, this function also includes the time independent term, which, however, is dependent on a magnetic field. The time independent term belongs to the long-living component, which can be approximated by a constant in the time-scale studied. Radiationless processes induced by an external field were directly observed. The magnetic field and pressure dependences of the processes induced by a field were studied under excitation of the SO₂ fluorescence by light of a different wavelength. The data obtained were explained by the direct mechanism.     

Structure of atoms and fields

In a previous paper the theory of the toroidal spiral field was employed to derive equations for the stationary orbits of particles that belong to both the atomic nucleus and electrons orbiting the nucleus. This theory offered new relativistic relationships for both the mass and electrical charges, leading to the existence inside the nucleus of particles with not only opposite electrical charges in comparison with the electrons, but also with the masses of opposite sign. In this paper, this theory was applied to create a model of the atom that consists of positive and negative muons, positrons and electrons. The two methods that are used to determine the stationary orbits of particles are: (1) quantizing the particle angular momentum, and (2) quantizing the particle relative electrical charge. The existence of particles with the charges 1/3 and 2/3 is explained by the relativistic dependence of the electrical charges on the particle velocity and also by the quantum character of these charges. Creation of the particles and their distribution in the orbits follows the proposed rule of duality and the rule of stability. The theory describes the processes of creation, excitation and annihilation of the positron-electron pairs inside the atoms. In addition, it explains the nature of the self-sustaining movement of particles inside the atom and illustrates the similarity between the propagation of the positron--electron pair inside the atom and the propagation of electromagnetic waves in a free space. It gives a novel interpretation of the physical meaning of Maxwell's displacement current and demonstrates that electromagnetic fields are intimately associated with electrical charges.     

Constructive analysis of Takens-Bogdanov points with Z2-symmetry

Assuming a 2-parameter-dependent family of smooth Z₂-equivariantvector fields, a symmetry-breaking Takens-Bogdanov point isconsidered as an isolated organizing centre. Two branches ofsymmetry-breaking and asymmetric Hopf bifurcation points aswell as one branch of Z₂-pitchforks which emanate from the organizingcentre are analyzed via asymptotic expansions. Leading termsof these expansions are calculated explicitly. The input dataare differentials (up to third order) of the mapping evaluatedat the organizing centre along specified directions.     

An Error Estimate for a Finite-element Approximation of an Elliptic Variational Inequality Formulation of a Hele--Shaw Moving-boundary Problem

It is the purpose of this paper to estimate the error in thefinite-element approximation of a variational inequality formulationof a moving-boundary problem arising in Hele-Shaw flow. Linearfinite elements on a triangulation of a polygonal approximationof the domain are used. The novelty of the problem lies in thetime dependence, the semi-coercivity of the bilinear form andthe change in domain. To analyse the approximation, operatorsare introduced which split the space H1. Order h convergenceis proved in the H¹-Sobolev norm.     

On approximate approximations using Gaussian kernels

This paper discusses quasi-interpolation and interpolation withGaussians. Estimates are obtained showing a high-order approximationup to some saturation error negligible in numerical applications.The construction of local high-order quasi-interpolation formulasis given. Supported in part by the International Centre for MathematicalSciences, Edinburgh.     

Corroding the chromium cation

Two [Cr,O₂]⁺ isomers have been selectively produced and studied by FT-ICR mass spectrometry. The Cr(O₂)⁺ complex was formed by supersonically expanding a plasma produced by laser vaporization of chromium metal with the helium carrier gas, which was seeded with traces of oxygen, while the chromyl cation is formed in an expansion with N₂O. The complex is stable against thermal collisions, but in a bimolecular reaction with water it is rapidly converted to the chromyl cation, with ligand exchange being only a minor side reaction. Isotopic studies suggest a side-on geometry for Cr(O₂)⁺, in accordance with density functional (B3LYP) calculations. The present work indicates that an investigation of the selected isomers can indeed be carried out, if appropriate chemical methods for the ion generation are applied.     

Quenching of SO2 phosphorescence by a magnetic field

Phosphorescence excitation spectra of the ã³B₁← [Xtilde]¹A₁ transition of SO₂ were measured in the absence and presence of a magnetic field (B = 0?44 T², P(SO₂) = 0?7 Torr). The absorption and phosphorescence excitation spectra of the ã³B₁← [Xtilde]¹A₁ transition of SO₂ measured in the absence of a magnetic field show that the relative intensity of the bands of the phosphorescence excitation spectrum is smaller than the relative intensity of the corresponding bands of the absorption spectrum beginning with the (0, 2, 0) band. In the presence of a magnetic field, the intensity of the phosphorescence excitation band falls, for ν_exc> 26400 cm^-1. Under the direct excitation of the ã³B₁← [Xtilde]¹A₁ transition, the dependence of the magnetic quenching of the SO₂ phosphorescence on the excitation frequency (ν_exc) was studied at P(SO₂) = 0?7 Torr and B = 0?44 T. The dependence of the magnetic field effect on ν_excshows that only the vibrationally excited levels of the ã³B₁ state are sensitive to an external magnetic field. The magnetic field strength and the pressure dependence of the magnetic field effects were studied under indirect excitation of the ã³B₁← [Xtilde]¹A₁ transition at λ_exc = 308 nm. The magnetic field and the pressure dependence were investigated for pure SO₂ and for SO₂ + RH (RH n-C₅H₁₂) mixtures. It was found that the magnetic field effect was saturated at B ? 0?25 T. The saturation value (Gr = l(0?3 T)/l(0)) increases with increasing gas pressure. The magnetic field, the pressure and the excess vibrational energy (ν_excess) dependence of the magnetic quenching of SO2 phosphorescence show that the data observed can be explained by an indirect mechanism within the framework of a low level density approximation.     

Magnetic field effect on the H2CS fluorescence from the first excited singlet state Ã1A2

Fluorescence intensity in thioformaldehide vapours (H₂CS), excited to the ÃA₂ different vibronic levels of the ùA₂ ? [Xtilde]¹A₁ transition, were measured as a function of an external magnetic field. On excitation to these levels, dynamics in zero and non-zero field may be described in the small-molecule limit, with fluorescence exhibiting an almost exponential decay. A magnetic field changes the integrated intensity and decay lifetime of the thioformal-dehide fluorescence induced from different vibronic levels of the ù A₂ state. We found that the magnetic field effect grows at lower gas pressures. The measured field dependences of the magnetic field effect can be fitted using field-saturated functions. The measured data were explained by the indirect mechanism theory (nuclear-spin and electron-spin decoupling mechnism).     

Probabilistic Inductive Classes of Graphs

A unifying framework—probabilistic inductive classes of graphs (PICGs)—is defined by imposing a probability space on the rules and their left elements from the standard notion of inductive class of graphs. The rules can model the processes creating real-world social networks, such as spread of knowledge, dynamics of acquaintanceships or sexual contacts, and emergence of clusters. We demonstrate the characteristics of PICGs by casting some well-known models of growing networks in this framework. Results regarding expected size and order are derived. For PICG models of connected and 2-connected graphs order, size and asymptotic degree distribution are presented. The approaches used represent analytic alternative to computer simulation, which is mostly used to obtain the properties of evolving graphs.