Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Far-infrared laser stark spectroscopy of CH3OH and13CH3OH

The high resolution laser Stark spectra of methanol and¹³C-substituted methanol have been studied up to Stark fields of about 60 000V/cm with the HCN and DCN lasers. Numerous families of absorption lines have been observed in both parallel and perpendicular polarizations. For methanol, the transitions J _k =7₅ 6₄ A, _t=0; J _k =11₄ 10₃ E _l , _t=0; and J _k =17₃ 16₂ E₂, _t=0 have been identified while the assignments for¹³C-substituted methanol are J _k =14₈ 15₇ A, _t=0; J _k =15₃ 14₂ A⁺, _t=0; J _k =10₇ 9₆ A, _t=0; and J _k =27₉ 27₈ E₁, _t=0. Zero-field frequencies for the assigned transitions are given with improved accuracy over those calculated from available molecular constants, especially for¹³CH₃OH.     

High-resolution laser spectroscopy of theQ v(0) transitions in solid parahydrogen

Our recent high-resolution laser spectroscopy of theQ _v(0) (=0,J=00) transitions in solid parahydrogen is discussed. The systems studied include the fundamental vibrational bands of impurity D₂ and HD, the first and second overtones of parahydrogen, and the charge-induced spectrum of-ray irradiated parahydrogen. Additionally, Stark and stimulated Raman-gain spectroscopies are applied to the solid. The linewidths are as sharp as 2 MHz HWHM, which is highly unusual for a solid. Our spectra demonstrate a variety of physical phenomena, particularly thek = 0 selection rule, as well asJ = 1/J = 0 pair intermolecular interactions.     

Far-infrared self-broadening and pressure shift measurements of methyl cyanide

Pressure shifts and self-broadening parameters of the J=4342, J=4443, J=5655 and J=6867 sub-bands of the¹A₁ ground state of CH₃C¹⁴N up to K=10 were determined using the NIST tunable far-infrared (TuFIR) spectrometer. The pressure shift agrees well with theoretical predictions made using Anderson-Tsao-Curnutte theory. The self-broadening parameter shows the expected K depencence. However, the predictions are systematically too large for decreasing J. The influence of the TuFIR power spectrum on the derived experimental parameters was evaluated and a comparison was made between two-wave and three-wave mixing spectroscopy.     

Identification and imaging of hot O2 (v″=2, 3, or 4) in hydrogen flames using 193 nm- and 210 nm-range light

Some simple molecules can be excited by light within the tuning ranges of ArF (193–194 nm) and KrF (247.8–248.8 nm) excimer lasers and their fluorescence has been previously used for imaging. Additional wavelength ranges should become available by Raman shifting. As a demonstration, we present excitation and fluorescence spectra from hot O₂ obtained (a) with tunable 193 nm-range light and (b) with that light shifted into the 210 nm range. All measurements are via predissociative upper states. In the 193 nm range, results are compared with those of Andresen's group. In the 210 nm range, the light is tuned to various excitation wavelengths in the (5 3), (8 4), and (7 4) bands of the B–X transition. The (7 4) excitations are well separated and the (7 v) fluoresence spectrum is in accord with Franck-Condon calculations. The wavelengths tend to overlap for the (5 3) and (8 4) excitations and the fluorescence is weaker. State-specific two-dimensional fluorescence images of an H₂-O₂ flame are obtained in both wavelength ranges to illustrate the use of the method.We acknowledge the National Science Foundation and the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research     

Laser stark spectroscopy of13CH3F

The far-infrared laser Stark spectrum of¹³CH₃F has been observed using the 190 m line of the DCN laser. The spectrum was taken at room temperature for both parallel and perpendicular polarizations up to 60,000V/cm. We identify the transition as J_k=32₁₄31₁₄ in the ground vibrational state. The measured zero-field frequency for this transition is in agreement with that calculated from the available molecular constants.     

Far-Infrared Laser Stark Spectroscopy of 1,1 Difluoroethylene

The far-infrared laser Stark spectrum of 1,1 difluoroethylene (H₂C=CF₂) has been investigated with the 311 m line of the hydrogen cyanide (HCN) laser. Numerous families of absorption lines have been observed for both parallel and perpendicular polarizations up to 60 000 V/cm. Three families of resonances have been identified as J(K_a,K_c) = 41(35,7) 40(33,8), 40(36,5) 39(34,6) and 43(35,8) 42(33,9). The Stark shift for the first two transitions can be adequately explained by quasi-first-order calculations, whereas the Stark shift for the third transition requires second-order corrections. The zero-field frequencies for these transitions have been experimentally determined and are reported with fractional uncertainties up to a few parts in 10⁶.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

On the question of the existence of a canonically defined distance function for metrics with indefinite signature on a given manifold

Let be the set of all inner products with a given indefinite signature on a finite-dimensional vector spaceV. It is shown that any continuous pseudometricd on which is canonical, i.e., invariant with respect to all automorphisms ofV, is of the formd(g, h)=f( _g / _h ), where _g , _h denote the volume elements associated withg andh, respectively, andf is a real-valued function; i.e., there are no nontrivial distance functions. This result shows that a reasonable distance function between metric fields on a manifoldM cannot be obtained in terms of canonical distances of the inner products induced in the tangent spaces. A similar result is proved even for uniform structures instead of pseudometrics.     

Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.     

Stochastic gravity

We investigate stochastic gravity as a potentially fruitful avenue for studying quantum effects in gravity. Following the approach of stochastic electrodynamics (sed), as a representation of the quantum gravity vacuum we construct a classical state of isotropic random gravitational radiation, expressed as a spin-2 field,h _µ (x), composed of plane waves of random phase on a flat spacetime manifold. Requiring Lorentz invariance leads to the result that the spectral composition function of the gravitational radiation,h(), must be proportional to 1/ ². The proportionality constant is determined by the Planck condition that the energy density consist of/2 per normal mode, and this condition sets the amplitude scale of the random gravitational radiation at the order of the Planck length, giving a spectral composition functionh() =16c ²L_p/². As an application of stochastic gravity, we investigate the Davies-Unruh effect. We calculate the two-point correlation function (R _iojo(O–/2)R _kolo(O,+/2)) of the measureable geodesic deviation tensor field,R _iojo, for two situations: (i) at a point detector uniformly accelerating through the random gravitational radiation, and (ii) at an inertial detector in a heat bath of the random radiation at a finite temperature. We find that the two correlation functions agree to first order ina/c provided that the temperature and acceleration satisfy the relationkT=a/2c.     

On a Static Solution of the Einstein Equation with Incoming and Outgoing Radiation

The Einstein equation with T = k k + where k, l are null is considered with spherical symmetry and staticity. The solution has a naked singularity and is not asymptotically flat. However, it may be interpreted as an envelope for any static spherical body making it more massive. Such an interpretation and some of its implications are detailed.     

Long-time tails in lattice Lorentz gases

We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ= _{x y} . Both functions showt ^–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt ^–2 andt ^–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters.     

Intensity anomaly in the A2∑+←X2∏ resonant-(2+2) multiphoton ionization spectra of NO

The two-photon resonant four-photon ionization spectra of NO via A²⁺X² (v=0,1) states have been measured. Some intensity-anomalous lines have been found. Based on the signal-power dependence measurement for the normal and anomalous lines, a double resonance and collision ionization model is suggested to elucidate the intensity anomaly.     

On the orientational properties of some one-dimensional model systems

We use the transfer matrix formalism to examine the behavior of some anisotropic hard-core fluids, the centers of whose particles are constrained to a line. At large elongation and pressure, the compressibility factorp/p is higher than that for a system with complete aligment by a factor 1+ that depends upon the molecular geometry. For molecules with a finite radius of curvature, e.g., ellipses,=d/2, while for objects with flat sides=d; hered is the number of orientational degrees of freedom. A connection is made to some recent studies of hard ellipsoid fluids. We also model the effect of an external field on physical adsorption and show the existence of a phase transition in certain limiting situations.     

The asymmetric contact process at its second critical value

The asymmetric contact process onZ has two distinct critical values ₁ > ₂ (at least with sufficient asymmetry). One can consider the process on {0,...,N} and analyze the time (which we call _N ) till complete vacany starting from complete occupation. Its behavior has already been resolved for all regions of except for =₂. For this value, Schinazi proved that lim _N log _N /logN=2 in probability and conjectured that _N /N ² converges in distribution. It is that result that we prove in this paper. We rely heavily on the Brownian motion behavior of the edge particle, which comes from Galves and Presutti and Kuczek.     

Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.     

Honeycomb domain structure

A theory is given of a new structure produced when demagnetizing uniaxial single crystals (e.g. magnetoplumbite) in a field normal to thec axis. The experimental results fully support the theory on the assumption that domain structures produced under normal conditions are metastable. Methods are given by which stable structures can be prepared from such metastable ones. On the basis of these results opinions are expressed as to the nucleation of plate and honeycomb structures, produced either by reducing the field from saturation or by cooling below the Curie point.

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In conclusion the authors would like to thank C. Novák from the Institute of Technical Physics, Czechoslovak Academy of Sciences, for checking the calculation of the harmonic analysis and Z. Málek and J. Eousek for carefully reading the paper and for valuable remarks.