The microwave spectrum of 2,4-dioxabicyclo[3.1.0]hexan-3-one

The R band (26.5–40 GHz) microwave spectrum of 2,4-dioxabicyclo[3.1.0]hexan-3-one is reported. Rotational constants for the ground vibrational state of the common ¹²C₄¹H₄¹⁶O₃ and ¹³C₁, ¹³C₆ isotopically substituted species (the latter observed in natural abundance) have been evaluated. In addition rotational constants of the V_B = 1 to V_B = 5 quanta associated with the bending vibration of the five membered ring have been determined. A partial r_s structure has been calculated:

$\text{r(}\text{C}{}_1\text{?}\text{C}{}_5\text{) = 1.497± 0.016}\text{A}\text{?}\text{, r(}\text{C}{}_1\text{?}\text{C}{}_6\text{) = r(}\text{C}{}_6\text{?}\text{C}{}_5\text{) = 1.522 ± 0.015}\text{A}\text{?}$

,

$\text{∠}\text{C}{}_6\text{C}{}_1\text{C}{}_5\text{= ∠}\text{C}{}_1\text{C}{}_5\text{C}{}_6\text{= 60°32′ ± 1°36′, ∠}\text{C}{}_1\text{C}{}_6\text{C}{}_5\text{= 58°′ ± 1°47′}$

. With certain assumed molecular information a least squares fit yields the following parameters:

$\text{β = 68.5 ± 0.02°, r(}\text{C}{}_1\text{O}{}_2\text{= 1.408 ± 0.004}\text{A}\text{?}$

,

$\text{∠}\text{C}{}_5\text{C}{}_1\text{O}{}_2\text{= 105.8 ± 0.02°, ∠}\text{C}{}_1\text{O}{}_2\text{C}{}_3\text{= 108.10 ± 0.03°}$

,

$\text{∠}\text{O}{}_2\text{C}{}_3\text{O}{}_4\text{= 112.8 ± 0.02°}$

.     

Anomalous temperature dependence of third-order elastic constants in NH4Cl and NH4Br near the λ point

Second order elastic constants of NH₄Cl and NH₄Br crystals were measured under hydrostatic and uniaxial pressures near the λ-type phase transitions. Third order elastic constants were calculated from the pressure derivatives of the second order elastic constants. Results show that the temperature dependences of the third order elastic constants of NH₄Cl differ from those of NH₄Br dramatically. In addition, it is found that the coefficients $\text{1}\text{54}\text{(C}{}_{111}\text{+ 6C}{}_{112}\text{+ 2C}{}_{123}\text{)}$ and $\text{(}\text{1}\text{24}\text{√3)(C}{}_{111}\text{? 3C}{}_{112}\text{+ 2C}{}_{123}\text{)}$ of strains in the free energy of NH₄Cl show quite different temperature dependences from those of NH₄Br.     

The influence of excess oxygen on the elastic properties of non-stoichiometric SrO crystals

Measurements have been carried out of the elastic constants of SrO in the virgin undoped state and of the changes produced in them by equilibrium doping with oxygen at ? 1200°C and oxygen partial pressure of 0.95 atm. The method used was Papadakis' pulse-echo overlap technique in conjunction with thermogravimetric analysis (T.G.A.) to determine mass and density changes due to oxygen doping.The values obtained for C₁₁, C₁₂ and C₄₄ of the virgin crystal at 23°C are

$\text{C}{}_{11}\text{= 17.60 ± 0.03 × 10}{}^{11}\text{dynes/cm}{}^2$

;

$\text{C}{}_{12}\text{= 4.808 ± 0.007 × 10}{}^{11}\text{dynes/cm}{}^2$

;

$\text{C}{}_{44}\text{= 5.577 ± 0.008 × 10}{}^{11}\text{dynes/cm}{}^2$

.(These values are in very good agreement with those of Son and Bartels [2].)Values for $\text{δC}{}_{11}\text{C}{}_{11}$ and $\text{δC}{}_{44}\text{C}{}_{44}$ were found to be ?1.74% and ?0.86% respectively. Accurate valu $\text{δC}{}_{12}\text{C}{}_{12}$ could not be obtained because of sample size limitations after quenching. However, C₁₂ was shown to definitely increase due to doping.Analysis of the results indicate that the elastic modulus changes can only be attributed to the formation of cation vacancies during doping. Analysis of the T.G.A. behavior indicates that this cation vacancy formation is probably associated with the presence of various tripositive cation and uninegative anion species depending upon the impurity concentrations of the sample. This implied impurity-controlled cation vacancy concentration is consistent with the earlier observed extrinsic nature of cation diffusion in SrO at 1200°C.     

Charmed baryon pair production in e+e− annihilation

Cross sections for charmed baryon pair production near threshold in e⁺e^? annihilation are calculated using pole-dominated form factors modified to take intoccount continuum effects. When the C₀⁺$\text{C}$₀^? production cross section is normalized with the help of data for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{p}\text{X}$ it is found that the total charmed baryon production cross $\text{(}\text{C}{}_0\text{C}{}_0\text{,}\text{C}{}_1\text{C}{}_1\text{,}\text{C}{}_1\text{C}{}_1{}^1\text{+}\text{C}{}_1{}^1\text{C}{}_1\text{,}\text{C}{}_1{}^1\text{C}{}_1{}^1\text{)}$ reaches a peak value of approximately 2.7 nb at √s = 5 GeV.     

CLL = (L,L; 0, 0) measurements and a structure due to a P partial wave in the pp system

Measurements of C_LL of pp elastic scattering near θ_c.m. = 90° at thirteen energies between 300 and 800 MeV are reported. These, together with previous values of C_NN, are used to extract values of two quantities, $\text{?}{}_{\mathrm{<mtext>s</mtext>}}$ and $\text{?}{}_{\mathrm{<mtext>t</mtext>}}$, which contain only spin-singlet and only coupled spin-triplet partial waves, respectively. The $\text{?}{}_{\mathrm{<mtext>s</mtext>}}$ curve, which is not dependent on C_LL, exhibits the behavior expected for the previously conjectured ¹D₂ resonance. The $\text{?}{}_{\mathrm{<mtext>t</mtext>}}$ curve also exhibits a resonance-like behavior, which could be due either to the ³P₀ or the ³P₂ partial wave.     

Landau-Placzek ratio of KBr single crystals—I

The Mandel'shtam-Brillouin and Gross scattering was measured for a series of purified KBr crystals. The ratio $\text{I}{}_{\mathrm{G}}\text{2I}{}_{\mathrm{MB}}$, which for a pure, perfect crystal would be the Landau-Placzek ratio, was found to vary with the type of reactive gas treatment used in the final purification. With these crystals both the longitudinal and mixed mode bands were observed with θ and φ equal to 90°. The ratio $\text{I}{}_{\mathrm{L}}\text{I}{}_{\mathrm{M}}$ was in agreement with calculated intensity ratios and the Δμ for these bands gave C₁₁ + C₁₂ = 41.6 GPa and C₄₄ = 5.18 GPa.     

Light scattering study of dispersion and attenuation of hypersound in adamantane

The Brillouin scattering techniques have been used to measure the velocity dispersion of hypersonic acoustic waves in the “high temperature” disordered cubic phase of adamantane. Shear waves, characteristic of the C₄₄ elastic constant, show no significant dispersion. Longitudinal waves propagating in the (001) plane show strong velocity dispersion. The measures have been performed at the same temperature T = 295.7 K. Using a classical single relaxation time model for the dispersion as a function of frequency at temperature T, the L-mode data have been correctly fitted.The importance of the dispersion $\text{(C}{}_{\mathrm{\infty }}\text{? C}{}_{\mathrm{o}}\text{)}\text{C}{}_0$ for the elastic constants is 20% for C₁₁, 51% for C₁₂ #1% for C₄₄ and ?2.8% for $\text{(C}{}_{11}\text{? C}{}_{12}\text{)}\text{2}$. The fitted relaxation time is τ ? 9 × 10^?11 sec.     

α(Q2) corrections to particle multiplicity ratios in gluon and quark jets

The order $\text{α(Q}{}^2\text{)}$ correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. We find

$\text{r=}\text{9}\text{4}\text{1?}\text{αC}{}_{\mathrm{<mtext>A</mtext>}}\text{2π}\text{1}\text{3}\text{+}\text{N}{}_{\mathrm{?}}\text{3C}{}_{\mathrm{<mtext>A</mtext>}}\text{?}\text{2N}{}_{\mathrm{?}}\text{C}{}_{\mathrm{<mtext>F</mtext>}}\text{3C}{}^2{}_{\mathrm{<mtext>A</mtext>}}$

with r=〈n〉_{gluon jet}/〈n〉_{quark jet}. The method used is systematic and could be used for an order α(Q²) calculation.     

Hyperfine structure of CH3OH

Hyperfine structure of the (0, 0, 1) - (1, 0, 1) transition of methanol has been investigated by beam absorption and of the (J, 1, 3?) → (J, 1, 3+) transitions for J = 2, 3, and 6 by beam-maser spectroscopy. The best-fit results for the spin-rotation and spin-spin coupling constants $\text{C}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$ and $\text{D}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$, respectively, are in kHz¹: $\text{C}{}_{101}{}^{\mathrm{(1)}}\text{= 2.4(10)}$, $\text{C}{}_{101}{}^{\mathrm{(2)}}\text{= ?0.6(10)}$, $\text{D}{}_{101}{}^{\mathrm{(1)}}\text{= ?13.8(9)}$, $\text{D}{}_{101}{}^{\mathrm{(2)}}\text{= 7.0(9)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(1)}}\text{= ?5.0(10)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(2)}}\text{= ?5.5(10)}$ and ($\text{C}{}_{\mathrm{J13?}}{}^{\mathrm{(2)}}\text{- C}{}_{\mathrm{J13+}}{}^{\mathrm{(2)}}\text{) = 0.98(9)}$.     

Statistical flow-oscillator modeling of vortex-shedding

The very important engineering problem of modeling the fluid-structure interaction occurring during the shedding of vortices has defied, and will probably continue to defy, a closed form exact solution for the foreseeable future. Therefore, an attempt must be made to extract relevant information about the process in order to be able to have a basic understanding of it for the purpose of analysis. A useful method involves the flow-oscillator concepts of Hartlen and Currie [1] redefined here for stochastic processes. The fluid-structure system is assumed to be governed by the cross-coupled equations

$\text{x}\text{?}\text{(t)+2ξω}{}_{\mathrm{n}}\text{x}\text{?}\text{(t)+ω}{}^2{}_{\mathrm{n}}\text{=C}{}_{\mathrm{e}}\text{(t)pV}{}^2{}_0\text{(t)DL/2m (i)}$

$\text{C}\text{?}{}_{\mathrm{e}}\text{(t)+{α ? βC}{}^2{}_{\mathrm{e}}\text{(t)+γC}{}^4{}_{\mathrm{e}}\text{(t)}}\text{C}\text{?}{}_{\mathrm{e}}\text{(t)+ω}{}^2{}_0\text{C}{}_{\mathrm{e}}\text{(t)=b}\text{x}\text{?}\text{(t), (ii)}$

where these equations govern the structure and fluid oscillators, respectively. The fluid damping is non-linear. These equations are taken as stochastic differential equations because of the many unpredictable, random effects that determine the loading and response. The lift coefficient C_$\text{l}$(t) is assumed to be a zero mean, narrow band process and the velocity V₀, composed of a uniform, constant velocity current plus oscillating wave, a broad band process. The analysis is based on solving equation (i) for x(t) by using Duhamel's integral and substituting its derivative $\text{x}\text{?}\text{(t)}$ into equation (ii). This equation is then used to derive the Fokker-Planck equation for the process C_$\text{l}$(t). To obtain the Fokker-Planck equation, slowly varying variables are replaced by their long-time averages [2] and then the method of stochastic averaging is employed [3, 4]. The moment equation for the lift-oscillator process is derived from the Fokker-Planck equation and, as equation (ii) is non-linear, one finds the moment equation to be in terms of higher order moments. A truncation scheme [5] is used to derive the moment generating function. It is possible then to generate the first and second order statistics of the lift coefficient and the structure response in terms of the empirical parameters of fluid damping. This work was carried out in conjunction with an analysis of ocean wave-current forces with application to offshore fixed structures [6].     

The ultraviolet absorption spectrum of thioformaldehyde

The spectra of H₂CS and D₂CS were surveyed over the wavelength region from 230 to 180 nm and four distinct absorptions were identified. These are assigned to transitions from the $\text{X}\text{?}{}^1\text{A}{}_1$ ground state to the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π, π}{}^1\text{)}$, $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$, $\text{D}\text{?}{}^1\text{A}{}_1\text{(n, 3p}{}_{\mathrm{y}}\text{)}$, and $\text{E}\text{?}{}^1\text{B}{}_2\text{(n, 3p}{}_{\mathrm{z}}\text{)}$ electronic states. A vibrational and rotational analysis of the second system was undertaken. The results indicate that the molecule is planar in the $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$ state and that while the CH and CS bond lengths remain near their ground-state values, the HCH angle increases substantially.     

Elastic moduli and mode gammas of GaP: Their relationship to those of other isomorphic crystals and the high pressure structural-electrical transition

The transit times of ultrasonic waves associated with piezoelectrically inactive modes have been measured in sulfur-dope, n-type GaP using hydrostatic pressures up to 5 kbar. The velocities and elastic constants of most modes increase linearly with pressure but $\text{C}{}_{\mathrm{S}}\text{=}\text{1}\text{2}\text{(}\text{C}{}_{11}\text{?}\text{C}{}_{12}\text{)}$ decreases slightly. The behavior of the elastic constants and their associated mode gammas are compared to those of other III–V compounds and of Si and Ge. We suggest that the behavior of C_S is related to the occurrence of the structural-electrical transition which occurs at high pressure. A modified Born criterion for lattice stability developed by Demarest $\text{et}$$\text{al}$. is used to explain this relationship. The contribution of thermal dilatation to the temperature dependence of each elastic constant is deduced. Using it and data from the literature we find that the explicit thermal contribution to each elastic constant is significant and in the case of C₁₂ has an anomalous sign.     

“Forbidden” rotational spectra of symmetric-top molecules: PH3 and PD3

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been constructed for observation of extremely weak millimeter-wave spectra of gases. It has been used to measure J → J, K = 0 ← 3 transitions in PH₃ and J → J, K = 0 ← 3 as well as K = ±1 ← ±4 transitions in PD₃. The B₀ and C₀ spectral constants (in MHz) are: for PH₃, B₀ = 133 480.15 ± 0.12 and C₀ = 117 488.85 ± 0.16; for PD₃, B₀ = 69 471.10 ± 0.03 and C₀ = 58 974.37 ± 0.05. The effective ground-state values obtained for the bond angle and bond length are: for PH₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.420}{}_0$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.34}{}_5$; for PD₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.417}{}_6$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.35}{}_9$. The corresponding zero-point-average values were calculated to be: for PH₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4269}{}_9\text{± 0.0002}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.228}{}_7$; for PD₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4226}{}_5\text{± 0.0001}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.256}{}_7\text{± 0.004}$. For both species, the equilibrium values are $\text{r}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{) = 1.4115}{}_9\text{± 0.0006}$ and $\text{α}{}_{\mathrm{e}}\text{(}{}^{\mathrm{o}}\text{) = 93.32}{}_8\text{± 0.02}$.     

Infrared bands of 12C2HD

The rotational structure of about 40 bands of ¹²C₂HD observed in the region 6000?600 cm^?1 has been measured and interpreted with the purpose of determining a comprehensive set of molecular constants for this isotopic variety of acetylene. Combining these data with the results for ¹²C₂H₂ and ¹²C₂D₂, a reevaluation of the equilibrium internuclear distances for the acetylene molecule has been made: $\text{r}{}_{\mathrm{e}}\text{(CH) = 1.06215 ± 17 × 10}{}^{\mathrm{?5}}\text{A}\text{?}$ and $\text{r}{}_{\mathrm{e}}\text{(CC) = 1.20257 ± 9 × 10}{}^{\mathrm{?5}}\text{A}\text{?}$ were obtained. This paper presents all the molecular constants derived in this study.     

The renormalization of the string operator in QCD

We shall observe that the renormalization of the string operator U(x₁, x₂; C) = Pexp{ig∫_x1^x2dx_μA^μ(x)} with an open path C (smooth and non-intersecting) is path-independently performed in any order of perturbation. To demonstrate this, the renormalization constants will be calculated up to order g⁴. Next the renormalization effect on the algebraic identity $\text{U(x}{}_1\text{, x}{}_2\text{;}\text{C}\text{)U(x}{}_2\text{, x}{}_3\text{;}\text{C}\text{) = U(x}{}_1\text{, x}{}_3\text{;}\text{C}\text{∪}\text{C}\text{)}$ will be discussed and it will be proved that the renormalization preserves the algebraic identity in any order of perturbation if the paths C and $\text{C}$ are smoothly connected at x₂. Finally, the string operator renormalization is extended to the case when the path C is smoothly closed (the Wilson loop operator). It is then shown that the renormalization factor which multiplicatively renormalizes the string operator in the case of the open path, is cancelled in any order of perturbation by the divergence appearing in the coincidence of the end points. As a results, the Wilson loop operator can be renormalized by the coupling constant renormalization alone.     

Information on the dynamics of the reaction KN → K1N from KLN interactions

If $\text{K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{is a K}{}^1$ resonance decaying into K_S,L (the short- and long-lived kaon) and a neutral system S^o of pions, one can isolate the C-even and C-odd, crossed-channel contributions to $\text{KN → K}{}^1\text{N}$ by using the reactions $\text{K}{}_{\mathrm{L}}\text{N → K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{N}$ whether S^o is a C-eigenstate, or a mixture of C-even and C-odd states. Applications to the production of K¹(890) and the Q-meson are discussed, and simple numerical predictions made for Q_S,L production. Q-production data indicate approximate t-channel helicity conservation for the ω and P' exchanges at vertices involving a spin change, in similarity to the belief for the pomeron. Q_S,L production data can give information also on Q-decays.     

Electrical and structural properties of iron-doped β-alumina

β-alumina containing 50 w/o Fe exhibits high electronic conductivity when sintered in air but Mössbauer studies have shown the presence of Fe₃O₄. Single-phase β-alumina containing 50 w/o Fe could be prepared by sintering at 1400°C for 4–4.5 h followed by annealing at 1300°C for 96 h encapsulated with coarse β-alumina powder enriched with Na₂CO₃. Mössbauer spectroscopy indicated that all iron was present as Fe(III). Complex-plane impedance data showed a maximum bulk $\text{σ}{}_{\mathrm{25°C}}\text{= 5.56 × 10}{}^{-4}\text{(Ω cm)}{}^{-1}$ with little electronic conductivity. Reduction treatments on Fe-doped β-alumina utilizing H₂:N₂ gas were successful in producing a mixed conductor containing Fe(II) and Fe(III) but also produced a distorted β-alumina lattice. This material exhibited an electronic conductivity $\text{σ}{}_{\mathrm{e,25°C}}\text{= 2 × 10}{}^{-4}\text{(Ω cm)}{}^{-1}$ and a bulk ionic conductivity $\text{σ}{}_{\mathrm{b,25°C}}\text{= 1.35 × 10}{}^{-4}\text{(Ω cm)}{}^{-1}$.     

Third order elastic constants of rubidium chloride

The third order elastic constants of RbCl, determined by measurements of the static stress dependence of ultrasonic waves, are found to be (in units of 10¹²$\text{dynes}\text{cm}{}^2$)

$\text{C}{}_{111}\text{= ?6.71 ± 0.1 C}{}_{123}\text{= 0.05 ± 0.07}$

$\text{C}{}_{112}\text{=?0.18 ± 0.04 C}{}_{144}\text{= 0.11 ± 0.02}$

$\text{C}{}_{166}\text{=?0.17 ± 0.01 C}{}_{456}\text{= 0.4 ± 0.01}$

. The calculation of third order constants using a rigid ion Born model is briefly discussed, and results are compared to the measurements. The comparison qualitatively supports the model, but no quantitative evaluation of the repulsive interaction is possible.     

Pressure dependence of elastic behaviour and force constants of GaP

The six third order elastic constants of GaP have been obtained from measurements of the effect of hydrostatic and uniaxial pressures on ultrasonic wave velocities. The valence force field model has been used to obtain the bond-bending and stretching force constants. Confirmatory evidence is added to the hypotheses that zinc blende structure crystals undergo the densification transition under pressure when (1) a modified Born stability criterion that $\text{1}\text{2}\text{(C}{}_{11}\text{? C}{}_{12}\text{)}\text{B}$ equals about 0.2 is reached at the phase transition pressure P_t, and (2) the ratio $\text{β}{}_{\mathrm{t}}\text{α}{}_{\mathrm{t}}$ of the second order bond-bending β_t to bond-stretching α_t, force constants is about 0.1. These findings suggest that a macroscopic shear takes place at the transition     

Acetylene fluorescence

Previously unobserved acetylene ${}^1\text{A}{}_{\mathrm{u}}\text{(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{) →}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ fluorescence occurs following 1933-Å ArF laser excitation of C₂H₂ or C₂H₄ and their deuterated analogs in solid Ne and Ar hosts at 4.2 K. Acetylene is a photolysis product of matrix-isolated ethylene. Ground-state vibrational levels as high as ν″₃ = 30 of the degenerate ν₃ bending vibration are observed for C₂D₂. Only ν₃ is appreciably active in the fluorescence. The negative ν₃ anharmonicity, previously observed in the gas phase, also occurs in Ne host. Consideration of rotational selection rules indicates that the Ne host strongly hinders free rotation about the low-moment-of-inertia $\text{a}\text{?}$ axis in the excited state.