Resistive MHD-equations for Tokamaks with arbitrary β and cross section

The complete set of hydromagnetic equations for the vector potential A and the momentum density a ≡ ?ν is transformed into a form appropriate for toroidal geometry. The toroidal components are represented by the usual poloidal flux functions Ψ and ψ, respectively, for which the equations of motion are derived. The poloidal components A_⊥ and a_⊥ are given by four potentials $\text{Φ}$, U, and φ, u for which we obtain Poisson equations in the poloidal plane. The corresponding source terms define the remaining variables, namely, $\text{Λ = ? · A, Ω = (? × A)}{}_{\mathrm{\zeta }}\text{/R, λ = ? · a, and ω = (? × a)}{}_{\mathrm{\zeta }}\text{/R}$, for which equations of motion are also derived. Finally, we find that in the limit of small toroidicity the scaling laws previously used are not applicable for toroidal geometry, and that the effort to obtain numerical solutions is not dramatically higher than without using any scaling law.     

Tetravalent vanadium in CaF2 and SrF2 crystals: An EPR study

An EPR study of tetravalent vanadium centers created by room temperature X-irradiation in CaF₂ and SrF₂ is presented. The production efficiency of these centers is enhanced by previous annealing of the samples at 1000 K in air. The symmetry of V⁴⁺ ions is tetragonal and its EPR spectrum can be described by an axial spin Hamiltonian including a Zeeman and hyperfine term with $\text{S =}\text{1}\text{2}$ and $\text{I =}\text{7}\text{2}$ (corresponding to ⁵¹V nuclei). The following values for the spin Hamiltonian parameters are obtained g_∥ = 1.947 ± 0.002, g_⊥ = 1.935 ± 0.005, A_∥ = 500 ± 5 MHz, A_⊥ = 150 ± 10 MHz in the case of SrF₂ and g_∥ = 1.945 ± 0.002, A_∥ = 505 ± 5 MHz and A_⊥ < 200 MHz, in the case of CaF₂. A model for the center including an interstitial O^2? ion is tentatively proposed.     

Anomalously enhanced plasma diffusion transverse to a magnetic field in n-Ge

From the broadening of a narrow plasma sheet drifting along E_x × B, we measured the transverse diffusion coefficient D_⊥ in n-Ge. Contrary to the classical theory, D_⊥ increases with the electric field E_x, increases with the magnetic field B up to μ⁺B ≈ 1, and decreases proportional to $\text{1}\text{B}$ in higher magnetic fields. The transverse drift velocity v_⊥ measured simultaneously shows a classical behavior over the whole field ranges of E_x = 3–110 $\text{V}\text{cm}$ and B = 0.1–2.3T, which were used in our experiment.The results correspond to those gained previously in n-InSb[13,14]. However, whereas in InSb plasma instabilities were observed together with the anomalous diffusion, no instabilities could be found in Ge. Various ways to arrive at an explanation of the anomalous effect are discussed and possible applications are indicated.     

On the bifurcations occurring in the parameter space of the sixteen vertex model: II. Bifurcations arising from degeneracies in the N-matrix

The analysis of the bifurcation structure in the 16-dimensional parameter space of homogeneous (sixteen-) vertex models, started in part I, is completed in this paper. As before equivalence classes of models having the same partition function are identified by means of a 4 × 4 diagonal matrix N and a pair of characteristic (2 × 2)-matrices A and B. The bifurcation classes of models studied in this part include also classes for which the N-matrix shows degeneracies.The four primary bifurcation classes, uncovered in part I, i.e. the general- and complementary eight-vertex models and the one sided- and doubly cyclic models, each give rise to a hierarchy of two kinds of subbifurcations: on the one hand the models corresponding to the different patterns of degeneracies of the N-matrix, and on the other hand the models for which the “rotation angles” α and β characterizing the matrices A and B have values $\text{α =}\text{2π}\text{n}{}_{\mathrm{a}}$ and $\text{β =}\text{2π}\text{n}{}_{\mathrm{b}}$ respectively, with n_a and n_b integers.     

Rate coefficient and transition probability of XeO

Rate coefficients of XeO(¹S) at various vibrational levels (v = 0, 1 and 2) were observed by measuring absolute intensities of the spectrum in the low-pressure d.c. glow of an Xe-O₂ mixture discharge. The association coefficients at the various levels are K_a0 = 2.4×10^-34 cm⁶ at v = 0, K_a1 = 1.1 × 10^-34 cm⁶ atv = 1, and K_a2 = 9.1 × 10^-35 cm⁶ at v = 2. The transition probability from XeO(¹S)₀ to $\text{XeO(}{}^1\text{D)u}$ is estimated to be A₀ = 1.3 × 10⁵ sec^-1.     

Infrared diode laser spectroscopy of the PO radical

Vibration-rotation transitions of the PO radical in the X²Π_r state have been observed by a tunable infrared diode laser spectrometer. The analysis of the observed spectra gave the molecular constants in the v = 1 state and the band origin to be B = 0.7250107(36), D = 1.0253(60) × 10^?4, A_J = 0.997(24) × 10^?4, p = 0.006323(33), A₁ - A₀ = 0.16354(78), and ν₀ = 1220.24901(43), all in cm^?1 units with three standard errors in parentheses, where the v = 0 parameters were fixed to the values previously reported. The equilibrium internuclear distance was determined to be $\text{r}{}_{\mathrm{<mtext>e</mtext>}}\text{= 1.476370(15)}\text{A}\text{?}$.     

Microwave spectrum,torsional excitation energy,partial structure,and dipole moment of oxiranecarboxaldehyde

The microwave spectrum of oxiranecarboxaldehyde (glycidaldehyde) has been studied in the 8–40 GHz region. Transitions in the ground and first seven excited states of the torsional motion of the aldehyde group have been assigned for the species with the oxygen atom of the aldehyde group trans to the oxirane ring. The v = 0 to v = 1 torsional excitation energy is estimated to be 140 ± 10 cm^?1. The population of any other torsional conformer is less than 5% of the trans species at 200 K. Structural parameters were derived from rotational constants of the three singly substituted ¹³C species, whose spectra were observed in natural abundance. Substitution parameters are $\text{r}{}_{\mathrm{<mtext>CC</mtext>}}\text{(ring) = 1.453 ±0.025}\text{A}\text{?}$, $\text{r}{}_{\mathrm{<mtext>CC</mtext>}}\text{(ald.) = 1.469 ± 0.010}\text{A}\text{?}$, ∠CCC = 119.8 ± 2.0°. The dipole moments determined by means of the Stark effect are μ_a = 1.932 ± 0.005 D, μ_b = 1.511 ± 0.017 D, and μ_c = 0.277 ± 0.156 D, with μ_t = 2.469 ± 0.031 D.     

Existence of three scaling regions at large transverse momentum

A model for large p_⊥ production, yielding three different scaling relations in different regions of s and p_⊥ is presented. The couplings may be chosen such that $\text{1}\text{s}{}^4$ scaling is valid at present energies while at higher energies $\text{1}\text{s}{}^2$ scaling should manifest itself.     

Electron paramagnetic resonance of 61Ni+ in CuGaS2

EPR of ⁶¹Ni⁺ doped CuGaS₂ at 4.2 K leads to the following experimental data: $\text{g = 1.918 ± 0.006 A  < 12 × 10}{}^{-4}\text{cm}{}^{-1}\text{, g}{}_{\mathrm{\perp }}\text{= 2.328±0.006 A}{}_{\mathrm{\perp }}\text{= (65±2) × 10}{}^{-4}\text{cm}{}^{-1}$. High axial field splitting of ²T₂ state stabilizes the center against Jahn-Teller interaction. Covalency reduction factor k is 0.76.     

Experimental means for distinguishing models of large p⊥ inclusive scattering

The scaling behavior, and to some extent the magnitude, of the ratio $\text{γ}\text{π}$ of large p_⊥ direct photon and pion inclusive production cross sections are shown to provide an excellent means of determining the fundamental mechanism of large p_⊥ scattering.     

Second-order Coriolis resonance between ν2 and ν5 of CH3F by microwave spectroscopy

The J = 1 ← 0 and J = 2 ← 1 transitions and the l-doubling transitions of J = 2 – 6 of ¹²CH₃F in the ν₂ and ν₅ states were analyzed by taking into account the Coriolis interaction between the two modes. The molecular constants which are derived are: ν₅ - ν₂, 252 412 ± 112; $\text{B}{}_5{}^1$, 25 611.60 ± 0.40; A_ζ5, ?38 772 ± 116; $\text{B}{}_2{}^1$, 25 432.52 ± 0.33; D, 21 838.4 ± 8.2; $\text{q}{}_5{}^1$, 39.58 ± 0.30 MHz; in addition to a few other minor constants. The present result is completely consistent with the recent Raman data of Escribano, Mills, and Brodersen, J. Mol. Spectrosc.61, 249 (1976). Molecular constants in the ν₃ and ν₆ states have also been obtained: B₃, 25 197.570 ± 0.020; B₆, 25 418.917 ± 0.047; A_ζ6ηJ, ?0.562 ± 0.030; |q₆|, 8.70 ± 0.13 MHz. Errors are 2.5 times the standard deviations.     

Anisotropy of X-ray critical scattering in 4,4-di-n-hexyl-biphenyl liquid crystal

We have carried out a high-resolution X-ray critical scattering experiment in the isotropic phase connected with the isotropic-smectic-B transition in 4,4-di-n-hexyl-biphenyl. The measurements yield the following parameter values: $\text{d = 23.92}\text{A}\text{?}$, $\text{q}{}_0\text{= 0.268}\text{A}\text{?}{}^{\mathrm{?1}}$ and the critical exponents γ = 1.51 ± 0.12, ν_∥ = 0.65 ± 0.06, ν_⊥ = 0.70 ± 0.08. At the temperature t = 10^?3 ($\text{t =}\text{T}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{?1}$) the correlation lengths are $\text{ξ}{}_{\mathrm{\parallel }}\text{= 390}\text{A}\text{?}$ and $\text{ξ}{}_{\mathrm{\perp }}\text{= 1080}\text{A}\text{?}$.     

The D′ → A′ transition in I2

A detailed vibrational analysis is given for the D′(2g) → A′(2u³Π) transition (3300–3460 Å) in I₂. The assignments include ～ 150 v′-v″ bands in ¹²⁷I₂ and ～100 in ¹²⁹I₂, spanning v′ levels 0–15 and v″ levels 4–30. These bands are mainly red-degraded but include some violet-degraded and line-like features. The analysis is corroborated by Franck-Condon and band profile calculations. The least-squares fit yields the following constants (cm^?1); ΔT_c = 30 340.8, ω′_e = 103.95, ω_eχ′_e = 0.206, ω″_e = 106.1, ω_eχ″_e = 0.81. Anomalous behavior in the vibrational level structure above v″ = 23 makes the extrapolation to the A′ dissociation limit uncertain, so the absolute energies of both states remain ill-defined. However there is a possibility that the D′ state is the state labeled α by King et al. [Chem. Phys. 56, 145–156 (1981)], in which case the energies are known precisely. There is evidence of weak emission from at least two other electronic transitions in this spectral region, probably $\text{D(0}{}^{\mathrm{+}}\text{u) → X(}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ ($\text{λ}\text{< 3300}\text{A}\text{?}$) and β → A(1u³Π) ($\text{λ}\text{> 3300}\text{A}\text{?}$).     

New evaluation of muon (g − 2) hadronic anomaly

The hadronic part a_H of the muon g-factor anomaly $\text{a ≡}\text{(g ? 2)}\text{2}$ is evaluated from latest data on σ(e⁺e^? → hadrons). For a p-wave ππ scattering length of a₁ = 0.04±0.005 we calculate a_H = (66±10) × 10^?9, compared to a(experiment) ? a(QED) = (60±29) × 10^?9. Half of the uncertainty on a_H is associated with the energy interval $\text{0.92 <}\text{s}\text{< 2}\text{GeV}$.     

Formaldehyde as a semirigid bender: The rotation-inversion spectrum in its Ã1A2 excited state

The semirigid bender Hamiltonian [Bunker and Landsberg, J. Mol. Spectrosc.67, 374–385 (1977)] was used to fit the rotation-inversion energy level separations in the $\text{A}\text{?}{}^1\text{A}{}_2$ excited state of formaldehyde. We fix the r⁰(CH) bond length and allow the R(CO) bond length and (H?H) bond angle to vary with the inversion angle ρ. The fit to 64 rotation-inversion energies (with v₄ and J < 4) is significantly better with a standard deviation of 0.199 cm^?1 than when the rigid bender [Bunker and Stone, J. Mol. Spectrosc.41, 310–332 (1972)] is used. The barrier height to planarity is 358 cm^?1 and the equilibrium ρ_e = 34.7°. The CO bond length is found to decrease by 0.034 from 1.3670 Å and the H?H angle by about 6 from 122.4° as the molecular configuration changes from planar to pyramidal. The rigid bender model developed earlier by Moule and Rao for formaldehyde [J. Mol. Spectrosc.45, 120–141 (1973)] is then used to fit the 32 rotation-(out-of-plane) bending energy levels (with v₄ = 0 and 1) of the $\text{X}\text{?}{}^1\text{A}{}_1$ ground electronic state of H₂CO. For this, a simple potential consisting of quadratic and quartic terms is used and the standard deviation of the fit is 0.148 cm^?1.     

Reexamination of the I2 spectrum near the B(3Π0u+) state dissociation limit

The disagreement of Danyluk and King's (Chem. Phys.25, 343 (1977)) rotational constants for levels lying near the dissociation limit of B-state I₂ with the mechanical behavior predicted by near-dissociation theory is investigated. The discrepancies are shown to be much too large to be explained by either the neglect of centrifugal distortion effects in the original analysis or by rotational or spin-rotation coupling to a nearby repulsive 1_u state. These differences are therefore attributed to experimental error, a conclusion which is confirmed by more recent experimental results. A reanalysis of the best available data for levels near the dissociation limit of B-state I₂ then yields improved values for the B-state dissociation limit $\text{D}$ = 20 043.16 (±0.02) cm^?1 of the vibrational index at dissociation v_$\text{D}$ = 87.32 (±0.04) and of the long-range potential constant $\text{C}{}_5\text{= 2.88 (±0.03) × 10}{}^5\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^5$. This in turn implies a slightly improved ground-state dissociation energy of $\text{D}$₀ = 12 440.18 (±0.02) cm^?1.     

Microwave spectral study of 2-fluorophenol: cis conformer

The microwave spectra of 2-fluorophenol and its deuterated species have been observed and analyzed in the frequency ranges 12.5–18.0 GHz (KU band) and 21.5–26.0 GHz (K band) in the ground vibrational state at room temperature. For the normal species, the radio frequency-microwave double resonance spectrum has been recorded in the frequency range 30.0–38.0 GHz. Three rotational and five quartic centrifugal distortion constants for the normal species, $\text{A}\text{?}\text{= 3337.86 ± 0.02}$, $\text{B}\text{?}\text{= 2231.92 ± 0.01}$, $\text{C}\text{?}\text{= 1337.52 ± 0.01}$, d_J = (3.5 ± 2.9) × 10^?4, d_JK = (?4.9 ± 1.5) × 10^?3, d_K = (?3.2 ± 1.0) × 10^?3, d_WJ = (?2.0 ± 1.0) × 10^?7, d_WK = (2.6 ± 0.8) × 10^?6 (in MHz), and three rotational constants for the deuterated species, $\text{A}\text{?}\text{= 3324.70 ± 0.03}$, $\text{B}\text{?}\text{= 2177.95 ± 0.03}$, $\text{C}\text{?}\text{= 1315.96 ± 0.03}$ (in MHz), have been obtained. Consideration of the r_s coordinate of the hydroxyl hydrogen atom leads to the assignment of the spectra to the cis conformer of the molecule. An r₀ structure for the cis conformer has been proposed. The nonbonded OH ? F distance is lower by about 0.3 Å than the sum of the van der Waals radii.     

NMR study of hydrogen diffusion in uranium hydride

The diffusion of hydrogen in uranium hydride is studied employing the NMR technique. From measurements of spin-spin relaxation time T₂, the activation energy for hydrogen diffusion in β-UH₃ is determined to be $\text{E}{}_{\mathrm{a}}\text{= (19.25 ± 0.4)}\text{kcal}\text{mole}$ and the preexponential factor to be A₀ ≈ 5 × 10¹⁴ Hz. It is shown that these results are in fair agreement with spin-lattice relaxation time T₁ data. Assuming that hydrogen diffusion proceeds via vacancies whose concentration is temperature dependent, it is concluded that E_a is the sum of the energies of vacancy formation and barrier height, and that A₀ contains an entropy change factor. Using vacancy concentration data calculated by Libowitz, we estimate the barrier height energy to be E_b ≈7 kcal/mole. Using a value for the frequency of hydrogen vibration v₀ determined from inelastic neutron scattering by Rush et al., we estimate the entropy change due to vacancy formation and the hydrogen atom jump to be about $\text{S}\text{k}{}_{\mathrm{B}}\text{≈3}$. Similar measurements on samples containing less hydrogen than is needed to compose stoichiometric UH₃, show that the rate of diffusion is enhanced by the presence of excess metal in the sample. The jump frequency at 500°K in UH₃ is found to be approximately 10⁶ Hz while for the two-phase samples of H/U = 2.8 and 2.5, it is larger by a factor of about 3 and 3.5, respectively.     

Rotational spectrum of sulfuryl bromide fluoride

The rotational spectra of SO₂⁷⁹BrF and SO₂⁸¹BrF have been obtained between 18 and 40 GHz. Both molecules are near-prolate symmetric rotors with a and b-type dipole components. A least-squares fit of the observed moments of inertia obtained by correcting for the bromine quadrupole interaction yields $\text{r}\text{(SBr) = 2.155 ± 0.006}\text{A}\text{?}$ and ? FSBr=100.6°±1.5° structural parameters when $\text{r}\text{(SO) = 1.407}\text{A}\text{?}$, $\text{r}\text{(SF) = 1.56}\text{A}\text{?}$, and ? OSO=123.7° are assumed.     

A note on the compression of cubic ZnS

Using X-ray diffraction the compression of cubic ZnS (sphalerite) has been measured to 9.4 GPa under hydrostatic pressure conditions. The results analysed using a two parameter Birch-Murnaghan equation may be presented by K₀ = 74.8 ± 3.2 GPa and K′₀ = 4.91 ± 1.2. These compare well with 3.76 ± 0.96 for K₀ = 76.5 GPa, the value calculated by Chang and Barsch from their wurzite data. $\text{Δa}\text{a}{}_{\mathrm{o}}$, the change in lattice parameter at 15 GPa in ZnS is $\text{0.255}\text{A}\text{?}\text{± 0.012}$ corresponding to a change of $\text{0.110}\text{A}\text{?}\text{± 0.005}$ in Zn-S distances at this transition to the metallic state.