Vibration-rotation spectra of ethane and deuteroethanes: The ν2 band of CH3CD3

The ν₂ band of CH₃CD₃ has been measured under an effective resolution of 0.04 cm^?1. About 400 transitions observed in the region from 2130 to 2060 cm^?1 have been identified as due to the ν₂ fundamental band. The least-squares analysis of these transitions yields the band constants: ν₀ = 2089.957, B′ = 0.548937, D_J′ = 6.97 × 10^?7, D_JK′ = 1.92 × 10^?6, A′ - A″ = ?0.01158, and D_K′ - D_K″ = 1.30 × 10^?6 cm^?1. The ground-state constants B″, D_J″, and D_JK″ are fixed to the values obtained from microwave spectroscopy.     

Conification of Kähler and Hyper-Kähler Manifolds

Given a Kähler manifold M endowed with a Hamiltonian Killing vector field Z, we construct a conical Kähler manifold ${\hat{M}}$ such that M is recovered as a Kähler quotient of ${\hat{M}}$ . Similarly, given a hyper-Kähler manifold (M, g, J ₁, J ₂, J ₃) endowed with a Killing vector field Z, Hamiltonian with respect to the Kähler form of J ₁ and satisfying ${\mathcal{L}_ZJ_2 = -2J_3}$ , we construct a hyper-Kähler cone ${\hat{M}}$ such that M is a certain hyper-Kähler quotient of ${\hat{M}}$ . In this way, we recover a theorem by Haydys. Our work is motivated by the problem of relating the supergravity c-map to the rigid c-map. We show that any hyper-Kähler manifold in the image of the c-map admits a Killing vector field with the above properties. Therefore, it gives rise to a hyper-Kähler cone, which in turn defines a quaternionic Kähler manifold. Our results for the signature of the metric and the sign of the scalar curvature are consistent with what we know about the supergravity c-map.     

Probabilities of rovibronic transitions in the I 1Π g − , J 1Δ g − →C 1Π ± u systems of bands of the deuterium molecule

Probabilities of spontaneous rovibronic transitions I ¹Π _g ^? , v′ J′, J ¹Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ of the D₂ molecule (for vibrational and rotational quantum numbers v′=v″=0–3 and J′=1–9, J″=J′±1) have been obtained for the first time. They were determined using (1) the previously proposed nonadiabatic model, which takes into account the electron-rotational interaction of the upper levels; (2) the coefficients of expansion of wave functions of perturbed states in the Born-Oppenheimer basis, which were found from the experimental data on rovibronic terms; and (3) semiempirical b initio data on electronic transition dipole moments of the 3dπ¹Π_g→2pπ¹Π_u and 3dπδ¹Δ_g→2pπ¹Π_u transitions. The dependences of the transition probabilities on J′ for the same bands of both hydrogen isotopomers H₂ and D₂ were found to be identical. They represent monotone functions for R and P branches and functions with a maximum (minimum) for Q branches. The ratios of transition probabilities of different isotopomers for different branches of the same systems of bands and for the same branches of different systems of bands were found to be correlated. The semiempirical values obtained in the paper agree with the experimental values within the limits of the errors of their determination. The nonempirical values of transition probabilities agree with the experiment considerably worse.     

Acetylene spectra with a tunable diode laser: (ν4 + ν5)0+−ν41fQ branches of 12C2H2 and 12C13CH2

The rotational structure of the Q branches of the (ν₄ + ν₅)⁰⁺?ν₄^1f bands of ¹²C₂H₂ and ¹²C¹³CH₂ at 13.7 μm has been observed in a natural sample of acetylene by using a tunable diode laser as a source in a high-resolution infrared grating spectrometer equipped with a precision grating drive. Altogether 23 lines from J = 6 to 28 for ¹²C₂H₂ and 15 lines from J = 6 to 20 for ¹²C¹³CH₂ have been identified. The observed full width at half maximum of the resolved lines of these Q branches is very close to the calculated Doppler width. Molecular constants ν₀ + B″, B′ ? B″ ? 2D″, D′ ? D″, and H′ ? H″ have been derived from the measured line positions of the rotational structure.     

Amino wagging and inversion in hydrazine: K′ = 1 levels in the first excited state of the antisymmetric wagging vibration

The infrared absorption spectrum of NH₂NH₂ vapor has been observed in the region 899–1077 cm^?1, where the antisymmetric wagging band (v_a = 1 ← 0) appears, by the use of a Fourier transform spectrometer with a practical resolution of 0.003 cm^?1. In the region 925.0–925.6 cm^?1, the spectrum was also observed with a tunable diode laser, and a component, β, of the ^pQ₂ cluster has been further resolved. Most of the absorption lines assignable to β-^pP₂(J″), γ-^pP₂(J″), β-^pQ₂(J″), γ-^rQ₀(J″), β-^rR₀(J″), and γ-^rR₀(J″), where J″ = 2 ～ 15, have been identified. From these observed transition frequencies, in combination with the ground state energy levels given by microwave spectroscopy, the energy level structure of the K′ = 1 rotational states was determined. From this, the following molecular parameters for the v_a = 1 state were determined: molecular asymmetry, B′-C″ = 0.00017 cm^?1; a parameter q₅ describing an umbrella motion Coriolis interaction (q₅K) about the a axis, q₅ = ?0.0030 cm^?1; its J(J + 1) variation, q_5j = 0.00014 cm^?1; and a parameter describing an umbrella-motion K-type doubling g₅J(J + 1), g₅ = 0.000021 cm^?1.     

Precision measurement of theg J factors of metastable atomic states of88Sr and138Ba using the atomic beam magnetic resonance method

Theg _J factors of the metastable states³ P ₂ of⁸⁸Sr and³ D ₁,³ D ₂,³ D ₃, and¹ D ₂ of¹³⁸Ba have been measured using the atomic-beam magnetic resonance method. The metastable states were populated by an electric discharge within the atomic-beam source. From the measurements of rf transitions between the Zeeman levels (m _J =+1)?(m _J =?1) we obtained:⁸⁸Sr:g _J (³ P ₂) =1.501124(10)¹³⁸Ba:g _J (³ D ₃)=1.3340823 (10)g _J (³ D′₂)=1.1637406(11)g _J (³ D ₁)=0.4985751(13)g _J (¹ D′₂)=1.003 1449(10). The relativistic and diamagnetic corrections for theg _J factor of the³ P ₂ state of Sr have been calculated. With these and the Schwinger correction included we getg _J (³ P ₂)=1.501119(12).     

Analysis of the laser magnetic resonance spectrum of HO2

An analysis of the previously detected laser magnetic resonance spectrum of HO₂ is carried out by (i) assigning M_J quantum numbers to each observed Zeeman line, (ii) determining the quantum numbers (N′_Ka′Kc′-N″_Ka″Kc″) and energies of the zero-field asymmetric rotor transitions involved, and (iii) determining the values of the zero-field spin-rotation doublet splittings in the upper and lower states of each asymmetric rotor transition. The rotational transitions obtained lie in the region 50–150 cm^?1, with quantum numbers 4 ≤ N ≤ 19 and 1 ≤ K_a ≤ 4. They are fit to an asymmetric rotor program to obtain the three rotational constants A, B, C and the three symmetric-top centrifugal distortion constants D_K, D_NK, D_N. The spin splittings are fit to an approximate theoretical expression involving two adjustable linear combinations of components of the spin-rotation interaction tensor ?. Because of the lack of spectra from other isotopic species, a unique molecular geometry cannot be derived.     

On the generality of the mass sum rule

The sum rule, Σ_i(?1)^2J_i(2J_i+1)m_i²=2Σ_aD^aTrQ^a, is studied to first order in supersymmetry breaking, treating the other interactions exactly. It is found to hold for spontaneous breaking and many types of explicit breaking.     

Theory of self-locking phenomena in the pressure broadened three-mode He-Ne laser

Taking account of pressure broadening the coefficients in Lamb's third-order amplitude and phase determining equations for three modes are evaluated in the Doppler limit, and comparison is made with other theories. After expanding the coefficients to first order in the detuning ε from the linecenter an expression is presented for the frequency range where mode locking will occur. Using experimental data of several authors for the 6328 Å Ne-transition numerical values are obtained for the pressure dependent decay rates Υ _a , Υ _b , of the upper and lower laser level and the linewidth Υ _ab ^′ , viz.:Υ _a =17.7+(12.6±0.6)P _He, Υ _b =8.3+(12.6±0.6)P _He, and Υ _ab ^′ =13.0+(91±6)P _He MHz, whereP _He is measured in torr.     

Collision-induced 1st overtone infrared absorption band of deuterium

The collision-induced 1st overtone infrared absorption band of deuterium has been observed at room temperature. The band was studied in the pure gas and in binary mixtures with argon and nitrogen at a path length of 194.3 cm at pressures up to 800 atm. The observed absorption profiles of the band do not show any splitting of the Q branch and this indicates that the contribution of the short-range overlap forces to the intensity of the band is negligible. The enhancement absorption profiles of D₂-Ar mixtures show only single-transition quadrupolar lines, but the enhancement profiles of D₂-N₂ mixtures, in addition, show the double transitions Q₂(J) of D₂ + S₀(J) of N₂, and double vibrational transitions Q₁(J) of D₂ + Q₁(J) of N₂ which occur on the low frequency side of the pure overtone band. Major contribution to the intensity of the absorption profiles of pure deuterium comes from the double transitions Q₁(J) + Q₁(J), Q₁(J) + S₁(J) and Q₂(J) + S₀(J) in the colliding pairs of D₂ molecules. Integrated absorption coefficients were measured and binary and ternary absorption coefficients were derived.     

Colored,spinning classical particle in an external non-abelian gauge field

We derive classical non-relativistic equations of motion for a colored, spinning point-like particle in an external SU(2) gauge field from Dirac equation. We find that in addition to the classical spin and color spin vector, S, I, it is necessary to introduce a new classical dynamical variable [J^ab], a, b = 1, 2, 3, describing a mixing of the spin and color. The constraint relations between [J^ab], S, I are also found.     

Analysis of the ν6(A″2) band of cyclopropane-d6 recorded under high resolution

The parallel band ν₆(A″₂) of C₃D₆ near 2336 cm^?1 has been studied with high resolution (Δν = 0.020 – 0.024 cm^?1) in the infrared. The band has been analyzed using standard techniques and the following parameters have been determined: B″ = 0.461388(20) cm^?1, D″_J = 3.83(17) × 10^?7 cm^?1, ν₀ = 2336.764(2) cm^?1, α^B = (B″ ? B′) = 8.823(12) × 10^?4 cm^?1, β^J = (D″_J ? D′_J) = 0, and α^C = (C″ ? C′) = 4.5(5) × 10^?4 cm^?1.     

Molecular-Gas-Pressure-Induced Line-Shift and Line-Broadening in the ν2-Band of H2S

The pressure-induced shift and broadening of H₂S absorption lines in the ν₂-band due to collisions between H₂S molecules and quadrupole molecules, such as O₂, H₂, D₂, N₂, and CO₂, were studied in the spectral region between 1050 and 1325 cm⁻¹. The measurements were carried out using a pulse-driven diode laser spectrometer with two multipass Herriott cells. The data concerning the collisional broadening and shift coefficients, γ and δ, respectively, and their dependencies on the rotational quantum number J″ and the quadrupole moment Q of the molecular perturber are presented for 14 P-branch transitions (3≤J″≤8,0≤K_a^Prime;≤3, 2≤K_c^Prime;≤8), 7 Q-branch transitions (7≤J^Prime;≤10, 1≤K_a^Prime;≤2, 6≤K_c^Prime;≤9), and 18 R-branch transitions (2≤J^Prime;≤11, 0≤K_a^Prime;≤4, 0≤K_c^Prime;≤11). The broadening coefficients γ were determined with an accuracy to within 2% and shift coefficients δ were determined with an uncertainty of less than 10⁻³ cm⁻¹/atm for the majority of lines and broadening gases.     

The methane ν1(a1) vibrational state rotational structure obtained from high-resolution CARS-spectra of the Q-branch

The gaseous methane ν₁(a₁), Q-branch coherent anti-Stokes Raman scattering (CARS) spectra have been investigated at a resolution of 0.002 cm^?1. A complex rotational structure of the resolved Q-branch has been experimentally observed. This structure can be ascribed to strong tetrahedral splitting of the rotational levels of the upper vibrational state, which possibly occurs due to Fermi resonance between the ν₁(a₁) and 2ν₂(a₁) vibrational energy levels which are close to each other. An assignment of the observed spectral lines has been made, yielding the rotational constants B, D, and D_t for the ν₁(a₁) vibrational state of the methane molecule. The absolute Raman frequency ν₁ of the purely vibrational transition has been found.     

Electromigration and permeation of hydrogen and deuterium in silver

A steady state flow technique was used to measure the effective charge number (Z*) and permeability (N) of hydrogen and deuterium in silver. Over the range of temperature (485–720°C) and pressure (220–750 torr) the effective charge number is a constant. The interstitial impurity migrates in the direction of the electron wind with Z_H* = ?6·8 and Z_D* = ? 18. The values of Z* are of the same order as self-electromigration but the size of the isotope effect is surprising. The quantum theories used to explain the isotope effect for hydrogen electromigration in Fe and Ni appear to fail here. In order to determine the effective charge number is was necessary to measure the permeability. For both H₂ and D₂, the permeability in silver follows the equation N = N_O exp(? Q/RT) where N_0D = 2·39 ± 0·40, Q_D = 14400 ± 300, N_OH = 2·86 ± 0·70 and Q_H = 14200 ± 500. Here Q is in units of cal/mol and N is in units of cc(ntp)/(sec - atm² - cm) The isotope effect ratio N_H/N_D = 1·25 was smaller than the classically expected value of (2)^1/2, but could be explained by the theory of Ebisuzaki, Kass and O'Keeffe.     

Analysis of the 2ν3 band of 12CD3F at 5.06 μm recorded under high resolution

The 2ν₃(A₁) band of ¹²CD₃F near 5.06 μm has been recorded with a resolution of 20–24 × 10^?3 cm^?1. The value of the parameter (α^B ? α^A) for this band was found to be very small and, therefore, the K structure of the R(J) and P(J) manifolds was unresolved for J < 15 and only partially resolved for larger J values. The band was analyzed using standard techniques and values for the following constants determined: ν₀ = 1977.178(3) cm^?1, B″ = 0.68216(9) cm^?1, D″_J = 1.10(30) × 10^?6 cm^?1, α^B = (B″ ? B′) = 3.086(7) × 10^?3 cm^?1, and β^J = (D″_J ? D′_J) = ?3.24(11) × 10^?7 cm^?1. A value of α^A = (A″ ? A′) = 2.90(5) × 10^?3 cm^?1 has been obtained through band contour simulations of the R(J) and P(J) multiplets.     

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin-charge coupling

We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – J_c (T = 0). The critical value J_c(T = 0) = 3/16p_F^?1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Q^ab〉, a ≠ b, the diagonal 〈Q^aa〉 is confirmed as order parameter by the result 〈Q^aa〉 _SP ～ (δJ)^β, β = 1, and its susceptibility χ^aaaa ～(-δJ)^?γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Q^aa〉, ～ T is obtained exactly in the whole quantum disordered phase including the critical value.     

Diode laser spectroscopy of the ν6 band of 12CH3I

The vibration-rotation spectrum of the ν₆ fundamental of methyl iodide has been recorded in the 824 to 862 cm^?1 region by using a tunable semiconductor diode laser spectrometer. The rotational analysis performed for six Q branches ^pQ(J,3), ^pQ(J,4), ^pQ(J,5), ^pQ(J,6), ^pQ(J,7), and ^qQ(J,8) led to accurate values for several molecular constants. The nuclear quadrupole splitting arising from the spin of iodine has been observed very clearly in the low J transitions and for various K values.     

Line-Mixing Effects inQBranches of CO2

A theoretical model based on the energy corrected sudden (ECS) approximation is used in order to account for line-mixing effects in Δ ↔ Π infraredQbranches of¹²C¹⁶O₂. Its quality is demonstrated by comparisons with numerous laboratory spectra of CO₂–He and CO₂–N₂mixtures: threeQbranches in the 4 and 17 μm regions are investigated at room temperature in a wide pressure range. The influence of mixing betweenQ(J) lines associated with odd and even values of the rotational quantum numberJis demonstrated and analyzed in detail. It is shown that, in contrast to available fitting law approaches, the ECS model correctly predicts the influence of the parity of the rotational quantum numbersJandJ′ on coupling between theQ(J) andQ(J′) lines. Comparisons between the effects of collisions of CO₂with N₂and He are made and analyzed. They show that these two systems involve different line couplings within theQbranch.     

Jump diffusion coefficient of different cations intercalated into amorphous WO3

This work shows how the combination of quasi-equilibrium (chronopotentiometry) and kinetical measurements (electrochemical impedance) is able to extract ionic mobility values like the jump diffusion coefficient D_J. Results are presented on the jump diffusion coefficient variation with composition of several cations (Li⁺, Na⁺, and K⁺) intercalated into electron beam evaporation-prepared a-WO₃ thin films. D_J exhibits higher values for the smallest ion (Li⁺), and decreases as the ion size enlarges. In all cases D_J shows lower values for high intercalation levels. It is noted that the type of cation rather influences transport mechanisms than equilibrium properties (insertion thermodynamics). The energy barrier of ion hopping is analyzed in light of available microscopic diffusion models and theoretical simulations.