Elementary reactions of formyl (HCO) radical studied by laser photolysis—transient absorption spectroscopy

Several elementary reactions of formyl radical of combustion importance were studied using pulsed laser photolysis coupled to transient UV–Vis absorption spectroscopy: HCO → H + CO (1), HCO + HCO → products (2), and HCO + CH₃ → products (3). One-pass UV absorption, multi-pass UV absorption as well as cavity ring-down spectroscopy in the red spectral region were used to monitor temporal profiles of HCO radical. Reaction (1) was studied over the buffer gas (He) pressure range 0.8–100 bar and the temperature range 498–769 K. Reactions (2a), (2b), (2c), (3a) and (3b) as well as the UV absorption spectrum of HCO, were studied at 298 and 588 K, and the buffer gas (He) pressure of 1 bar. Pulsed laser photolysis (308, 320, and 193 nm) of acetaldehyde, propionaldehyde, and acetone was used to prepare mixtures of free radicals. The second-order rate constant of reaction (1) obtained from the data at 1 bar is: k₁(He) = (0.8 ± 0.4) × 10⁻¹⁰exp(−(66.0 ± 3.4) kJ mol⁻¹/RT) cm³ molecule⁻¹ s⁻¹. The HCO dissociation rate constants measured in this work are lower than those reported in the previous direct work. The difference is a factor of 2.2 at the highest temperature of the experiments and a factor of 3.5 at the low end. The experimental data indicate pressure dependence of the rate constant of dissociation of formyl radical 1, which was attributed to the early pressure fall-off expected based on the theory of isolated resonances. The UV absorption spectrum of HCO was revised. The maximum absorption cross-section of HCO is (7.3 ± 1.2) × 10⁻¹⁸ cm² molecule⁻¹ at 230 nm (temperature independent within the experimental error). The measured rate constants for reactions (2a), (2b), (2c), (3a) and (3b) are: k₂ = (3.6 ± 0.8) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ (298 K); k₃ = (9.3 ± 2.3) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹(298 and 588 K).     

Reentrant transitions in the van Hemmen model of a spin glass

The van Hemmen model of a spin glass, which is an Ising model with random couplings J_ij between sites i and j equal to J₀ + J(ξ_iη_j + ξ_jη_i), where (ξ_i, η_i) are independent, identically distributed random variables, is studied in the pair approximation of the cluster variation method. For the family of probability distributions (1 − p)δ(ξ_i − a) + pδ(ξ_i) + (1 − p)δ(ξ_i + a), where p is varied, phase diagrams are constructed. They are qualitatively different from the mean-field phase diagrams and display a competition between tendencies towards spin-glass and towards ferromagnetic ordering, which results in reentrant transitions. It is argued that the observed effects are not accidental but are borne by the competition of bonds of the underlying lattice system.     

Inverse Laplace transforms of osculatory and hyperosculatory interpolation polynomials

In the numerical calculation of f(t), the inverse Laplace transform of F(p), where f(′) = (1/2πi) °_c−i∞^c+i∞ e^pt F(p)dp, sufficient accuracy is usually obtainable when p³F(p), s > 0, is replaced by an interpolating polynomial in 1/p. From the values of F(p) with F′(p), or with F′(p) and F″(p), for p at points equally spaced on the real axis, an osculatory or hyperosculatory interpolation polynomial for p⁸F(p), namely L_2n−1(x) or L_3n−1(x), where x = 1/p, is obtained in barycentric form. Then f(t) is calculated by a Gaussian-type quadrature formula employing complex values of L_2n−1 or L_3n−1 and instead of p^sF(p) which may be unknown or more difficult to compute. For calculating L_2n−1 and L_3n−1, auxiliary coefficients, suitable for economical storage in the program, are given exactly for n = 2(1)11 and n = 2(1)7, furnishing up to 21st and 20th degree accuracy, respectively.     

The reaction of CH3 + O2: experimental determination of the rate coefficients for the product channels at high temperatures

The reaction of methyl radicals (CH₃) with molecular oxygen (O₂) has been investigated in high-temperature shock tube experiments. The overall rate coefficient, k₁ = k_1a + k_1b, and individual rate coefficients for the two high-temperature product channels, (1a) producing CH₃O + O and (1b) producing CH₂O + OH, were determined using ultra-lean mixtures of CH₃I and O₂ in Ar/He. Narrow-linewidth UV laser absorption at 306.7 nm was used to measure OH concentrations, for which the normalized rise time is sensitive to the overall rate coefficient k₁ but relatively insensitive to the branching ratio of the individual channels and to secondary reactions. Atomic resonance absorption spectroscopy measurements of O-atoms were used for a direct measurement of channel (1a). Through the combination of measurements using the two different diagnostics, rate coefficient expressions for both channels were determined. Over the temperature range 1590–2430 K, k_1a = 6.08 × 10⁷T^1.54 exp (−14005/T) cm³ mol⁻¹ s⁻¹ and k_1b = 68.6 T^2.86 exp (−4916/T) cm³ mol⁻¹ s⁻¹. The overall rate coefficient is in close agreement with a recent ab initio calculation and one other shock tube study, while comparison of k_1a and k_1b to these and other experimental studies yields mixed results. In contrast to one recent experimental study, reaction (1b) is found to be the dominant channel over the entire experimental temperature range.     

Analysis of the 2ν3 band of CD3F 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.     

Oxygen nonstoichiometry of Sr(Co,Fe)O3−δ-based perovskites: I. Coulometric titration of SrCo0.85Fe0.10Cr0.05O3−δ by the two-electrode technique

The p(O₂)–T–δ diagram of perovskite-type SrCo_0.85Fe_0.10Cr_0.05O_3−δ was determined by the coulometric titration technique in the temperature range 770–1250 K at oxygen partial pressures from 8 10⁻¹⁰ to 0.5 atm. Stability of the cubic perovskite phase of SrCo_0.85Fe_0.10Cr_0.05O_3−δ, existing down to the oxygen pressures of 10⁻³–10⁻⁵ atm, was found to be slightly higher than that of SrCo_0.80Fe_0.20O_3−δ, probably due to stabilization of oxygen octahedra neighboring Cr⁴⁺ cations. When the oxygen nonstoichiometry of the Cr-containing perovskite decreases from 0.47 to 0.38, the partial molar enthalpy and entropy for overall oxygen incorporation reaction vary in the ranges −165 to −60 kJ mol⁻¹ and 90 to 150 J mol⁻¹ K⁻¹, respectively. Within the stability limits of the single perovskite phase, the p(O₂)–T–δ diagram can be adequately described by equilibrium processes of oxygen incorporation, cobalt disproportionation and interaction of cobalt and iron cations, with the thermodynamic functions independent of defect concentrations. Increasing grain size in SrCo_0.85Fe_0.10Cr_0.05O_3−δ ceramics from submicron size to 100–200 μm has no effect on the oxygen thermodynamics. The two-electrode coulometric titration technique, based on the alternate use of electrodes for oxygen pumping and e.m.f. measurements, is described and verified by studying oxygen nonstoichiometry of La_0.3Sr_0.7CoO_3−δ and PrO_x.     

Dispersive Estimates for Schrödinger Equations with Threshold Resonance and Eigenvalue

Let H=−Δ+V(x) be a three dimensional Schrödinger operator. We study the time decay in L^p spaces of scattering solutions e^−itHP_cu, where P_c is the orthogonal projection onto the continuous spectral subspace of L²(R³) for H. Under suitable decay assumptions on V(x) it is shown that they satisfy the so-called L^p-L^q estimates ||e^−itHP_cu||_p≤(4π|t|)^{−3(1/2−1/p)}||u||_q for all 1≤q≤2≤p≤∞ with 1/p+1/q=1 if H has no threshold resonance and eigenvalue; and for all 3/2<q≤2≤p<3 if otherwise.     

Chiral approach to nuclear matter: role of two-pion exchange with virtual delta-isobar excitation

We extend a recent three-loop calculation of nuclear matter by including the effects from two-pion exchange with single and double virtual Δ(1232)-isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter, , ρ₀=0.16 fm⁻³, can be well reproduced by adjusting the strength of a two-body term linear in density (and tuning an emerging three-body term quadratic in density). The nuclear matter compressibility comes out as K=304 MeV. The real single-particle potential U(p,k_f0) is substantially improved by the inclusion of the chiral πNΔ-dynamics: it grows now monotonically with the nucleon momentum p. The effective nucleon mass at the Fermi surface takes on a realistic value of M^*(k_f0)=0.88M. As a consequence of these features, the critical temperature of the liquid-gas phase transition gets lowered to the value T_c15 MeV. In this work we continue the complex-valued single-particle potential U(p,k_f)+iW(p,k_f) into the region above the Fermi surface p>k_f. The effects of 2π-exchange with virtual Δ-excitation on the nuclear energy density functional are also investigated. The effective nucleon mass associated with the kinetic energy density is . Furthermore, we find that the isospin properties of nuclear matter get significantly improved by including the chiral πNΔ-dynamics. Instead of bending downward above ρ₀ as in previous calculations, the energy per particle of pure neutron matter and the asymmetry energy A(k_f) now grow monotonically with density. In the density regime ρ=2ρ_n<0.2 fm⁻³ relevant for conventional nuclear physics our results agree well with sophisticated many-body calculations and (semi)-empirical values.     

Condition for adiabatic passage in the earth’s-field NMR technique

The equation of motion dM/dt=γ M×B(t) is solved for the case B(t)=jB_p(t)+kB_e. The field B_e is a small static field, typically the earth’s field. The field B_p(t) decays exponentially toward zero with time constant T. This decay is produced by an overdamped switching transient that occurs near the end of the rapid cutoff of the coil current used to polarize the sample. It is assumed that B_p is initially large compared to B_e, and that magnetization M is initially along the resultant field B. Exact solutions are obtained numerically for several decay time constants of B_p, and the motion of M is depicted graphically. It is found that for adiabatic passage, the final cone angle β of the precession in field B_e is related to the decay time constant of B_p by β=2e^{−(π/2)ω_eT}. This is confirmed by measurements of the amplitudes of the ensuing free-precession signals for various decay rates of B_p. Near-perfect adiabatic passage (magnetization aligned within 2° of the earth’s field) can be achieved for time constants T2.6/ω_e. For the case of sudden passage, an approximate analytic solution is developed by linearizing the equation of motion in the laboratory frame of reference. For the adiabatic case, an approximate analytic solution is obtained by linearizing the equation of motion in a rotating frame of reference that follows the resultant field B=B_p+B_e.     

Observation of the π(1800) and (1880) mesons in decay

A partial-wave analysis of the reaction π⁻p→ηηπ⁻p at 18 GeV/c has been performed on a data sample of approximately 4000 events obtained by Brookhaven experiment E852. The J^PC=0⁻⁺π(1800) state is observed in the a₀(980)η and f₀(1500)π decay modes. It has a mass of 1876±18±16 MeV/c² and a width of 221±26±38 MeV/c². The J^PC=2⁻⁺π₂(1880) meson is observed decaying through a₂(1320)η. It has a mass of 1929±24±18 MeV/c² and a width of 323±87±43 MeV/c². Both states are potential candidates for non-exotic hybrid mesons.     

A new level at 192.5 keV in Ge

In the experiments on ⁷⁴Ge(d, pγ)⁷⁵Ge, a 52.5±0.1 keV γ-ray was found in ⁷⁵Ge with a half-life of 216±5 ns. From the analysis of the γ-ray spectra the conversion coefficient of the 52.5 keV γ-ray was determined. Then, a new level of is confirmed to exist at 192.5 keV. The reduced transition probabilities of the 52.5 keV transition are deduced to be (6.9^+5.6 _−2.1) × 10⁻⁵ for B(M1) and 31⁺³ ₋₂ for B(E2) in Weisskopf units.     

Thermodynamics on noncommutative geometry in coherent state formalism

The thermodynamics of ideal gas on the noncommutative geometry in the coherent state formalism is investigated. We first evaluate the statistical interparticle potential and see that there are residual “attraction (repulsion) potential” between boson (fermion) in the high temperature limit. The characters could be traced to the fact that, the particle with mass m in noncommutative thermal geometry with noncommutativity θ and temperature T will correspond to that in the commutative background with temperature T(1+kTmθ)⁻¹. Such a correspondence implies that the ideal gas energy will asymptotically approach to a finite limiting value as that on commutative geometry at T_θ=(kmθ)⁻¹. We also investigate the squeezed coherent states and see that they could have arbitrary mean energy. The thermal properties of those systems are calculated and compared to each other. We find that the heat capacity of the squeezed coherent states of boson and fermion on the noncommutative geometry have different values, contrast to that on the commutative geometry.     

Line Positions and Intensities of the ν1+ ν2+ 3ν3, ν2+ 4ν3, and 3ν1+ 2ν2Bands of Ozone

Using a Fourier transform spectrometer, we have recorded the spectra of ozone in the region of 4600 cm⁻¹, with a resolution of 0.008 cm⁻¹. The strongest absorption in this region is due to the ν₁+ ν₂+ 3ν₃band which is in Coriolis interaction with the ν₂+ 4ν₃band. We have been able to assign more than 1700 transitions for these two bands. To correctly reproduce the calculation of energy levels, it has been necessary to introduce the (320) state which strongly perturbs the (113) and (014) states through Coriolis- and Fermi-type resonances. Seventy transitions of the 3ν₁+ 2ν₂band have also been observed. The final fit on 926 energy levels withJ_max= 50 andK_max= 16 gives RMS = 3.1 × 10⁻³cm⁻¹and provides a satisfactory agreement of calculated and observed upper levels for most of the transitions. The following values for band centers are derived: ν₀(ν₁+ ν₂+ 3ν₃) = 4658.950 cm⁻¹, ν₀(3ν₁+ 2ν₂) = 4643.821 cm⁻¹, and ν₀(ν₂+ 4ν₃) = 4632.888 cm⁻¹. Line intensities have been measured and fitted, leading to the determination of transition moment parameters for the two bands ν₁+ ν₂+ 3ν₃and ν₂+ 4ν₃. Using these parameters we have obtained the following estimations for the integrated band intensities,S_V(ν₁+ ν₂+ 3ν₃) = 8.84 × 10⁻²²,S_V(ν₂+ 4ν₃) = 1.70 × 10⁻²², andS_V(3ν₁+ 2ν₂) = 0.49 × 10⁻²²cm⁻¹/molecule cm⁻²at 296 K, which correspond to a cutoff of 10⁻²⁶cm⁻¹/molecule cm⁻².     

High-resolution infrared study of the 2ν3 (A1, E) and ν1 + ν3 (E) bands of NF3

The 2ν₃ overtone (A₁, E) and the ν₁ + ν₃ (E) combination bands of the oblate symmetric top ¹⁴NF₃ were studied by FTIR spectroscopy with a resolution of 2.5 × 10⁻³ cm⁻¹. Nearly 500 lines up to K_max/J_max = 30/43 were observed for the weak A₁ component reaching the v₃ = 2⁰ substate (1803.1302 cm⁻¹), the majority of which corresponded to reinforced K = 3p-type transitions. For the strong E component reaching the v₃ = 2^±2 substate (1810.4239 cm⁻¹), about 3550 transitions were assigned up to K_max/J_max = 65/69, favoring a clear observation of the ℓ(4, −2) and ℓ(4, 4) splittings within the kℓ = −2 and +4 sublevels, respectively. The two v₃ = 2 substates are linked by the ℓ(2, 2)- and ℓ(2, −1)-type interactions, providing severe crossings, respectively, at K′ = 6 and near K′ = 24 on the v₃ = 2⁺² side. A model working in the D-reduction and including all these ℓ-type interactions could reproduce together 3695 nonzero weighted experimental data (NZW) through 33 free parameters with a standard deviation of σ = 0.357 × 10⁻³  cm⁻¹. As for the ν₁ + ν₃ (E) combination band, about 3690 lines were assigned up to K_max/J_max = 45/55. Its v₁ = v₃ = 1 upper state (1931.577 5 cm⁻¹) was treated using the same model recently applied to the v₃ = 1 (E, 907.5413 cm⁻¹) state. It yielded 21 free parameters through 3282 NZW experimental data, adjusted with σ = 0.344 × 10⁻³  cm⁻¹ in the D-reduction. For the two excited states, the small and unobserved ℓ(0, 6) interaction was tested as useless. To confirm the adequacy of the vibrationally isolated models used, some other reductions of the Hamiltonian were tried. For the v₃ = 2 state, the D-, L-, and LD-reductions led to similar σ’s, while the Q one was not successful. For the v₁ = v₃ = 1 state, the D- and Q-reductions gave comparable σ’s, while the QD-reduction was not as good. The corresponding unitary equivalence relations are generally more nicely fulfilled for the v₃ = 2 state than for the v₁ = v₃ = 1 state. The three derivable anharmonicity constants in cm⁻¹ are x₃₃ = −4.1528, g₃₃ = +1.8235 and x₁₃ = −7.9652.     

Polarization spectroscopy of ion-pair states of ICl

Molecular constants for the E0⁺(³P₂) and 1(³P₂) ion-pair states of ICl vapor have been determined using sequential two-photon polarization-labeling spectroscopy. The two states are coupled by a heterogeneous perturbation which is analyzed in some detail for low-lying vibrational levels of 1(³P₂). The I³⁵Cl potential constants for the 1(³P₂) state and the rotation-vibration constants for the set of f sublevels—i.e., the constants unaffected by coupling with the E state—are (in cm⁻¹) 1(³P₂): Y_0,0= 39103.814(32), Y_1,0= 170.213(15), Y_2,0= −0.4528(22), Y_3,0= −7.0(12) × 10⁻⁴, Y_4,0= −1.48(24) × 10⁻⁵ and Y_5,0= −6.6(19) × 10⁻⁸, Y^(f)_0,1= 5.6878(17) × 10⁻² Y^(f)_1,1= −2.110(24) × 10⁻⁴, Y^(f)_2,1= −1.23(62) × 10⁻⁷, and Y^(f)_0,1= −3.08(22) × 10⁻⁸Likewise, the I³⁵Cl constants determined for the E 0⁺(³P₂) state are E 0⁺(³P₂: Y_0,0= 39054.38(61), Y_1,0= 166.96(10), Y_2,0 = −0.3995(42), Y_0,1= 5.738(31) × 10⁻², and Y_1,1= −1.67(26) × 10⁻⁴Practical constraints in pumping the sequence E 0⁺ ← B 0⁺ ← × 0⁺ restrict the analysis of the E state to levels v = 9–15. Given the long extrapolation to the equilibrium state the 3σ statistical uncertainties quoted for these constants should be treated with caution.     

Thermogalvanic power and fast ion conduction in δ-Bi2O3 and δ-(Bi2O3)1−x(R2O3)x with R = Y, Tb---Lu

The thermogalvanic power (Seebeck coefficient) of O^2- conducting δ-Bi₂O₃ and δ-(Bi₂O₃)_1−x(Y₂O₃)_x has been measured directly as a function of temperature and partial oxygen pressure in N₂---O₂ mixtures. The of δ-(Bi₂O₃)_0.75(R₂O₃)_0.25 with R = Tb---Lu was indirectly determined using an isothermal concentration cell technique. Except for pure δ-Bi₂O₃, the heat of transport is much smaller than the activation energy for O^2- conduction for all materials. The vibrational freedom of O²⁻ ions in all δ-stabilized materials is reflected in their IR spectra at room temperature. Two prototypes of a thermogalvanic P_O2 meter were tested.     

Determination of the (Na) Sternheimer antishielding factor by Na NMR spectroscopy on sodium oxide chloride, Na3OCl

The (Na⁺) Sternheimer antishielding factor γ_∞ (Na⁺) was determined by ²³Na NMR spectroscopy on sodium oxide chloride, Na₃OCl. The quadrupolar coupling constant of the sodium ion in Na₃OCl was determined to QCC=11.34 MHz, which presents the largest coupling constant of a sodium nucleus observed so far. Applying a simple point charge model, the largest principal value of the electric field gradient at the sodium site was calculated to V_zz=−6.76762·10²⁰ V/m². From these values we calculated the (Na⁺) Sternheimer antishielding factor to γ_∞ (Na⁺)=−5.36. In sodium oxide, Na₂O, we observed an isotropic chemical shift of δ_CS=55.1 ppm, referenced to 1 M aqueous NaCl (δ=0 ppm).     

Observation of χb production in the exclusive reaction ′→γγχb→γγ→γγ(eeorμμ−)

We report on the observation of 1 ³P_J (χ_b) production in the reaction ′→γχ_b→γγ→γγ(e⁺e⁻ or μ⁺μ⁻). The data were recorded with the nonmagnetic CUSB detector at the Cornell Electron Storage Ring, CESR. We observe 124 γγ events with either an electron or muon pair in the final state. In the γγ correlation plot about 40% of the events cluster around (120, 430) MeV.     

Contribution to the Analysis of theA2←XA1“Wulf” Transition of Ozone by High-Resolution Fourier Transform Spectrometry

The analysis of the rotational structure of the high-resolution Fourier transform 0⁰₀absorption spectrum of the³A₂←X¹A₁band system of the “Wulf” transition of the isotopomer¹⁶O₃of ozone is reported for the first time. With a near pure case (b) coupling model for the upper triplet state, we have assigned a significant portion of the spectrum, mainly theF₁(J=N+ 1) andF₂(J=N) spin components, primarily in the lower frequency region of the band. The lines corresponding to theF₃(J=N− 1) component are weak at lower frequencies and heavily congested in the central and higher frequency regions of the spectrum. Perturbations and predissociation phenomena have reduced the effective lifetime of the metastable³A₂state and have also limited the number of transitions included in the least-squares fit of the band. Approximately 100 lines have been assigned in the range from 9100–9550 cm⁻¹. Three rotational, three centrifugal distortion, three spin–rotation, and one spin–spin constant were varied. The geometry of the molecule in the³A₂state, as determined from these constants, isr= 1.345 Å and θ = 98.9°, in good agreement withab initioresults.     

Spectral characterization and energy levels of Cr:Sc2(MoO4)3 crystal

This paper reports the spectral properties and energy levels of Cr³⁺:Sc₂(MoO₄)₃ crystal. The crystal field strength Dq, Racah parameter B and C were calculated to be 1408 cm⁻¹, 608 cm⁻¹ and 3054 cm⁻¹, respectively. The absorption cross sections σ_α of ⁴A₂→⁴T₁ and ⁴A₂→⁴T₂ transitions were 3.74×10⁻¹⁹ cm² at 499 nm and 3.21×10⁻¹⁹ cm² at 710 nm, respectively. The emission cross section σ_e was 375×10⁻²⁰ cm² at 880 nm. Cr³⁺:Sc₂(MoO₄)₃ crystal has a broad emission band with a broad FWHM of 176 nm (2179 cm⁻¹). Therefore, Cr³⁺:Sc₂(MoO₄)₃ crystal may be regarded as a potential tunable laser gain medium.