Sea Level Muon Spectrum Derived from Bugaev Model

The pion and kaon spectra in the atmosphere are derived from primary nucleon spectrum determined by GRIGOROV et al.; they satisfy the relations N(E_π) dE_π = 0.187 EdE_π and N(E_k) dE_k = 0.017 E dE_k, respectively. By using the pion-kaon atmospheric diffusion equation the sea level muon spectrum is calculated and the result compared with the magnetic spectrograph data of ALLKOFER et al. and AYRE et al.     

An ab initio study of CX3‐substitution (X = H,F, Cl,Br, I) effects on the static electric polarizability and hyperpolarizability of diacetylene

We report a systematic ab initio and density functional theory (DFT) study of the electric properties of the X₃C? C≡C? C≡C? H (X = H, F, Cl, Br, and I) sequence of substituted diacetylenes. We rely on finite‐field Møller–Plesset perturbation theory and coupled‐cluster calculations with large, flexible basis sets. Our best values at the second‐order Møller–Plesset perturbation theory level for the mean dipole polarizability and second hyperpolarizability are $\overline {{\alpha} } $ /e²aE = 64.46 (? CH₃), 65.59 (? CF₃), 110.11 (? CCl₃), 138.90 (? CBr₃), 184.98 (? CI₃) and $\overline {{\gamma} } $ /e⁴aE = 21020 (? CH₃), 13469 (? CF₃), 32708 (? CCl₃), 57599 (? CBr₃), and 105251 (? CI₃). For comparison, the analogous MP2 values for diacetylene [P.Karamanis and G.Maroulis, Chem. Phys. Lett. 2003 , 376, 403.] are $\overline {{\alpha} } $ /e²aE = 49.17, and $\overline {{\gamma} } $ /e⁴aE = 16227. For the mean first hyperpolarizability we report $\overline {{\beta} } $ /e³aE = ?205.8 (? CH₃), ?55.7 (? CF₃), 120.8 (? CCl₃), 443.8 (? CBr₃), and 725.4 (? CI₃). Copyright © 2010 John Wiley & Sons, Ltd.     

The reaction of •OH with O2, the decay of O and the pKa of HO – interrelated questions in aqueous free‐radical chemistry

In the reactions of ozone with organic compounds in aqueous solution, O is an abundant intermediate. A basic aspect of its conversion into ^?OH is addressed here. The reactions O^?? + O₂ ? O (1), H⁺ + O^?? ? ^?OH (8), ^?OH + O₂ ? HO (6), and H⁺ + O ? HO (5) are interconnected by a thermodynamic cycle. For equilibria (1) and (8) reliable equilibrium constants, and hence Gibbs energies are available (ΔG⁰(1) = ?32 kJ mol^?1, ΔG⁰(8) = 67 kJ mol^?1). For reaction (6), a Gibbs energy of ΔG⁰(6) = 47 kJ mol^?1 (K₆ = 10^?8.2 M) has now been calculated by G1. From the thermodynamic cycle one hence arrives at ΔG⁰(5) = ?12 kJ mol^?1. This relates to pK_a(HO) = ?2.1. Thus, the HO radical is a very strong acid. This value agrees with a value of ?2.0 obtained from the Bielski and Schwarz relationship for pK_a values of O_xH_y compounds. Reaction (6) must be very slow, 0.1 < k₆ < 10⁴ M^?1 s^?1. Copyright © 2010 John Wiley & Sons, Ltd.     

The Spectra of Cosmic Pions and Nucleons at Low and High Geomagnetic Latitudes at the Top of the Atmosphere

The spectra of cosmic pions and nucleons at an atmospheric depth of 100 g cm^?2 have been derived from sea level muon spectra at low and high latitudes. The derived spectra of pions and nucleons at low and high latitudes follow the relations N(Eπ) dEπ = 0.23 E_π^?2.68dEπ and N(E_p) dE_p = 2.98 E dE_p per cm² sec str GeV in the energy range 15–1200 GeV. Below 15 GeV it is found that the exponent of the energy spectrum is very much dependent upon the incident energy and latitude of the location. The major difference between low and high latitude pion spectra can be explained in terms of geomagnetic effects.     

Kinetic Study of the Emission of the First Negative System in an Argon-Nitrogen Plasma at Atmospheric Pressure

Quantitative optical spectroscopy measurements of the emission spectra of the N(B²∑_u,)ν′→X²∑_gν″ transition (first negative system) in an Ar-N₂ microwave discharge at atmospheric pressure have allowed determination of the rate coefficient of the production of N molecules in the B² ∑_u, state with vibrational level ν′ = 0. The N(B²∑_u, ν′) molecules are produced by the reaction in a surface-wave-induced microwave discharge (2450 MHz) sustained in an open-ended dielectric tube. The rate coefficient K (T) has been obtained for ν′ν″ = 0 for different gas temperatures by varying the incident microwave power. The K₀₀(T) values are between 7.10^?10 and 4.10^?10 cm³ s^?1 for the temperature range 2500 to 3450K.     

Hyperfine Structure of the Configuration lll

The matrix elements for the hyperfine structure of the configuration lll in SL-Kopplung are expressed as linear combinations of the electron coupling constants α_li(10), α_li(01), α_li(12).     

On a Mechanical Model of the Bopp-Podolsky Potential

For an arbitrary given distribution of dislocations and disclinations the general state of stress of a mechanical continuum is investigated. The medium is reacting with stresses and momentum stresses (Cosserat continuum). By means of differential geometry it is shown that the deformations _ik and ?_ik of two arbitrary materials with identical distributions of defects differ merely by a displacement field u_i(x^r, t). If _ik are the eigendeformations of an isotropic medium, then in the linear theory the field u_i of a Cosserat continuum can be separated from _ik. If the problem is static the u_i obey the potential equation of Bopp-Podolsky electrodynamics. As source only torsion (dislocations and torsion of disclinations) is acting. To give an example the field u_i for straight dislocations and disclinations is calculated. Especially the problem of singularities is discussed.     

On the heat of formation of nitromethane

Two experimental values (?19.3 ± 0.3 and ?17.8 ± 0.1 kcal/mol) for the gas phase heat of formation (δ_fH) (298k) of nitromethane have been reported. Although these values differ by only 1.5 kcal/mol, substantially greater differences in theoretical and experimental results occur when these differing values are used to calculate thermodynamic properties. This is especially evident when these two values for the δ_fH of nitromethane are used to calculate thermodynamic properties of polynitro compounds. For example, when density functional theory (DFT) is coupled with the use of isodesmic reactions, the Δ_fH of octanitrocubane is calculated to be 160.6 or 172.6 kcal/mol, depending on which value is used. It should also be appreciated that several computational theories depend upon having access to reliable experimental data for testing and development. We have examined this discrepancy using several computational models and several levels of theory. Our results coupled with a comprehensive review of the literature support the lower (?19.3 ± 0.3 kcal/mol) experimental value. This is problematic because the higher value (?17.8 ± 0.1 kcal/mol) has been used in the development and/or testing of several semiempirical quantum mechanical models as well as ab initio Gaussian theory (G2 and G3). Copyright © 2008 John Wiley & Sons, Ltd.     

On the Theory of Gravitational Field in Finsler Spaces

Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as g_λχ(x, y) = γ_λχ(x) + h_λχ(x, y) is proposed, where γ_λχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric h_ij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ?ⁱ = K(x, y) y^j in the internal field, is grasped by the Finslerian parallelism δyⁱ (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy^χ = e(x) δyⁱ. The whole metrical Finsler connection D for g_λχ(i.e., Dg_λχ = 0) is determined by taking account of the intrinsic behaviour δy^χ.     

Gas‐phase basicities of acetophenones toward lanthanum cation [La(OMe)]

The relative free energy changes (lanthanum cation basicity, LaCB[L₂]) for the reaction [La(OMe)₂]L ? La(OMe) + 2L were determined in the gas phase for m‐ and p‐substituted acetophenones based on the measurement of ligand exchange equilibria using an FT‐ICR mass spectrometer. The substituent effect on ΔLaCB[L₂] of acetophenone is described in terms of the Yukawa–Tsuno equation, ΔG = ρ(σ° + r⁺ Δ σ ), with a ρ value of ?11.2 and an r⁺ value of 0.49. From this result, a ρ value of ?7.0 and an r⁺ value of 0.49 were estimated for the monomeric complex [LLa(OMe)] with the aid of theoretical calculations. This ρ value was found to be significantly smaller than that for protonation, and even smaller than Li⁺ basicity. Such a small ρ value has been attributed to the largely ionic (ion–dipole interaction) nature of the bonding interaction between La(OMe) and the carbonyl oxygen atom and, in part, to the long distance between La(OMe) and the substituent. Contrary to the ρ value, the r⁺ value is identical in both La(OMe) and Li⁺ basicities, suggesting that the r⁺ value of 0.49 can be regarded as a limiting one in a series of Lewis cation basicities of the acetophenone system, H⁺ (0.86) > Me₃Si⁺ (0.75) > Me₃Ge⁺ (0.71) > Cu⁺ (0.60) > Li⁺ = La(OMe) (0.49). Since the binding interaction between La(OMe) or Li⁺ and a neutral ligand is mostly electrostatic, the moderate r⁺ was interpreted to result from the redistribution of the induced positive charge within the acetophenone moiety upon binding with a metal ion rather than transfer of positive charge from a metal ion to the aromatic moiety. Copyright © 2010 John Wiley & Sons, Ltd.     

A novel probe for determination of electrical surface potential of surfactant micelles: N,N'‐di‐n‐octadecylrhodamine

The peculiarities of the structure of the fluorescent dye N,N'‐di‐n‐octadecylrhodamine advantage its using as an interfacial acid–base probe in aqueous micellar solution of colloidal surfactants. Two long hydrocarbon tails of the dye provide similar orientation of both cation and zwitterion on the micelle/water interface, with the ionizing group COOH exposed to the Stern region in all the systems studied. Further, the charge type of the acid–base couple, A⁺B^±, ensures similar values of the ‘intrinsic’ contribution, pK, to the ‘apparent’ pK value in micelles of different surfactants. This makes the indicator suitable for determination of electrical surface potentials, Ψ. The pKs have been obtained in cationic, anionic, zwitterionic, and nonionic surfactant systems, at various salt background. In total 17 systems were studied. At bulk counterion concentration of ca. 0.05 M, the pK values vary from 2.14 ± 0.07 in n–C₁₈H₃₇N(CH₃)Cl^– micelles to 5.48 ± 0.06 in n–C₁₆H₃₃OSONa⁺ micelles. The Ψ values, corresponding to the Stern region of micelles, have been evaluated as Ψ = 59.16 pK–pK for T = 298.15 K. The pK parameter was equated to the average value of 4.23 in nonionic surfactants (4.12–4.32, depending on the surfactant type). For cetyltrimethylammonium bromide and sodium n‐dodecylsulfate micelles, the Ψ values (±(7–11) mV) appeared to be +118 mV and at bulk Br^? concentration 0.019 M and ?76 mV at bulk Na⁺ concentration 0.020 M, respectively. This satisfactorily agrees with the theoretical values +111 and ?84 mV, estimated using the Oshima, Healy, and White equation for these well‐defined colloidal systems. Finally, not only absorption, but also fluorescence spectra display the same response to changes in bulk pH. Copyright © 2007 John Wiley & Sons, Ltd.     

Primary kinetic hydrogen isotope effects in deprotonations of a nitroalkane by intramolecular phenolate groups

Rate constants and kinetic isotope effects have been determined for the formation of nitronate anions from the ethers 1‐(2‐methoxyphenyl)‐2‐nitropropane, 7 (X = H, L = H and D) and 1‐(2‐methoxy‐5‐nitrophenyl)‐2‐nitropropane, 7 (X = NO₂, L = H and D), and from the corresponding phenols, 1‐(2‐hydroxyphenyl)‐2‐nitropropane, 3 (X = H, L = H and D), and 1‐(2‐hydroxy‐5‐nitrophenyl)‐2‐nitropropane, 3 (X = NO₂, L = H and D), in aqueous basic medium. For the ethers 7 , rates of deprotonation by hydroxide are comparable with those found for deprotonations of 2‐nitropropane, with k^H/k^D (25 °C) = 7.7 and 7.8, respectively. In both the cases, the isotope effects are conventionally temperature dependent. For the corresponding phenols 3 , conditions have been established under which the deprotonations of the nitroalkane are dominated by intramolecular deprotonation by the kinetically first‐formed phenolate anion, with an estimated effective molarity EM ～ 250. For 3 (X = H, L = H or D), k^H/k^D (25 °C) = 7.8, with E ? E = 6.9 kJ mol^?1 and A^H/A^D = 0.5. For 3 (X = NO₂, L = H or D), rates of intramolecular deprotonation are reduced 30‐fold, and an elevated kinetic isotope effect is found (k^H/k^D (25 °C) = 10.7). Activation parameters (E ? E = 17.8 kJ mol^?1 and A^H/A^D = 0.008) are compatible with an enhanced tunnelling contribution to reactivity in the H‐isotopomer. Copyright © 2009 John Wiley & Sons, Ltd.     

A non‐enzymatic model based on an acyl transfer reaction for the formation of energy‐rich acetyl phosphate in organic solvents and in a biphasic system

The formation of acetyl phosphate (AcP), an energy‐rich phosphate compound, was studied through the reaction of 2,4‐dinitrophenyl acetate with H₂PO solubilized with Kryptofix® 222 or as a tetra‐n‐butylammonium ((n‐C₄H₉)₄N⁺) salt in organic media. The results indicated that the rate of the reaction in acetonitrile is strongly inhibited by the addition of water, suggesting that the water added to the medium preferentially solvates the H₂PO anion, inhibiting its action as a nucleophile and allowing it to act as a general base catalyst, which leads to the hydrolysis of the ester. The utilization of various organic solvents in the acetyl transfer process demonstrated that the specific interaction of the solvent with water accelerates the process, by desolvation of H₂PO, which can act as a nucleophile. Finally, a formation/transformation cycle of AcP was studied in a biphasic system (water/CH₂Cl₂) using Kryptofix® 222 and (n‐C₄H₉)₄N⁺BF as both the carrier and solubilizing agent for KH₂PO₄. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of ortho‐substituents in SE1 protonolysis of phenylmercuric chloride

The kinetics of the reactions of o‐substituted phenylmercuric chlorides, o‐RC₆H₄HgCl (R = CH₃, H, C₂H₅O, CH₃O, C₆H₅, F, COOC₂H₅, Cl, Br, CF₃, NO₂), with hydrochloric acid in 80% aqueous dioxane in the presence of NaI were studied. The reactions are of the first order. The rate constant at 40°C decreases in the order of R: CH₃ > H > C₂H₅O > CH₃O > C₆H₅ > F > COOC₂H₅ > Cl > Br > CF₃ > NO₂. The analysis of effects of those o‐substitutes is carried out through multiple regression of log k/k_H with the corresponding inductive substituent constants σ_I and the various resonance substituent constants σ, σ_R(BA), σ, σ and σ_x, and the corresponding Swain–Lupton field effect constant and resonance effect constant . The results showed that o‐substituent intramolecular coordination with the neighbor mercury (field effect) is the main effect in effects of o‐substituents on rate of the S_E1 protonolysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Radiation induced oxidation of hydroxy indoles by NO and Br radicals: effect of pH

The reactions of NO and Br radicals with 5‐hydroxyindole (HIn), 5‐hydroxytryptophol (HTpl), 5‐hydroxytryptophan (HTpn) and 5‐hydroxytryptamine (HTpe) were studied using pulse radiolysis. The rate constants for their reaction with NO radical were found to vary from 10⁵ to 10⁷ dm³ mol^?1 s^?1 in the pH range 5–9 but a higher value (k = 1.4 ± 0.01 × 10⁸ dm³ mol^?1 s^?1) was noticed in HTpe at pH 9. The gradual increase in reactivity with pH is due to the decrease in the reduction potentials of indoloxyl radicals with E = 0.55 V at pH 9. In contrast, the rate constants with Br radical were found to be diffusion controlled and remained unaffected by the pH. The transient spectra measured are attributed to the indoloxyl radical formed on oxidation with λ_max at 420 nm. The indoloxyl radicals further react with the parent hydroxy indole derivative forming the radical adduct and their decay was found to be pH dependent in derivatives containing an amino group. At pH 5, no decay of the radical adducts was seen in all derivatives up to 5 ms whereas those with the amino group decayed faster at pH 9. The total yields of the oxygen centred and carbon centred radicals formed in the reaction of NO radical with hydroxy indoles were found to be nearly equal to G(NO). Our results suggest that NO radical is inefficient in oxidizing hydroxy indoles under physiological conditions preventing the formation of toxic dimers of indole derivatives. Copyright © 2010 John Wiley & Sons, Ltd.     

Li (i = 1, 2, 3) sub‐shell fluorescence yields for 79Au, 80Hg and 81Tl

The L _i (i = 1, 2, 3) sub‐shell x‐ray fluorescence yields (ω _i ) for ₇₉Au, ₈₀Hg and ₈₁Tl were deduced from the measured cross‐sections for the L _i (i = 1, 2, 3) sub‐shell x‐rays following ionization by 59.54 keV γ‐rays (B < E_inc < B_K) and for the L₃ sub‐shell x‐rays following ionization by Rb K x‐rays (B < E_Kα < B, B < E_Kβ < B_K), where B is the K shell/L _i sub‐shell ionization threshold of the target element. An energy‐dispersive x‐ray fluorescence setup, involving photon sources consisting of a ²⁴¹Am annular source in the direct and secondary excitation modes along with RbCl secondary exciter and an Si(Li) detector, was used for the measurements. The measured ω₂ and ω₃ values exhibit good agreement with those based on the relativistic Dirac–Hartree–Slater (RDHS) calculations, while the ω₁ values are found to be higher by ～25%. The present data indicate that the L₁–L₃ Coster–Kronig yield f₁₃ based on the RDHS calculations are overestimated. Copyright © 2004 John Wiley & Sons, Ltd.     

Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field

We study the Schwinger mechanism for gluon-pair production in the presence of an arbitrary time-dependent chromo-electric background field E ^a (t) with arbitrary color index a=1,2,…,8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon-pair production per unit time per unit volume and per unit transverse momentum, , from arbitrary E ^a (t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate, . We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives , where n=1,2,…,∞, and that it has the same functional dependence on the two Casimir invariants, [E ^a (t)E ^a (t)] and [d _abc E ^a (t)E ^b (t)E ^c (t)]², as the constant chromo-electric field E ^a result with the replacement: E ^a →E ^a (t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark–gluon plasma at RHIC and LHC.     

Vibrational Population of Hydrogen Molecules Excited by an RF Discharge in an Expanding Thermal Arc Plasma as Determined by Emission Spectroscopy

This work is devoted to the determination of the vibrational population of hydrogen molecules in the ground and excited electronic states from the analysis of visible spectra of the H₂ molecules excited by an RF discharge in an expanding thermal arc plasma. Comparison of the experimental results on relative electron-impact excitation cross sections for the transition H₂(X¹Σ, υ⁰ = 0)→ H₂(d³II_u, υ′) with other experiments, and with calculations based on the Franck-Condon principle, shows good agreement. This means, that for plasma under investigation: 1) in the ground electronic state H₂(d³II_u,υ′), only the lowest vibrational level with υ⁰ = 0 is significantly populated, and 2) direct electron exictation of H₂(d³II_u, υ′, υ′) state from the ground state H₂(X¹Σ, υ⁰ = 0) dominates.     

Transition from SU(2)L × SU(2)R × U(1)B-L representation to SU(2)L × U(1)Y by q-deformation and the corresponding classical breaking term of chiral U(2)

The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the VEV and the hypercharge splitting Δ = (y-y)/2 of right-handed leptons (quarks) in a family vanish and Q = T₀ + Y independently in each helicity sector. As a generalization, we start with SU(2)_L × SU(2)_R × U(1)_(B-L) and introduce Δ as a continuous parameter which is a measure of explicit symmetry breakdown. Values 0 ? Δ ? 1/2 take the neutral generator of the isospin ½ representation to the singlet representation, i.e. ‘deformes’ the LR representation into the minimal Standard one. The corresponding classical O(3)-breaking term is a magnetic field perpendicular to the x₃-axis. A simple mapping on the fundamental Drinfeld-Jimbo q-deformed SU(2) representation is given.     

Diffusion Model of Saturation Current Collection by a Planar Langmuir Probe in a Strong Magnetic Field

Plasma presheath and saturation current collection by a planar Langmuir probe in a strong magnetic field perpendicular to the probe surface ares described with the diffusion model. The model takes into consideration the geometry of the probe, that is its size and shape, and dependence of the cross-field charged particles' transport into the effective collection region of the probe on the parallel-field transport to the probe. Experimental study of planar Langmiur probe I—V characteristics in D.C. discharge argon plasma in strong magnetic fields confirms the possibility of deriving the cross-field diffusion coefficient, D, from the measured electron satuation current. Additional dependence of the electron saturation current on the parallel-field diffusion coefficient, D, and the ion temperature, T_i, derived in the approximate Stangeby's study using the diffusion model of current collection by a planar surface (Stangeby, P. C., J. Phys. D: Appl. Phys. 15 (1982) 1007) can be eliminated with more rigorous calculation. Series of measurements on two neutral pressures and various magnetic fields gave reproducible values of D, approximately given by relation D ≈ (δn/〈n〉) k_BT_e/(eB).