Comment on: “Universal relation between spectroscopic constants”

Kaur and Mahajan [1] have claimed to derive a universal relation InG = 1.91578(±0.09727) + 0.97111(±0.03809) In Δ between the Sutherland parameter Δ(=ω _er _e ² /2D_e) and the dimensionless parameterG(= 8ω _ex_e/B_e) for the ground as well as excited electronic states of diatomic molecules. Validity of this relation is checked and we find that the relation is not correct. Next, we checked the validity of the relation Δ = 2.2r_e for the alkali group diatomic molecules. This relation is also found not to be correct.     

New results from the HAPPEX Experiments at Q<Superscript>2</Superscript> = 0.1GeV/c<Superscript>2</Superscript>

The nucleon's strange electric and magnetic form factors G _E ^s and G _M ^s can be probed via parity-violating electron scattering. The HAPPEX Collaboration has made new measurements of the parity-violating asymmetry A _PV in elastic scattering of 3GeV electrons off hydrogen and ⁴He targets with 〈θ_lab〉 ≈ 6.0^° . For ⁴He the preliminary result is A _PV = (+ 6.43±0.23(stat)±0.22(syst))×10^-6 . For hydrogen the preliminary result is A _PV = (- 1.60±0.12(stat)±0.05(syst))×10^-6 . From these values we extract G ^s _E = 0.004±0.014±0.013 at 〈Q ²〉 = 0.077 GeV/c^2 , and G ^s _E +0.09G ^s _M = 0.004±0.011±0.005 at 〈Q ²〉 = 0.109 GeV/c^2 , both consistent with zero, providing stringent new limits on the role of strange quarks in the vector structure of the nucleon.     

Aggregation of 1,3,7-trimethylxanthine with methylene blue in aqueous solution

We have studied self-association of aromatic molecules of the thiazine dye methylene blue in aqueous solution, using a dimer model. We have determined the dimerization equilibrium constant for the dye molecules K_D = 3900 ± 800 M⁻¹ at T = 293 K. We have decomposed the experimental spectrum into dimer and monomer components. Using the ratio of the molar absorption coefficients for two absorption bands of the dimer spectrum, we obtained the “average” value of the angle between the electronic transition moments of the molecules in the dimers, α = 48°. We have studied heteroassociation of methylene blue (MB) and 1,3,7-trimethylxanthine (caffeine) molecules in aqueous solution. We have calculated the heteroassociation constant as 200 ± 34 M⁻¹. We conclude that heteroassociation of methylene blue and caffeine molecules leads to a lower effective dye concentration in solution, which hypothetically may affect its biological activity. We have determined the values of the Gibbs free energy, the enthalpy, and the entropy for dimerization of methylene blue molecules: ΔG₂₉₃ = −(20 ± 3) kJ/mol, ΔH = −(25 ± 9) kJ/mol, Δ S₂₉₃ = −(17 ± 6) J/mol·K; and for methylene blue-caffeine heteroassociation: ΔG₂₉₃ = −(13 ± 3) kJ/mol, ΔH = −(14 ± 10) kJ/mol, ΔS₂₉₃ = −(2.4 ± 0.2) J/mol·K, respectively. We have shown that the methylene blue aggregates and the heteroassociates with caffeine are predominantly stabilized by dispersion interactions between the chromophore molecules in the associates. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 2, pp. 158–163, March–April, 2006.     

Kinetics of formation of O2(1Σ) molecules in reactions involving excited O2(1Δ) oxygen molecules and I(2P1/2) iodine atoms

The results of our experimental study of the kinetics of formation of O₂(¹Σ) molecules in energy-exchange reactions O₂(¹Δ) + I(⁵ p,² P _1/2) and O₂(a,¹Δ) + O₂(a,¹Δ) are presented. The ratio of rate constants was obtained for these reactions (4800 ± 300). Setting the rate constant of the deactivation of O₂(¹Σ) molecules on CO₂ molecules at 4.1 · 10^–13 cm³/s, we evaluated the rate constants for these reactions at a temperature of approximately 330 K: (1.7 ± 0.2) · 10⁻¹³ and (3.6 ± 0.5) · 10⁻¹⁷ cm³/s, respectively.     

The gluonic condensate from the hyperfine splitting M cog(XcJ) — M(h c) in charmonium

The precision measurement of the hyperfine splitting, Δ_HF(1P, c-c) = M _cog(xcJ) — M(h _c), in the Fermilab-E835 and CLEO experiments allows one to determine the gluonic condensate G ₂ with high accuracy if the gluonic correlation length T _g is fixed. In our calculations, the negative value of Δ_HF = −0.5 ± 0.4 MeV, as in the E835 experiment, is obtained only if the relatively small T _g = 0.16 im and G ₂ = 0.060(3) GeV⁴ are taken. For T _g ≥ 0.2 fm, the hyperfine splitting is positive and grows for increasing T _g. In particular, for T _g = 0.2 fm and G ₂ = 0.045(2) GeV⁴, the splitting Δ_HF = 1.0(5) MeV is just in accordance with the recent CLEO result. The values of G ₂ taken correspond to the “physical” string tension σ ≈ 0.18 GeV². The text was submitted by the authors in English.     

Determination of the gluon polarization at RHIC and COMPASS

The most recent determinations of the gluon polarization in the nucleon, , obtained at RHIC and COMPASS experiments, are reviewed. The former accesses the gluon polarization mainly through the production of neutral pions (PHENIX) or jets (STAR) in polarized proton collisions. The latter uses the photon-gluon fusion in polarized lepton-nucleon scattering, tagged either by open charm or high-p_T hadrons production. All the results are in good agreement, and favour values of ΔG roughly between 0 and 0.5 at a few (GeV/c)² , thus in contradiction with what could be derived from the Ellis-Jaffe sum rule and the axial anomaly. Much stronger constraints will be obtained in a near future by both programs, helping us to clarify the role of gluons in the nucleon spin.     

Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

Observation of Δ+→ pπ0 decay in heavy-ion collisions

Proton-π⁰ coincidences have been measured at the beam energy of 180A MeV in the reaction Ar+Ca studied by TAPS at SIS/GSI. In the proton-π⁰ invariant mass spectrum we observe a significant excess of strength above the background obtained by event mixing. We attribute this signal to the strength distribution N _Δ of the Δ baryonic resonance. No correlation is observed in the case of deuteron-π⁰ coincidences. Assuming isotropic emission of π⁰ and Δ⁺ from a midrapidity thermal source and isospin symmetry, we determined the global N _Δ/N _πratio of 0.79 ±0.30(stat) ±0.2(syst). This value indicates that most pions produced at subthreshold energy in heavy-ion reaction are mediated by the Δ-resonance. Received: 7 April 2000 / Accepted: 29 August 2000     

The estimates of periodic potentials in terms of effective masses

LetG _n=(A _n ⁻ , A _n ⁺ ),n≧1, denote the gaps,M _n ^± be the effective masses and Σn=[A _n−1 ⁺ ,A _n ^- ],A ₀ ⁺ =0, be the spectral bands of the Hill operatorT=−d ²/dx ²+V(x) inL ² (R), whereV is a 1-periodic real potential fromL ²(0,1). Let the length gapL _n=|G_n|, h_n be the height of the corresponding slit on the quasimomentum domain and Δ_n=π²(2n−1)−∣Σ_n∣>0 be the band reduction. Let ,n≧1, denote the gap length for the operator . Introduce the sequencesL={L_n}, h={h_n}, l={l_n}, Δ={Δ_n},M ^±={M _n ^± } and the norms ,m≧0. The following results are obtained: i) The estimates of‖V‖, ‖L‖, ‖h‖ ₁, ‖l‖₁, ‖δ‖ in terms of ‖M^±‖₂, ii) identities for the Dirichlet integral of quasimomentum and integral of potentials and so on, iii) the generation of i), ii) for more general potentials. The research described in this publication was made possible in part by grant from the Russian Fund of Fundamental Research and INTAS.     

Fractal simulation of the resistivity and capacitance of arsenic selenide

The temperature dependences of the ac resistivity R and ac capacitance C of arsenic selenide were measured more than four decades ago [V. I. Kruglov and L. P. Strakhov, in Problems of Solid State Electronics, Vol. 2 (Leningrad Univ., Leningrad, 1968)]. According to these measurements, the frequency dependences are R ∝ ω^{−0.80±0.01} and ΔC ∝ ω^{−0.120±0.006} (ω is the circular frequency and ΔC is measured from the temperature-independent value C ₀). According to fractal-geometry methods, R ∝ ω^1−3/h and ΔC ∝ ω^−2+3/h , where h is the walk dimension of the electric current in arsenic selenide. Comparison of the experimental and theoretical results indicates that the walk dimensions calculated from the frequency dependences of resistivity and capacitance are h _R = 1.67 ± 0.02 and h _C = 1.60 ± 0.08, which are in agreement with each other within the measurement errors. The fractal dimension of the distribution of conducting sections is D = 1/h = 0.6. Since D < 1, the conducting sections are spatially separated and form a Cantor set.     

High order electron paramagnetic resonance transitions of Gd3+ in Pr2Zn3(NO3)12·24H2O single crystals

Electron paramagnetic resonance of Gd³⁺ in Pr₂Zn₃(NO₃)₁₂ · 24H₂O single crystals has been studied at ∼ 9.45 GHz and at 285 K. In addition to the allowed fine structure lines (ΔM=± 1) some weak low field lines identified as ΔM = ± 2 transitions have been observed.     

Kinetic regularities and mechanism of polymerization of perfluoromethylvinyl ether at high pressures

The kinetics of the thermal polymerization of perfluoromethylvinyl ether (PFMVE) is studied at pressures of 3–13 kbar (300–1300 MPa) and temperatures of 80–260°C. The activation energy (E _act = (76 ± 3) kJ/mol) and activation volume (ΔV₀^⪼ = −(27 ± 2) cm³/mol) for the overall polymerization rate are determined. The inhibition method is used to estimate the activation energy of thermal initiation (E _in = (79.9 ± 3) kJ/mol). The quantity E _p − (1/2)E _t was calculated to be 36.6 ± 3 kJ/mol. The limiting polymerization temperature was evaluated: T _lim = (180 ± 3)°C. A mechanism of PFMVE polymerization is proposed on the assumption that the reaction is bimolecular.     

Kerr effect of molecular oxygen at λ=1064 nm

We report a new measurement of the Kerr effect of molecular oxygen at λ= 1064 nm. The experimental value reported for the anisotropy of the index of refraction Δ n_u^l, (3.15±0.85)×10^-25 m² V^-2 atm^-1, is in good agreement with the value of 3.4×10^-25 m² V^-2 atm^-1 obtained via an ab initio calculation. We show that the dependence of the effect on the pressure is not linear because of the presence of a collision-induced absorption band around 1060 nm due to the transition from the X³ Σ^-_g ground state to the ¹Δ_g state. We also give the value of the quadratic anisotropy Δn_u^q (-1.03±0.68)×10^-25 m² V^-2 atm^-2. We finally compare our ab initio theoretical and experimental results with previous existing data.     

Gravity of monopole and string and the gravitational constant in 3He-A

We discuss the effective metric produced in superfluid ³He-A by such topological objects as the radial disgyration and monopole. In relativistic theories these metrics are similar to that of the local string and global monopole, respectively. But in ³He-A they have a negative angle deficit, which corresponds to a negative mass of the topological objects. The effective gravitational constant in superfluid ³He-A, deduced from a comparison with relativistic theories, is G∼Δ⁻², where the gap amplitude Δ plays the part of the Planck energy. G depends on temperature roughly as (1−T ²/T _c ² )⁻² and corresponds to a screening of Newton’s constant. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 666–671 (10 May 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Search for and study of low-mass scalar mesons in reaction np → npπ+π? at neutron beam momentum Pn = (5.20 ± 0.12) GeV/c

We present the results of a search for and study of the resonance effects in the system of π⁺π⁻ from the reaction np → npπ⁺π⁻ at the momentum of quasi-monochromatic neutrons P _n = (5.20 ± 0.12) GeV/c from the data obtained in an exposure of the 1-m hydrogen bubble chamber of Veksler and Baldin Laboratory of High Energies, Joint Institute for Nuclear Research (VBLHE JINR). After the supplementary selection of the events where a secondary proton was emitted in the forward hemisphere in the general c.m.s. of the reaction (cosθ* _p > 0) in the effective mass spectrum of π⁺π⁻ combinations, we found nine peculiarities at the masses (350 ± 3), (408 ± 3), (489 ± 3), (579 ± 5), (676 ± 7), (762 ± 11), (878 ± 7), (1036 ±13), and (1170 ± 11) MeV/c ² with experimental widths of no more than several tens of MeV/c ². We carried out a direct measurement of the spins of resonances and also obtained other quantum numbers. All of these peculiarities have a similar set of quantum numbers I ^G (J ^PC ) = 0⁺ (0⁺⁺). We investigated a sequence of scalar-isoscalar resonances f ₀(σ₀) with masses in the range M ≤ 1200 MeV/c ². We found a phenomenological dependence of the resonance mass on its number. This dependence covered not only the resonances shown in this paper, but also those present in PDG tables with quantum numbers of f ₀(σ₀) mesons.     

Study of the isobar configurations in the <Superscript>12</Superscript>C and <Superscript>16</Superscript>O ground states

Experimental research on positive-pion photoproduction on the oxygen nucleus in the ¹⁶O(γ, π⁺p) reaction at high recoil momenta of the residual nuclear system was performed. The yield for the ¹⁶O(γ, π⁺p) reaction was analyzed using a model that takes Δ-isobar configurations in nuclei ground states into account, together with the earlier-measured yield of the¹²C(γ, π⁺p) reaction. The estimated number of isobars per nucleon N _Δ = 0.012 ± 0.005 was obtained for the ¹²C nucleus, and ¹⁶O N _Δ = 0.018 ± 0.004 was obtained for the ¹⁶O nucleus.     

A regular potential which is nowhere in L 1

A nonnegative potential V: ℝ^v→ℝ is constructed for which V ∉ L _q (G) for any nonempty open G⊂→^v, q>0, and for which nevertheless W _inf2 ^sup1 ∩ Q(V) is dense in W _inf2 ^sup1 , i.e., is a form core for −1/2Δ in L ₂.     

Quark momentum-space charge distribution in deuteron and neutron/proton structure functions ratio

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant α _p(E ₀₊) = + 3.2, α _n(E ₀₊) = + 4.1, the t-channel α ^t _{p, n} = - β ^t _{p, n} = + 7.6 and the resonant β _{p, n}(P ₃₃(1232)) = + 8.3 contributions (in units of 10^-4fm^3). The remaining deviations from the experimental data Δα _p = 1.2±0.6, Δβ _p = 1.2±0.6, Δα _n = 0.8±1.7 and Δβ _n = 2.0±1.8 are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon coupling to the σ-meson having the predicted mass m _σ = 666MeV and two-photon width Γ _γγ = 2.6keV.     

EPR Equilibration Study of the O–H Bond Dissociation Enthalpy in a Benzyl Phenolic Antioxidant

The equilibrium of the reaction galvinoxyl radical + 4,4′-methylene-bis(2,6-di-tert-butyl-phenol) (IOH) ⇆ hydrogalvinoxyl + 4,4′-methylene-bis(2,6-di-tert-butyl-phenoxyl radical) was monitored by electron paramagnetic resonance spectroscopy between 213 and 293 K. The equilibrium constant was calculated for each temperature point and correlated to T ⁻¹ applying the Van't Hoff relationship lnK _R = (−ΔH _R ⁰/RT) + (ΔS _R ⁰/R). The reaction enthalpy was found to be 12.0 ± 0.9 kJ/mol and the bond strength in IOH (BDE_(O–H)) = 340.7 ± 3.0 kJ/mol. The thermochemical stabilization of the involved phenoxyls is discussed. Authors' address: Sara N. Mendiara, Departamento de Química, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, Mar del Plata 7600, Argentina