The Effect of Increasing the Rate of Repetitions of Classical Reactions

Using quantum theory operator method, we discuss the general reversible classical reactions A ₁ + A ₁ + A _r B ₁ + B ₂ + + B _s, where r and s are arbitrary natural positive numbers. We show that if either direction of the reaction is repeated a large number of times N in a finite total times T then in the limit of very large N, keeping T constant, one remains with the initial reacting particles only. We also show that if the reaction evolves through different possible paths of evolution, each of them beginning at the same side of the reaction, proceeds through different intermediate consecutive reactions and ends at the other side, then one may realize any such path by performing in a dense manner the set of reactions along it. the same results are also numerically demonstrated for the specific reversible reaction A + B A + C. We note that similar results have been shown to hold also in the quantum regime.     

Energetics of naphthalene derivatives,IV+: a calorimetric and calculational thermochemical study of the isomeric naphthalenemethanols

The standard (p°?=?0.1?MPa) molar energies of combustion in oxygen, at T?=?298.15?K, of 1-naphthalenemethanol and 2-naphthalenemethanol were measured by static bomb calorimetry. The values of the standard molar enthalpies of sublimation, at T?=?298.15?K, were obtained by Calvet microcalorimetry. Combining these results the standard molar enthalpies of formation of the compounds, in the gas phase, at T?=?298.15?K, have been calculated.

Energetics of naphthalene derivatives, IV+ ⁺Paper III: Roux, M.V., Temprado, M., Notario, R., Verevkin, S.P., Emel’yanenko, V.N., DeMasters, D.E., Liebman, J.F. Mol. Phys., 102, 1909 (2004). : a calorimetric and calculational thermochemical study of the isomeric naphthalenemethanols

All authors

M. A. R. Matos, V. M. F. Morais, C. C. S. Sousa, M. V. Roux, R. Notario &; J. F. Liebman

https://doi.org/10.1080/00268970701413891

Published online:

04 December 2010

Table     

Diffusion in a periodic potential with a local perturbation

We consider the diffusion of a particle at X_t in a drift field derived from a smooth potential of the formV+B, whereV is periodic andB is a bump of compact support. With no bump,B=0, the mean squared displacementE(t) E |X _t – X₀|² =D(V)t +C +O(e ^–t ),>0, in any dimension. WhenB0, we establish in one dimension the asymptotic expansion , 0, ast. Our analysis relies on the Nash estimates developed in previous work for the transition density of the process and their consequences for the analytic structure,of the Laplace transform ofE(t).     

Mössbauer studies on the series La1-xSrxFeO3

Mössbauer spectra have been recorded at 4.2 and 300 K on the series La_1–x Sr _x FeO₃, wherex varies from 0 to 1.0 in steps of 0.1. Neutron diffraction experiments have shown that the crystal structure is orthorhombic for 0x<0.3, rhombohedral for 0.4x0.7, and cubic for 0.8<x1.0. Mössbauer spectra at 4.2 K are composed of magnetic sextet components arising from different charge states of iron ions. In the orthorhombic and rhombohedral phases, the charge states Fe³⁺ and Fe⁵⁺ coexist. In the cubic phase, iron is present as Fe³⁺ and Fe⁴⁺ states. At 300 K, the samples are magnetically ordered in the range 0 x0.3 and the coexistence of Fe³⁺ and Fe⁵⁺ remains. For samples 0.4x1.0, the samples are paramagnetic. Fits to these spectra require two components, one corresponding to an Fe⁴⁺ state, the other being best described as an Fe³⁺ ion forx0.7 but forx>0.7 having a mean charge state which increases to 3.5 forx=1.0.     

No Zero Energy States for the Supersymmetric x 2 y 2 Potential

We show that the positive supersymmetric matrix-valued differential operator H = p _x ² + p _y ² + x ² y ² + x₃ + y₁ has no zero modes, i.e., H = 0 implies = 0. The result depends on a virial type argument for the corresponding supercharge. The model may be regarded as a simple relative of dimensional reductions of supersymmetric Yang–Mills theories.     

Mössbauer effect in inorganic glasses

⁵⁷Fe- and¹¹⁹Sn-Mössbauer effects become a very effective tool for the local structural study of inorganic glasses. Fe³⁺ and Sn⁴⁺ occupy network former (NWF) sites in several oxide glasses, while they are present at interstitial sites as network modifier (NWM) in phosphate, germanate and sulfate glasses. Characteristic-ray or thermal neutron irradiation effect indicates the structural role of Mössbauer ions; an increase in the 4s electron density or a reduction of Fe³⁺ to Fe²⁺ is observed due to the charge transfer from oxygen to Fe³⁺ when iron occupies NWF sites. By contrast, oxidation of Fe²⁺ to Fe³⁺ takes place when iron occupies NWM sites. Debye temperatures ( _D) obtained from low-temperature Mössbauer measurements are higher than 280 K when Fe³⁺ and Sn⁴⁺ are covalently bonded to oxygen at NWF sites, while the _D is lower than 270 K when these ions are ionically bonded to oxygen or halogen at NWM sites. A linear relationship between the glass transition temperatureT _g and the quadrupole splitting () of Fe³⁺, named T_g- rule, also indicates the structural role of Fe³⁺, i.e.,T _g versus plot yields a large slope of 680°C/mm s^–1 when Fe³⁺ occupies NWF sites, whereas it is only 35°C/mm s^–1 when the iron is present at NWM sites.     

Pattern formation in systems with nonlocal interactions

One-dimensional lattices with harmonic coupling between neighboring lattice sites and an on-site anharmonic potential V()=A²ⁿ⁺² + ⁿ⁺² + C² + D are examined in the displacive limit. Kink solutions, interpolating between the coexistent phases =0 and =±(C/A)^1/2n at theT=0 first-order phase transition pointB ²=4AC,A, C>0,B<0,D=0 are found in simple analytic form and their dependence on the degree of anharmonicity (n=2, 4, 6, ...) is discussed. It is shown that, at the phase transition point, the kinks are accompanied by a continuous spectrum of periodic nonlinear excitations (periodons) having finite energy density.Work supported by the Swiss National Science Foundation     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

Unconventional large-N limit of the Gaussian effective potential and the phase transition in λφ 4 theory

In the conventional large-N limit the coupling constant is required to scale as 1/N. While the Gaussian effective potential (GEP) is known to contain the exact result in this limit, it shows a phase transition only when 1/N (in units of the renormalized mass in the symmetric vacuum). Here we determine the asymptotic behaviour, asN, of and other quantities at the phase transition of the GEP. We find _crit to be finite in 0+1 dimensions; of order 1/lnN in 1+1 dimensions; 1/N ^1/3 in 2+1 dimensions; and in 3+1 dimensions. The GEP's first-order phase transition is shown to become asymptotically second-order in 1+1 dimensions and below. We also discuss non-integer dimensions and the approach to the non-trivial autonomous theory in 3+1 dimensions.     

Structures of the f 0(980), a 0(980) mesons and the strong coupling constants g_{f_0 K^+ K^-} , g_{a_0 K^+ K^-} with light-cone QCD sum rules

Making the assumption of explicit isospin violation arising from f ₀(980)-a ₀(980) mixing, we take the point of view that the scalar mesons f ₀(980) and a ₀(980) have both strange and non-strange quark-antiquark components and evaluate the strong coupling constants within the framework of the light-cone QCD sum rules approach. The large strong scalar-KK couplings through both the and components , , and will support the hadronic dressing mechanism; furthermore, in spite of the constituent structure differences between the f ₀(980) and a ₀(980) mesons, the strange components have larger strong coupling constants with the K ⁺ K ^- state than the corresponding non-strange ones, and . From the existing controversial values, we cannot reach a general consensus on the strong coupling constants and the mixing angles.Received: 9 January 2004, Revised: 23 July 2004, Published online: 2 September 2004     

A Class of Generalized Gamma Functions

We study a family of holomorphic functions defined by infinite products of the form (a, r real, ar > 0) which generalize Eulers definition since . We obtain analogues of classical formulas (e.g. Gauss multiplication and complement formulas) for these functions _a,r(s)     

Anomalies and curvature ofW manifolds

We study the holomorphic structure of certain complex manifolds associated withW algebras, namely, the flag manifoldsW /T andW ₁₊/T ₁₊, and the spacesW /SL(),R) andW ₁₊/GL(,R), whereT andT ₁₊ are the maximal tori inW andW ₁₊. We compute their Ricci curvature and show how the results are related to the anomaly-freedom conditions forW andW ₁₊. We discuss the relation of these manifolds with extensions of universal Teichmüller space.Supported in part by the U.S. Department of Energy, under grant DE-AS05-81ER40039Supported in part by the U.S. Department of Energy, under grant DE-FG03-84ER40168     

The photoassociative spectroscopy, photoassociative molecule formation, and trapping of ultracold \mathsf{^{39}K^{85}Rb}

We have observed the photoassociative spectra of colliding ultracold ³⁹K and ⁸⁵Rb atoms to produce KRb* in all eight bound electronic states correlating with the ³⁹K (4s) + ⁸⁵Rb(5p _1/2 and 5p _3/2) asymptotes. These electronically excited KRb* ultracold molecules are detected after their radiative decay to the metastable triplet (a state and (in some cases) the singlet (X ground state. The triplet (a ultracold molecules are detected by two-photon ionization at 602.5 nm to form KRb ⁺ , followed by time-of-flight mass spectroscopy. We are able to assign a majority of the spectrum to three states (2(0 ⁺ ), 2(0^-), 2(1)) in a lower triad of states with similar C ₆ values correlating to the K(4s) + Rb (5p _1/2) asymptote; and to five states in an upper triad of three states (3(0 ⁺ ), 3(0^-), 3(1)) and a dyad of two states (4(1), 1(2)), with one set of similar C ₆ values within the upper triad and a different set of similar C ₆ values within the dyad. We are also able to make connection with the short-range spectra of Kasahara et al. [J. Chem. Phys. 111, 8857 (1999)], identifying three of our levels as v = 61, 62 and 63 of the 1 4(1) state they observed. We also argue that ultracold photoassociation to levels between the K(4s) + Rb (5p _3/2) and K(4s) + Rb (5p _1/2) asymptotes may be weakly or strongly predissociated and therefore difficult to observe by ionization of a (or X molecules; we do know from Kasahara et al. that levels of the 1 4(1) and 2 5(1) states in the intra-asymptote region are predissociated. A small fraction ( 1/3) of the triplet (a ultracold molecules formed are trapped in the weak magnetic field of our magneto-optical trap (MOT).Received: 22 September 2004, Published online: 23 November 2004PACS: 33.20.Fb Raman and Rayleigh spectra (including optical scattering) - 34.20.Cf Interatomic potentials and forces - 33.80.Ps Optical cooling of molecules; trapping     

Studies of the spin-Hamiltonian parameters, d–d transitions and defect structures for two tetragonal Cu centers in Ba2ZnF6:Cu crystal

Two theoretical methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM), are applied to calculate the spin-Hamiltonian parameters (g-factors g, g and hyperfine structure constants A, A, obtained from electron paramagnetic resonance (EPR) spectra) and d–d transitions (obtained from optical spectra) for two tetragonal Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ crystals. The Cu²⁺(I) ion replaces the Zn²⁺ ion at tetragonally compressed octahedral coordination and has the ground state ²A₁(|d_z²), whereas the Cu²⁺(II) ion is at an interstitial site with a square-planar F⁻coordination and has the ground state ²B₂(|d_x²-y²). The calculated spin-Hamiltonian parameters and d–d transitions from the PTM and CDM coincide and are in reasonable agreement with the experimental values. This suggests that both methods are effective for the theoretical studies of EPR and optical spectral data for 3d⁹ ions in tetragonal symmetry with different ground states. The defect structures of the two Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ are also estimated.     

Secondary Neutral Pion-nucleon Flux Ratio at the Top of the Atmosphere

The CERN Intersecting Storage Ring data on the inclusive reaction p + p → π° + X has been fitted with a phenomenological form where W_c(a,b,z) is the generalized confluent function defined by . M(a, b, z) being the well known Kummer's function. Using this form and primary proton spectrum of Goddard Space Flight Center Group the secondary neutral pion-nucleon flux ratio at the top of the atmosphere has been estimated. The derived result has been compared with those expected from p + p → π^± + X data, via different models.     

The electronic structure of Rhodium: Angle-resolved studies of photoelectron and secondary electron emission

We report electron spectroscopic studies of the Rh(111) surface, with the aim to obtain bulk band-structure information. We have measured normal photoemision using tunable synchrotron radiation in the range of photon energies between 11 eV and 55 eV, and angle-dependent photoemission along the LUX and LKL azimuths using the He resonance lines (=21.2 eV, 40.8 eV). To complement these data, we studied angleresolved secondary electron emission after excitation with electrons and photons. We derive parts of the one-electron energy dispersionE(k) along L, and determine the energies of several bulk critical points (in eV):E(> ₇₊/₈₊)=–2.75±0.10,E(> ₈₊=–0.85±0.10,E(> _7–=16.1±0.5,E(> _6–/> _8–)=20.5±0.5,E(X ₇₊)=–5.0±0.1,E(L ₆₊)=–5.6±0.5,E(L ₆₊/L ₄₊₊₅₊)=–2.65±0.10,E(L ₆₊)=9.0±0.5 eV. Our results are compared to several available band structure calculations.     

ENDOR-investigations of iron doped GaAs and GaP

From ENDOR-measurements of GaAs:Fe³⁺ the symmetries and hyperfine parameters of three groups of neighbour nuclei have been obtained. The values of ||², r ^–3 and of the electric field gradients at the sites of the neighbour nuclei have been determined for GaAs:Fe³⁺ and GaP:Fe³⁺. The comparison of our results with those of NMR-investigations indicates the Fe³⁺-ion to be an interstitial impurity surrounded by four groupV atoms in a tetrahedral arrangement.     

Invariant curves for area-preserving twist maps far from integrable

One-parameter families of area-preserving twist maps of the formF (x, y)=(x +y +f(x),y +f(x)) are considered. Various invariant curves, for the maps corresponding tof(x)=sin andf(x)=sinx+(1/50) sin(5x), are rigorously constructed forlarge values of the nonlinearity parameter . For larger values of , close to critical, some numerical experiments are briefly discussed.     

A Mössbauer spectroscopic study of cobalt-iron molybdates

Fe _x Co_1–x MoO₄ compounds prepared by coprecipitation were studied by XRD, electrical conductivity and mainly by absorption and emission Mössbauer spectroscopy. FeMoO₄ and CoMoO₄ samples were shown to contain Fe³⁺ and Co³⁺, respectively, in solid solution. Three kinds of Fe _x Co_1–x MoO₄ solids can be described. Forx0.16: one has a -Co(Fe²⁺, Fe³⁺)MoO₄ solid solution. For 0.17x0.25: one has the same solid solution with its surface rich in Fe³⁺. Forx0.26: one has the same solid solution with only bulk Fe³⁺, and ferric molybdate. Studies of reduction by hydrogen and of catalytic reaction of mechanical mixtures of CoMoO₄ and ferric molybdate support these statements.     

Isospin mixing in the 4<Superscript> + </Superscript> doublet of <Superscript>54</Superscript><Emphasis Type="Italic">Co</Emphasis>

The T = 1 admixture into the T = 0 member of a recently discovered isospin-doublet in ⁵⁴Co is obtained from the measured electromagnetic E2/M1 multipole mixing ratio, of the transition. Combining these data with shell model calculations for strong isovector M1 and isoscalar E2 electromagnetic matrix elements one obtains a value for the T = 1 admixture into the T = 0, 4 ⁺ state of . The corresponding mixing matrix element in the 4 ⁺ doublet is keV.Received: 31 October 2002, Published online: 9 March 2004PACS: 21.10.Hw Spin, parity, and isobaric spin - 21.60.Cs Shell model - 23.20.Gq Multipole mixing ratios