The long-time behaviour of the electric-field autocorrelation function in a finite photon gas

We investigate an autocorrelation function of a soluble three-dimensional system, namely the temporal coherence functionC _E(t)∝<E(0)E(t)> of the thermal radiation field in a cube-shaped cavity for the stochastic electrical fieldE. In the thermodynamic limit,C _E(t) relaxes exponentially at intermediate times, but a “long-tail” behaviourC ₀(t)=At^?4 withA<0 is predominant for long times. In the case of a finite, but not too small, cavity lengthL obeyingΛ=hc/k _BT?L and at timest withct?L, C _E(t) is described by an asymptotic expansion in powers ofL ^?1 using generalized Riemann zeta functions. Surface-and shape-effects enhance the long-tail. In the case of very small cavities withL«Λ, we calculate an expansion ofC _E(t) in terms of exp(?L ^?1) and cosines. An oscillatory, but not strictly periodic, long-time behaviour is observed in this case.     

Effect of kink-rounding barriers on step edge fluctuations

The effect that an additional energy barrier E_kr for step adatoms moving around kinks has on equilibrium step edge fluctuations is explored using scaling arguments and kinetic Monte Carlo simulations. When mass transport is through step edge diffusion, the time correlation function of the step fluctuations behaves as C(t)=A(T)t^1/4. At low temperatures the prefactor A(T) shows Arrhenius behavior with an activation energy (E_det+3?)/4 if E_kr<? and (E_det+E_kr+2?)/4 if E_kr>?, where ? is the kink energy and E_det is the barrier for detachment of a step adatom from a kink. We point out that the assumption of an Einstein relation for step edge diffusion has lead to an incorrect interpretation of step fluctuation experiments, and explain why such a relation does not hold. The theory is applied to experimental results on Pt(1 1 1) and Cu(1 0 0).     

The microwave spectrum of IF5 in excited vibrational states: Accidental degeneracy and avoided crossing of the kl = 3 and kl = −1 levels in the state v9(E) = 1

Measurements of the microwave spectrum of the C_4v molecule IF₅ in the excited vibrational states v₉(E) = 1 and v₅(B₁) = 1 are reported for the transitions J12 ← 11 and J13 ← 12 (65–72 GHz). The considerable spectral perturbations produced by an accidental degeneracy and avoided crossing of the ψ^? (kl = 3) and ψ^? (kl = ?1) levels of the v₉(E) = 1 state have been measured and analyzed. A spectroscopic determination of the axial rotation constant C₉ is reported and its implications for the molecular structure of IF₅ discussed.     

Stark spectroscopy with the CO2 laser: The ν5 band of 12CD3F

The ν₅ band of ¹²CD₃F was studied using coincidences with the 9.4-μm band of the ¹²C¹⁶O₂ laser and the 9.25-μm band of the ¹²C¹⁸O₂ laser. The resonances were analyzed together with the infrared spectra and recent microwave results to give the following vibration-rotation parameters and dipole moment in the ν₅ state: ν₀ = 1072.35093 (11) cm^?1; B = 0.681137 (4) cm^?1; A₅-A₀ = ?0.01437 (3) cm^?1; Aζ_z = ?0.81453 (3) cm^?1; μ_ν5 = 1.8751 (25) D. The parameters should be useful in assigning some near millimeter laser lines in CD₃F.     

Absorption spectrum of the Mn2+ ions in crystals of lanthanum manganese double nitrate and praseodymium manganese double nitrate

The optical absorption spectrum of the Mn²⁺ ions in the two double nitrates La₂Mn₃(NO₃)₁₂ ? 24H₂O and Pr₂Mn₃(NO₃)₁₂ ? 24H₂O were measured up to 30000 cm^?1. Uniaxial stress was applied to the crystals to determine the multiplicity of the observed zero phonon lines belonging to the transitions from the groundstate⁶ A ₁ (⁶ S) to the excited states⁴ E(⁴ G) and⁴ T ₂(⁴ D). The Zeeman effect of the states⁴ A ₁(⁴ G) and⁴ E(⁴ G) was measured with magnetic fields up to 6.4T. The effect of covalency and trigonal field, especially to the states⁴ A ₁ (⁴ G) and⁴ E(⁴ G), is briefly discussed.     

Dielectric behavior and low temperature phase transition in NH4IO3

The electrical properties namely ac conductivity σ(ω,?T) and the complex dielectric permittivity (ε*) are measured at selected frequencies (5–100?kHz) as function of temperature (95?K?T?4IO₃. The ferroelectric hysteresis loops and the X-ray diffraction pattern are also measured. The analysis of the data indicates that the compound undergoes a structural phase transition at ～103?K and the behavior of σ(ω,?T) obeys the power law. The trend of the temperature dependence of the angular frequency exponent s (0?s?4IO₃; (2) the data indicate that the compound undergoes a structural phase transition at 103?K; (3) the originality of this transition has been confirmed by X-ray diffraction; (4) no evidence for the existence of a ferroelectric transition at 103?K as mentioned earlier; and (5) the quantum mechanical tunneling is proposed as the main mechanism of the electric conduction.     

Large-scale structure of isotropic homogeneous turbulence

It is shown that the longitudinal correlation functionf is asymptotically proportional tor ^?3 asr→∞ and the energy spectrum function is asymptotically proportional toκ ² asκ→0 if and only if 0<〈(f u d ³ x)·u〉<∞. Moreover, the latter finiteness condition is shown to be essentially equivalent to 〈(fy·ud ³ x)²〉<∞ for nonstochasticyεL ²(R₃). Confirmed by recent experimental measurements, the larger dependencef ∝r ^?3 is concomitant with anO(r ^?6)=O(f ²) fall-off of the viscous force term in the Kármán-Howarth equation.     

Temperature dependence of the fine structure of the C and E absorption bands in RbMnF3 below the Néel temperature

The variation in the parameters (width, position, intensity) of the fine structure lines in the C[⁶ A _1g → ⁴ A _1g , ⁴ E _g(⁴ G)] and E[⁶ A _1g → ⁴ E _g(⁴ D)] bands in RbMnF₃ with temperature is studied in the temperature range 10–70 K. In the C band, two narrow (<6 cm^?1) lines are are distinguished at distances of 77 and 80 cm^?1 from the exciton line at T = 10 K. The other lines in the C band and all lines in the E band are more than 20 cm^?1 wide. It is demonstrated that the narrow lines become allowed because of the spin-exchange interaction within a long-range magnetic order model and originate from the excitation of exciton-magnon bound states and that the other lines are made allowed by the exchange-vibronic mechanism within a short-range magnetic order model and originate from the excitation of bound states composed of an exciton, magnon, and oddparity phonon. The vibrational replicas of the main exciton-magnon-phonon lines are due to the quadratic vibronic interaction with odd-parity vibrations. Variations of the intensities and widths of the absorption lines with temperature indicate that these parameters are affected by relaxation and delocalization of the bound states.     

Hyperfine structure investigations in the4F9/2 atomic ground state of191Ir and193Ir

The5d ⁷6s^{2 4}F_9/2 atomic ground state of¹⁹¹Ir and¹⁹³Ir has been studied using the atomic-beam magnetic-resonance method. The results are:¹⁹³Ir:g _J(⁴F_9/2)=1.29694 (3)¹⁹¹Ir:Δv(⁴F_9/2; F=6?F=5)=659.26496 (12) MHzΔv( ⁴F_9/2; F=5?F=4)=189.44002 (09) MHzΔv( ⁴F_9/2; F=3?F=4)=84.05040 (80) MHzA=57.52148 (04) MHzB=471.20425 (57) MHzC=?0.020 (30) kHz¹⁹³Ir:Δv( ⁴F_9/2; F=6?F=5)=660.09043 (12) MHzΔv( ⁴F_9/2; F=5?F=4)=224.47848 (13) MHzΔv( ⁴F_9/2; F=?F=4)=33.53453 (89) MHzA=62.65556 (05) MHzB=426.23546 (64) MHzC=0.020 (30) kHz Using the magnetic dipole moments known by NMR-technique [1] we obtained for the electric quadrupole moments as calculated from the hyperfine interaction constantsA andB:Q(¹⁹¹Ir)=0.78 (20) barns,Q(¹⁹³Ir)=0.70 (18) barns (uncorrected for core polarization effects). A calculation of the hyperfine anomaly yields:₁₉₁ Δ ₁₉₃=?0.00023 (10). The ratio of theB factors which should be the same as for the quadrupole moments turned out to be:B(¹⁹¹Ir)/B(¹⁹³Ir)=Q(¹⁹¹Ir)/Q(¹⁹³Ir)=1.105502(3).     

SiO2 surface defect centers studied by AES

A theoretical model is proposed on how a Si dangling bond associated with an oxygen vacancy on a SiO₂ surface (E_s′ center) should be observed by Auger electron spectroscopy (AES). The Auger electron distribution N_A(E) for the L₂₃VV transition band is calculated for a stoichiometric SiO₂ surface, and for a SiO_x surface containing Si-(e^?O₃) coordinations. The latter is characterized by an additional L₂₃VD transition band, where D is the energy level of the unpaired electron e^?. The theoretical N_A(E) spectra are compared with experimental N(E) spectra for a pristine, and for an electron radiation damaged quartz surface. Agreement with the theoretical model is obtained if D is assumed to lie ≈2 eV below the conduction band edge. This result shows that AES is uniquely useful in revealing the absolute energy level of localized, occupied surface defect states. As the L₂₃VD transition band (main peak at 86 eV) cannot unambiguously be distinguished from a SiSi₄ coordination L₂₃VV spectrum (main peak at 88 eV), supporting evidence is presented as to why we exclude a SiSi₄ coordination for our particular experimental example. Application of the Si-(e^?O₃) model to the interpretation of SiO₂Si interface Auger spectra is also discussed.     

Structure,vibrational study and conductivity of the trihydrated uranyl bis(dihydrogenophosphate): UO2(H2PO4)2·3H2O

The X-ray structure (293 K) of UO₂(H₂PO₄)₂·3H₂O has been refined (R = 0.062): M_r = 518g, space group: P2₁/c (Z = 4); $\text{a = 10.816(1)}\text{A}\text{?}$, $\text{b = 13.896(2)}\text{A}\text{?}$, $\text{c = 7.481(1)}\text{A}\text{?}$, β = 105.65(1)^°, $\text{V = 1082.7(2)}\text{A}\text{?}{}^3$; D_c = 3.17 Mg m^?3. The structure consists of infinite chains along the (101) axis with U atoms bridged by two H₂PO₄ groups. The U atom is surrounded by a pentagonal bipyramid of oxygen atoms, one of them being an equatorial water molecule. The cohesion between the chains is ensured by hydrogen bonds involving the two last water molecules. An assignment of IR and Raman bands with isotopic substitution spectra is proposed. A phase transition at 128 K was made evident by DSC and spectroscopy. The room-temperature phase is characterized by a high disorder of the OH bond orientation while in the low-temperature phase H₂O and POH species appear well oriented. The conductivity seems to occur by proton transfer and protonic-species rotation at the POH-water molecular interface between the chains. ac conductivity has been determined by means of the complex-impedance method ($\text{σ}{}_{\mathrm{<mtext>RT</mtext>}}\text{～ (3?12) × 10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$; E ～ 0.20 eV).     

Strong-coupling constant in coordinate space

The coordinate-space behavior of (vector) strong-coupling constant in the background field α_B(r) is compared with that in standard perturbation theory α_v(r). The numerically calculated two-loop coupling constant α_B(r) is shown to exceed α_v(r) by 1–5% at very small distances, r?0.02 fm, and to be in agreement with lattice measurements of the static potential. At large distances, α_B(r) approaches the freezing value at r?0.5 fm. An analytic form of α_B(r) is proposed that approximates α_B(r) with a precision ?2% in the region r?0.5 fm.     

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.     

The p-40Ca and n-40Ca mean fields from the iterative moment approach

The real part V(r; E) of the p-⁴⁰Ca and n-⁴⁰Ca mean fields is extrapolated from positive towards negative energies by means of the iterative moment approach, which incorporates the dispersion relation between the real and imaginary parts of the mean field. The potential V(r; E) is the sum of a Hartree-Fock type component V^HF, (r; E) and a dispersive correction δV(r; E); the latter is due to the coupling of the nucleon to excitations of the ⁴⁰Ca core. The potentials V(r; E) and V_HF(r; E) are assumed to have Woods-Saxon shapes. The calculations are first carried out in the framework of the original version of the iterative moment approach, in which both the depth and the radius of the Hartree-Fock type contribution depend upon energy, while its diffuseness is constant and equal to that of V(r; E). The corresponding extrapolation towards negative energies is somewhat sensitive to the detailed parametrization of the energy dependence of the imaginary part of the mean field, which is the main input of the calculation. Moreover, the radius of the calculated Hartree-Fock type potential then increases with energy, in contrast to previous findings in ²⁰⁸Pb and ⁸⁹Y. A new version of the iterative moment approach is thus developed in which the radial shape of the Hartree-Fock type potential is independent of energy; the justification of this constraint is discussed. The diffuseness of the potential V(r; E) is assumed to be constant and equal to that of V_HF(r; E). The potential calculated from this new version is in good agreement with the real part of phenomenological optical-model potentials and also yields good agreement with the single-particle energies in the two valence shells. Two types of energy dependence are considered for the depth U_HF(E) of the Hartree-Fock type component, namely a linear and an exponential form. The linear approximation is more satisfactory for large negative energies (E < −30 MeV) while the exponential form is better for large positive energies (E > 50 MeV). This is explained by relating the energy dependence of U_HF(E) to the nonlocality of the microscopic Hartree-Fock type component. Near the Fermi energy the effective mass presents a pronounced peak at the potential surface. This is due to the coupling to surface excitations of the core and reflects the energy dependence of the potential radius. The absolute spectroscopic factors of low-lying single-particle excitations in ³⁹Ca, ⁴¹Ca, ³⁹K and ⁴¹Sc are found to be close to 0.8. The calculated p-⁴⁰Ca and n-⁴⁰Ca potentials are strikingly similar, although the two calculations have been performed entirely independently. The two potentials can be related to one another by introducing a Coulomb energy shift. Attention is drawn to the fact that the extrapolated energy dependence of the real part of the mean field at large positive energy sensitively depends upon the assumed behaviour of the imaginary part at large negative energy. Yet another version of the iterative moment approach is introduced, in which the radial shape of the HF-type component is independent of energy while both the radius and the diffuseness of the full potential V(r; E) depend upon E. This model indicates that the accuracy of the available empirical data is probably not sufficient to draw reliable conclusions on the energy dependence of the diffuseness of V(r; E).     

Orthomodular Lattices of Subspaces Obtained from Quadratic Forms

Being given a field K of characteristic different from 2 and 3, a 3-dimensional vector space E over K, and a nonsingular symmetric bilinear form φ over E, we define a structure of orthomodular lattice T(E,φ) on the set of all nonisotropic subspaces of E. We give a structure Theorem about the irreducible and 3-homogeneous subalgebras of T(E,φ). In particular, these subalgebras are all of the form T(E',φ ') where E' is a 3-dimensional subspace of E, if E is regarded as a vector space over a subfield K' of K, and φ ' is induced by φ. This structure Theorem allows us to achieve an old project, concerning minimal orthomodular lattices (an orthomodular lattice L is called minimal if it is nonmodular and if all its proper subalgebras are either modular, or isomorphic to L).     

The microwave spectrum of cis-2-pentene

The microwave spectrum of cis-2-pentene has been shown to originate from molecules in the skew-conformation (dihedral angle φ = 119 ± 3°). From A-E doublet splittings the barrier to internal rotation about the C₁C₂ axis was found to be 280 ± 4 cm^?1; furthermore the dipole moment components and centrifugal distortion constants are reported. In excited states of the C₃C₄ torsion the spectra exhibit further splittings; these are due to tunneling between the two equivalent skew-conformations through a barrier of 210 ± 20 cm^?1.     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

X-ray structure refinement and ionic conductivity of Na6.69Ca3.355(SO4)6Cl0.77F0.63

The structure of Na_6.69Ca_3.355(SO₄)₆Cl_0.77F_0.63, isostructural with fluorapatite, was determined by X-ray powder diffraction methods. The results of Rietveld refinement revealed a space group P6₃/m with lattice parameters of a?=?9.477 (2) Å, c?=?6.865 (5) Å. Final refinement led to R _F?=?1.83 % and R _B?=?7.64 %. The location of Na⁺ ions in the M (2) sites surrounding the channels was related particularly to the high polarizability of the Ca²⁺. The ionic conductivity over a wide range of temperature was investigated according to the complex impedance method. The highest overall conductivity values were found at σ _500 °C?=?1.03?×?10^?5?S?cm^?1 and E_a?=?0.70 eV.     

Optical and ESR spectra of the C4H radical in rare gas matrices at 4 K

C₄H (butadinyl) was trapped in Ar and Ne matrices at 4 K by the uv photolysis of a mixture of C₄H₂ and the rare gas. CC stretching and CH bending modes have been identified in the ir at 2060 and 735 cm^?1. A band system appearing in the 2500–3000 Å region with (0, 0) at 33 800 cm^?1 has been analyzed and tentatively assigned to a ²Π_r ← X²Σ transition. C₄D: Ar spectra confirm the optical assignments. The ESR spectrum exhibits a proton hyperfine splitting b = A_⊥(H) = 16.5 MHz, at g_⊥ = 2.0004(5). The spin-doubling constant, γ, is estimated to be +0.0006(2) cm^?1.     

Investigation of the kinetics of OH∗ and CH∗ chemiluminescence in hydrocarbon oxidation behind reflected shock waves

The temporal variation of chemiluminescence emission from OH^?(A² Σ ⁺) and CH^?(A² Δ) in reacting Ar-diluted H₂/O₂/CH₄, C₂H₂/O₂ and C₂H₂/N₂O mixtures was studied in a shock tube for a wide temperature range at atmospheric pressures and various equivalence ratios. Time-resolved emission measurements were used to evaluate the relative importance of different reaction pathways. The main formation channel for OH^? in hydrocarbon combustion was studied with CH₄ as benchmark fuel. Three reaction pathways leading to CH^? were studied with C₂H₂ as fuel. Based on well-validated ground-state chemistry models from literature, sub-mechanisms for OH^? and CH^? were developed. For the main OH^?-forming reaction CH+O₂=OH^?+CO, a rate coefficient of k ₂=(8.0±2.6)×10¹⁰ cm³?mol^?1?s^?1 was determined. For CH^? formation, best agreement was achieved when incorporating reactions C₂+OH=CH^?+CO (k ₅=2.0×10¹⁴ cm³?mol^?1?s^?1) and C₂H+O=CH^?+CO (k ₆=3.6×10¹²exp(?10.9 kJ?mol^?1/RT) cm³?mol^?1?s^?1) and neglecting the C₂H+O₂=CH^?+CO₂ reaction.