Molecular constants for the I1Πg and J1Δg states of the 3d complex in H2, HD,and D2

The experimental rovibronic energies of the 3dπI¹Π_g^? and 3dδJ¹Δ_g^? states of H₂ and D₂ (v = 0–4 and N = 1–11) have been fitted by rovibronic constants, including L-uncoupling through constants B_v^ΠΔ and D_v^ΠΔ. Comparison of the constants obtained for H₂ and D₂ yields information on the Born-Oppenheimer and adiabatic electronic energies T_e^BO and T_e^AD, and on the diagonal corrections for nuclear motion. T_e^BO derived from experiment for the I¹Π_g state lies 2 cm^?1 below the ab initio calculation of Ko?os and Rychlewski (J. Mol. Spectrosc., 66, 428–440 (1977). The nuclear mass dependence of the ω_e and B_e values in H₂ and D₂ deviates from simple isotope relationships but agrees with expectations based on the R-dependence of the diagonal corrections for nuclear motion through the term $\text{〈L}{}^2\text{?2}\text{Λ}{}^2\text{〉}\text{2μR}{}^2$, i.e., $\text{+2}\text{μR}{}^2$ for 3dπ and $\text{?1}\text{μR}{}^2$ for 3dδ.     

Vibrational spectra and force constants of symmetric tops: Rotational analysis of ν3 and 2ν3 of H3Si35Cl and H3Si37Cl

The gas-phase infrared spectra of natural and ³⁵Cl isotopically enriched H₃SiCl have been recorded with a resolution of 0.04 cm^?1 in the regions of ν₃ (～550 cm^?1) and 2ν₃ (～1100 cm^?1). The fundamentals of species with ²⁸Si, ²⁹Si, ³⁰Si, ³⁵Cl, and ³⁷Cl and several hot bands of the series nν₃ + mν_i ? mν_i (n, m = 1, 2; i = 3 and 6) have been detected. The parameters ν₀, x₃₃, x₃₆, B₀, α₃^A, D_J⁰ and D_J³ were determined by a combination of least-squares analysis of P and R branches resolved into J peaks (J ≤ 90) and a band contour simulation. Possible resonances of nν₃ and (n ? 1)ν₃ + ν₆ are discussed.     

Heat capacity and thermodynamic properties of α-Fe2O3 in the region 300–1050 K. antiferromagnetic transition

The heat capacity of synthetic α-Fe₂O₃ has been measured in the range 300–1050K by adiabatic shield calorimetry with intermittent energy inputs and temperature equilibration in between. A λ-type transition, related to the change from antiferro- to paramagnetism in the compound, is delineated and a maximum heat capacity of about 195 JK^?1 mole^?1 is observed over a 3 K interval around 955 K. Values of thermodynamic functions have been derived and C_P (1000K), [H⁰(1000K)-H⁰(0)], and [S⁰(1000K)-S⁰(0)] are 149.0JK^?1 mole^?1, 115.72 kJ mole^?1, and 252.27 JK^?1 mole^?1, respectively, after inclusion of earlier low-temperature results [X⁰ (298.15K)-X⁰(0)]. The non-magnetic heat capacity is estimated and the thermodynamic properties of the magnetic transition evaluated. The results are compared with spin-wave calculations in the random phase approximation below the Néel temperature and the Oguchi pair model above. An upper estimate of the total magnetic entropy gives 32.4JK^?1 mole^?1, which compares favorably with that calculated for randomization of five unpaired electron spins on each iron, ΔS = 2R ln 6 = 29.79 JK^?1 mole^?1 for α-Fe₂O₃. The critical exponent α in the equation $\text{C}{}_{\mathrm{m}}\text{= (}\text{A}\text{α}\text{) [(|T}{}_{\mathrm{<mtext>n</mtext>}}\text{?T|/T}{}_{\mathrm{<mtext>n</mtext>}}\text{)?1]}{}^{\mathrm{?\alpha }}\text{+ B}$ is ?(0.50±0.10) below the maximum and 0.15±0.10 above, for T_n = 955.0K. The high temperature tail is discussed in terms of short range order.     

Radiative corrections to νμ + N → μ− + X and their effect on the determination of ϱ2 and sin2θW

We study the O(α) corrections to σ_T(ν_μ + N → μ^? + X). The coefficient of the leading O(αln m_Z) contribution is given by a general theorem as in the case of β decay, while the energy scale accompanying m_Z in the argument of the logarithm as well as mass singularities and non-logarithmic terms are obtained by a detailed quark-parton model calculation. The effect of muon mass singularities, when there is an experimental vut in the low range of the y distribution, is also investigated. Combining these new results with our previous analysis of σ_T(ν_μ + N → ν_μ + X), we calculate theSU(2)_L × U(1) parameter ?_(νμ;h)² and evaluate the effect of the O(α) corrections on the determination of sin²θ_W^exp from deep inelastic ν_μ scattering. Applying these corrections to existing data, we obtain the weigthed average sin²θ_W^exp = 0.216 ± 0.010 ± 0.004. This value when used in conjuction with our previous analysis of the W^± and Z⁰ masses provides the predictions m_W = 83.0_?2.8^+3.0 GeV and m_Z = 93.8_?2.4^+2.5 GeV. For the weak interaction angle defined by modified minimal subtraction we find sin²θ_W(m_W) = 0.215 ± 0.010 ± 0.004, which is in very good agreement with the SU(5) prediction we have recently given.     

Laser-induced fluorescence and microwave-optical double-resonance study of the B1Σ+-X1Σ+ system of magnesium monoxide

Doppler-limited, laser-induced fluorescence spectra on the B¹Σ⁺-X¹Σ⁺ (v′ = v″ = 0 and 1) system of MgO have been obtained. The results of the optical analysis were merged with our microwave-optical double-resonance measurements to produce the following set of spectroscopic parameters for the B and X states, where the units are in cm^?1, and the uncertainties represent 95% confidence limits: T′_0.0 = 20003.594(2); B′₀ = 0.58004(3); D′₀ = 1.13(2) × 10^?6; B″₀ = 0.57198(3); D″₀ = 1.20(2) × 10⁶; T′_1.1 = 20043.423(2); B′₁ = 0.57528(4); D′₁ = 1.14(11) × 10⁶; B″₁ = 0.56674(4); D″₁ = 1.22(10) × 10⁶.     

Far-infrared laser magnetic resonance spectra of the PH and PD radicals in X3Σ−

Far-infrared laser magnetic resonance (LMR) spectra of PD in the ground vibronic state (X³Σ^?, v = 0) were observed using the 570.6-, 380.6-, 287.3-, 232.9-, 191.6-, and 164.6-μm laser lines as sources, and the v = 1 spectrum was also observed with the 392.1-μm laser line. By combining the present results with mid-infrared LMR and optical spectroscopic data already reported, the molecular constants of PD in X³Σ^? were refined as follows: B₀ = 4.362 8675(77), D₀ = 0.000 118 03(24), λ₀ = 2.208 48(57), γ₀ = ?0.039 900(34), B₁ = 4.269 248(65), λ₁ = 2.209 5(10), γ₁ = ?0.038 82(21), and ν₀ = 1653.284 91(51), all in cm^?1 with 3σ in parentheses. The ³¹P hyperfine coupling constants were determined to be α_P = 0.004 330(39) and β_P = ?0.005 312(32) for the v = 0 state and α_P = 0.004 66(40) and β_P = ?0.004 79(69) for the v = 1 state, again in cm^?1 with 3σ in parentheses. The far-infrared LMR spectra of PH in the X³Σ^?, v = 0 state were measured on five new laser lines, and an analysis of the observed spectrum combined with that already reported yielded molecular constants much improved in precision. Using the results on both PD and PH, the equilibrium structure and the potential constants up to the fourth order were derived, where allowance was made for adiabatic and nonadiabatic corrections: $\text{r}{}_{\mathrm{e}}{}^{\mathrm{BO}}\text{= 1.42140(22)}\text{A}\text{?}$, ω_e(PH) = 2366.79(16) cm^?1, a₁ = ?2.3797(18), and a₂ = 3.461(14).     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: binary non-isotopic mixtures of atoms

Extensive molecular dynamics calculations have been used to study systematically for the first time the dependence of the self-diffusion coefficients D_i (i = 1,2) in binary equimolar non-isotopic atomic mixtures (mole fractions x ₁ = x ₂ = 0.5, reduced temperature T? = 1.6) on the particle mass ratio m?₂ = m ₂/m ₁ (1 ≤ m?₂ ≤ 16.5) in the ranges of reduced particle number density 0.15 ≤ n? ≤ 0.85 and reduced length parameter 0.5 ≤ σ?₂₂ ≤ 2.0 for a Lennard-Jones 12-6 potential. The calculated D_i values can be represented quantitatively by an exponential estimate of the form: D_i = D ⁰ _i (m?₂) ^ex _i . D ⁰ _i are the self-diffusion coefficients in reference mixtures with m?₂ = 1. The observed dependence of the exponents ex _i (m?₂, n?, σ?₂₂) on m?₂, n? and σ?₂₂ is discussed in this paper.     

Magnetic properties of the compounds N(CH3)4MnIIMIII(CN)6 ·8 H2O(MIII = Mn,Fe)

In the isostructural cyanobridged chain compounds N(CH₃)₄Mn^IIM^III(CN)₆ · 8H₂O high spin Mn(II) ions couple antiferromagnetically to low spin Mn(III) of Fe(III) ions. The Mn^II–Mn^III compound orders ferrimagnetically below T_N = 28.5 ± 1 K. The tetragonal a and b axes are easy ones for the magnetic moments. In the Mn^II–Fe^III compound antiferromagnetic order occurs below T_N = 9.3 K, with spins aligned along the tetragonal c axis. The compound undergoes a meta-magnetic transition from the antiferromagnetic to a ferrimagnetic phase. This occurs at 2 K for a field H_crit ≈ 1.2 T. The temperature dependence of H_crit, which vanishes at T_N, is followed. The tricritical temperature T¹ is ～ 5 K.     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: binary and ternary isotopic mixtures of atoms

Extensive molecular dynamics calculations have been used to study for the first time systematically the dependence of the self-diffusion coefficients D_i (i = 1, 2, 3) in binary and ternary atomic isotopic mixtures on the particle mass ratios m*₂ = m ₂/m ₁ and m*₃ = m ₃/m ₁ at different reduced temperatures T* and reduced particle number densities n*, using a Lennard-Jones 12-6 potential and a hard-soft-spheres potential. In addition, the dependence of D_i values of binary mixtures on the mole fraction x ₁ = 1—x ₂ was also investigated for some thermodynamic states. The calculated values of D_i can be represented quantitatively by exponential estimates of the form D_i = D* _i (m*₂)^ex _i in the case of binary mixtures and D_i = D ⁰ _i (m*₂)^{ex _i} (m ₃)^{ext _i} in the case of ternary mixtures. D ⁰ _i are the self-diffusion coefficients in reference mixtures of mass ratios m*₂ = m*₃ = 1. The dependence of the exponents ex _i (m*₂, T*, n*, x ₁) of binary mixtures on m*₂, T*, n*, and x ₁ and the dependence of the exponents ext _i (m*₂, m*₃, n*) of equimolar ternary mixtures at T* = 1.8 on the exponents ex _i of the constituent binary mixtures and on m*₂, m*₃, and n* are discussed.     

Tunable diode laser measurements of N2- and air-broadened halfwidths: Lines in the (ν4 + ν5)0 band of 12C2H2 near 7.4 μm

Nitrogen- and air-broadened Lorentz halfwidths have been determined for 29 lines in the P and R branches of the (ν₄ + ν₅)⁰ combination band of ¹²C₂H₂ using a tunable diode laser spectrometer. Two tunable diode lasers operating in the region 1250–1380 cm^?1 were used in recording the data. For nitrogen broadening, the measured halfwidths at 296 K decrease from about 0.11 cm^?1 atm^?1 at |m| = 1 to about 0.05 cm^?1 atm^?1 at |m| = 30, where m = J″ + 1 for R-branch lines, m = ?J″ for P-branch lines, and J″ is the lower state rotational quantum number. On the average, the air-broadened halfwidths are 97% of the N₂-broadened halfwidths.     

Intensity of CO2 bands in the 4.8- to 5.3-μm region. The (1110,0310)II-0000 band

Measurements of the line strengths of the (11¹0,03¹0)_II-00⁰0 band of CO₂ (1932.466 cm^?1) have been made with high resolution. They exhibit a strong Coriolis interaction which enhances the P-branch intensity while reducing that of the R branch. The rotationless dipole moment of the transition and the ξ-constant representing this interaction have been determined as: R(0) = (6.57 ± 0.03) × 10^?4D, ξ = ?0.0598 ± 0.0002.     

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.     

Gamma rays and neutrons following preequilibrium 165Ho(p, xcnypγ) reactions at Ep = 60 MeV

Neutrons and γ-rays following 60 MeV proton bombardment of ¹⁶⁵Ho were measured in coincidence with discrete γ-rays characteristic of the reaction channels (residual nuclei). The cross sections for the (p, xcnγ) reactions with x = 2–6, the γ-ray multiplicities, and the energy and angular distributions of the emitted neutrons were analyzed in terms of the preequilibrium and equilibrium deexcitation processes. Characteristic behaviours of the preequilibrium process were found in the (p, 2nγ) and (p, 4nγ) reactions where the sum E_T, = ∑^xE_i of the energies E_i of the emitted neutrons was large, while those of the equilibrium process were typical for the (p, 6ny) reaction with small E_T. The reactions are well reproduced by the expression σ. ≈0.35∑_xσ (2, x?2) + 0.4∑_xσ(1, χ?1)+ 0.25∑_xσ(0, x), where σ(n_p, n_c) stands for emission of n_p neutrons at the preequilibrium stage followed by evaporation of n_c neutrons at the equilibrium stage.     

Optical absorption spectra of s2 impurity ions in aqueous halide ion glasses

The optical absorption bands of aqueous 0·05 M Sn²⁺ in 7 M LiI at 77°K appear at 361, 352, 325, 310, 300, 292 and 262 nm. They are considered to be the A₁, A₂, B, C₁, C₂, C₃ and D′ bands since the positions and relative intensities lie within the range of those bands for Sn²⁺-doped alkali iodide crystals. Upon warming the glass there is an uncorrelated increase in the B band and a decrease in the A₁ band. In 3·6, 4·1, 4·6 and 5·1 M CaCl₂ glasses with 5×10^?3 M Sn²⁺ the A₁ and A₂ bands show uncorrelated increases with increasing concentration of Cl^?. Comparable observations are reported for Pb²⁺-doped glasses of lithium halides and CaI₂. In general the spectra of the Sn²⁺- and Pb²⁺-doped glasses correlate well with those of the corresponding crystal systems. The effect of temperature and halide-ion concentration are attributed to shifts in chemical equilibria among the well-known halo complexes, MX_n^2?n MX_n?1^1?n+X^?, each having a characteristic, absorption and emission. Absorptions may be attributed to M²⁺(³P₁ ← ¹S₀) and M²⁺(¹P₁ ← ¹S₀) in the complex, shifted by partially covalent bonding of n halide ions.     

A monte-carlo/molecular dynamics study of the diffusional recombination kinetics of C(a) + O(a) → CO(g) on Pt(111)

The diffusion constants for C and O adsorbates on Pt(111) surfaces have been calculated with Monte-Carlo/Molecular Dynamics techniques. The diffusion constants are determined to be D_C(T)=(3.4 × 10^?3e^{$\text{?13156}\text{T}$})cm²s^?1 for carbon and D_O(T) = (1.5×10^?3 e^{$\text{?9089}\text{T}$}) cm² s^?1 for oxygen. Using a recently developed diffusion model for surface recombination kinetics an approximate upper bound to the recombination rate constant of C and O on Pt(111) to produce CO_(g) is found to be (9.4×10^?3 e^{$\text{?9089}\text{T}$}) cm² s^?1.     

A CP5 calculus for space-time fields

Compactified Minkowski space can be embedded in projective five-space CP⁵ (homogeneous coordinates Xⁱ, i = 0, …, 5) as a four dimensional quadric hypersurface given by $\text{Ω}{}_{\mathrm{ij}}\text{X}{}^{\mathrm{i}}\text{X}{}^{\mathrm{j}}\text{= 0.}$ Projective twistor space (homogeneous coordinates Z^α, α = 0, …, 3) arises via the Klein representation as the space of two-planes lying on this quadric. These two facts of projective geometry form the basis for the construction of a global space-time calculus which makes use of the coordinates Xⁱ?X^αβ(=-X^βα) to represent spinor and tensor fields in a manifestly conformally covariant form. This calculus can be regarded as a synthesis of work on conformal geometry by Veblen, Dirac, and others, with the theory of twistors developed by Penrose.We provide here a systematic review of the basic framework: the underlying projective geometry; the calculus of tensor fields; the characterization of spinors as twistor-valued fields ψ^α(X) which satisfy a geometrical condition ($\text{ψ}{}^{\mathrm{\alpha }}\text{X}{}_{\mathrm{\alpha \beta }}\text{= 0 on Ω}$ ); and the introduction of the conformally invariant Laplacian operator $\text{?}{}^2\text{= Ω}{}^{\mathrm{ij}}\text{?}{}^2\text{/?}\text{X}{}^{\mathrm{i}}\text{?}\text{X}{}^{\mathrm{j}}$. In addition a number of subsidiary topics are discussed which illustrate the general scheme, including: the breaking of conformal symmetry to Poincaré symmetry; a derivation of the zero rest mass equations for all helicities; and a new and manifestly conformally covariant form of the twistor contour integral formulae for massless fields.     

n体聚集过程和联合聚集过程的集团尺寸分布

本文研究n体聚集过程和联合聚集过程的集团分布演化。从广义Smoluchovki方程出发,给出聚集核K(i₁,i₂,…,i_n)=A sumfrom i=1 to n i₁+B(A,B均为常数)的显解;利用聚集核K(i₁,i₂,…,i_n)=(Ai₁+B)(Ai₂+B)…(Ai_n+B)和核K(i₁,i₂,…,i_n)=A sumfrom i=1 to n i₁+B的方程之间的联系,得出核K(i₁,i₂,…,i_n)=S_(i1)S_(i2)…S_(in)(S_K=AK+B)的凝前解。而且,根据联合聚集动力学方程,讨论了聚集和型核分别为K₂(i,j)=i+j,K₃(i,j,k)=i+j+k的集团尺寸分布C_m(t)的长时行为,并将结论推广到一般的联合聚集过程。 关键词：     

Studies of defect clustering in CaF2: Y3+ by ionic conductivity and thermal depolarization

Measurements of the ionic conductivity σ of yttrium-doped calcium fluoride reveal a complex and highly unusual dependence of logσT on T^?1, where T denotes the temperature. This conductivity curve has been interpreted in terms of a model that assumes frozen-in defects on the cation sub-lattice together with charge-compensating interstitial fluoride ions and anion vacancies. At low temperatures the conductivity is dominated by mobile interstitial fluoride ions (F_i^?) in equilibrium with trapping centres that may include substitutional yttrium ions (Y_s³⁺), Y_s³⁺?F_i^? complexes (monomers) and larger clusters. At intermediate temperatures the charge-carrying F_i^? are considered to arise by ionization from dimers (the 2:2:2 complexes) and at higher temperatures still from larger clusters which are probably tetramers, although the possibility that the mobile F_i^? in these two temperature regions are those that had formerly been trapped by dimers and tetramers cannot be excluded. The thermal depolarization spectrum of CaF₂: Y³⁺ is very complicated and reveals six different relaxations. One of these is associated with the type I (nn) and type II (nnn) Y_s³⁺?F_i^? complexes and a second with 2:2:2 clusters. The remaining four relaxations were not identified but almost certainly provide evidence for the existence of polarizable defect clusters in CaF₂: Y³⁺.     

On the Deser,Gilbert, Sudarshan representation for functions Wi(ν, q2)(i = 1, 2) describing the electroproduction process

The Deser, Gilbert, Sudarshan representation (D.G.S.R.) for the functions W_i(ν, q²) (i = 1,2) is considered as equations determining spectral functions h_i(a, α) via the values W_i(ν, q²) in the physical region of the electroproduction channel. It is shown that if W_i(ν, q²) obey the microcausality and spectrality conditions, then the equations for h_i(a, α) have solutions in the class of Schwartz temperated distributions and thereby the D.G.S.R. is proved. Formulae are obtained expressing spectral functions in the D.G.S.R. through the values of functions W_i(ν, q²) in the physical region of the electroproduction channel.     

Muon-electron universality at high energies and hadronic corrections to e+e− → μ+μ−

It is argued that unitarity and muon-electron universality are sufficient to determine the contribution of hadrons to the imaginary part of the forward amplitude for the process e⁺e^? → μ⁺μ^?. With these assumptions Im T₁^h(e⁺e^? → μ⁺μ^?) = sσ(e⁺e^? → hadrons) to all orders in α. Some consequences of this formula are discussed.