Study on charge transfer interaction and valence state of layered perovskite-type mixed valence complex [NH3(CH2) n NH3]2[(AuII2)(AuIIII4)(I3)2] (n = 7, 8), by means of 197Au Mössbauer spectroscopy

Cs₂[Au^I X ₂][Au^III X ₄](X = Cl, Br, and I) is well known for the three-dimensional perovskite-type gold mixed valence system. Recently, layered perovskite-type gold mixed valence complexes, [NH₃(CH₂) _n NH₃]₂[(Au^II₂)(Au^IIII₄)(I₃)₂] (n = 7 and 8), have been synthesized. We have investigated the relationship between the structural dimensionality and the Au^I–Au^III charge transfer interaction for Cs₂[Au^II₂][Au^IIII₄] and [NH₃(CH₂) _n NH₃]₂[(Au^II₂)(Au^IIII₄)(I₃)₂] (n = 7 and 8) by means of ¹⁹⁷Au Mössbauer spectroscopy.     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

Moments of the Percus-Yevick hard-sphere correlation function

A simple recursive relation is derived for the momentsM _n ,n=1, 2,..., of the Percus-Yevick correlation functionh(r) for identical hard spheres. TheM _n are rational functions of the volume fractionw occupied by the spheres; the first ten are given explicitly, and a single-term asymptotic form is obtained to suffice for the rest. Applications of theM _n(w) include testing different approximations forh by numerical integration ofh(r) r ⁿ . We compare exact moments with shell approximationsM _n [h ^s ] corresponding to integration fromr=0 tos+1 fors=3–8, and with hybrid approximationsM _n [h ^s +h ^a ] which supplement the shell approximations with integrals of an asymptotic tail froms+1 to . For a givens, the hybrid approximation is better forw increasing than the shell approximation, andM _n [h ³+h ^a ] is even better thanM _n [h ⁸]     

带栅极纳米线冷阴极的场增强因子研究

场增强因子是体现场发射冷阴极器件性能优劣的重要参数.利用静电场理论给出了一种带栅极(normal-gated)纳米线冷阴极的场增强因子表示式β=k₁{N²·(L-d₁)²+［1/k₁+(L-d₁)］²}^1/2，且进一步分析了几何参数对场增强因子的影响.结果表明，纳米线突出栅孔的部分(L-d₁)与栅孔半径越大，则场增强因子越大；而纳米线半径越小，则场增强因子越大；当L远大于d₁时满足β∝L/r₀.其中N=N₁(k₁r₀)/N₀(k₁r₀)，N₀(k₁r₀)和N₁(k₁r₀)分别代表零阶和一阶Neumann函数，k₁=0.8936/R，R为栅孔半径，L为纳米线长度，r₀为纳米线半径，d₁表示阴极与栅极间距.     

Realizability of Point Processes

There are various situations in which it is natural to ask whether a given collection of k functions, ρ _j (r ₁,…,r _j ), j=1,…,k, defined on a set X, are the first k correlation functions of a point process on X. Here we describe some necessary and sufficient conditions on the ρ _j ’s for this to be true. Our primary examples are X=ℝ ^d , X=ℤ ^d , and X an arbitrary finite set. In particular, we extend a result by Ambartzumian and Sukiasian showing realizability at sufficiently small densities ρ ₁(r). Typically if any realizing process exists there will be many (even an uncountable number); in this case we prove, when X is a finite set, the existence of a realizing Gibbs measure with k body potentials which maximizes the entropy among all realizing measures. We also investigate in detail a simple example in which a uniform density ρ and translation invariant ρ ₂ are specified on ℤ; there is a gap between our best upper bound on possible values of ρ and the largest ρ for which realizability can be established.     

New data for the 197Au(γ, nX) and 197Au(γ, 2nX) reaction cross sections

The results from experimental and theoretical studies of the total and partial cross sections of photoneutron reactions on the ¹⁹⁷Au isotope were analyzed. The cross sections for reactions σ(γ, nX) = σ(γ, n) + σ(γ, np) + … + σ(γ, 2nX) = σ(γ, 2n) + σ(γ, 2np) + … were evaluated in the energy range 7 ≤ E _γ ≤ 30 MeV using an approach free of the shortcomings of experimental photoneutron multiplicity sorting methods. The total photoneutron reaction cross sections σ^exp(γ, xn) = σ^exp(γ, nX) + 2σ^exp(γ, 2nX) + … = σ^exp(γ, n) + σ^exp(γ, np) + 2σ^exp(γ, 2n) + 2σ^exp(γ, 2np) + … were used as the initial experimental data. The contributions from the cross sections σ(γ, nX) and σ(γ, 2nX) to the cross sections σ^exp(γ, xn) were separated using the multiplicity transition functions F ₁ ^theor = σ^theor(γ, 1nX)/σ^theor(γ, xn) and F ₂ ^theor = σ^theor(γ, 2nX)/σ^theor(γ, xn), calculated within an updated version of the pre-equilibrium model of photonuclear reactions. New evaluated data for both partial reaction cross sections, i.e., σ^eval (γ, 1nX) = F ₁ ^theorσ^exp(γ, xn) and σ^eval(γ, 2nX) = F ₂ ^theorσ^exp(γ, xn), were obtained. The cross sections σeval(γ, nX) and σ^eval.(γ, 2nX) evaluated using the theoretically calculated functions F _1,2^theor are consistent with the Livermore data, but substantially contradict the Saclay data.     

Temperature dependence of muonium spin exchange with O2 in the range 88 K to 478 K

Our group at TRIUMF reported earlier a study of the spin exchange reactions of Mu with O₂ and NO in the range 295 K to 478 K. We have extended the measurement with O₂ to a low temperature region down to 88 K. From 135 K to 296 K, the spin depolarization rate constantk _d(T) was found to vary according to the relative velocity of the colliding species,T ^1/2, which indicates that the spin exchange cross section of Mu-O₂ is temperature independent in this temperature range. The value ofk _d(T) at 296 K is in good agreement with our earlier study. However, it was found that below 105 K and above 400 K,k _d(T) tends to have stronger temperature dependences (T ⁿ , withn>1/2). This deviation fromT ^1/2-behavior can be attributed to the velocity (energy) dependence of the spin exchange cross section.     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}     

Role of metastable atoms and molecules of helium in excitation transfer to hydrogen atoms

The afterglow of a discharge in helium with a small admixture of hydrogen is studied spectroscopically (p=40 Torr, [e]≤10¹¹ cm^?3). The time-resolved measurements of intensities of the first four lines of the Balmer series are performed. The concentrations of metastable helium atoms and molecules are evaluated from the relative intensity of the absorption lines. The ratios of excitation transfer rates from atoms He(2 ³ S ₁) k ₁(n) and molecules of helium He₂(a 2sσ ³Σ _u ⁺ ) k ₂(n) to atomic hydrogen H*(n) are measured to be k ₁(n=3)/k ₂(n=3)=0.04±0.02 and k ₁(n=4)/k ₂(n=4)=0.01±0.02. The ratios of excitation rate constants k ₂(n) corresponding to different states H(n) are measured to be k ₁(n=4)/k ₂(n=3)=0.023±0.01; k ₁(n=5)/k ₂(n=3)≤0.013; and k ₁(n=6)/k ₂(n=3)≤0.007.     

Analytic Bethe ansatz for fundamental representations of Yangians

We study the analytic Bethe, ansatz in solvable vertex models associated with the YangianY(X _r ) or its quantum affine analogueU _q (X _r ⁽¹⁾ ) forX _r =B _r ,C _r andD _r . Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations ofY(X _r ). Under the Bethe ansatz equation, we explicitly prove that they are pole-free, a crucial property in the ansatz. Conjectures are also given on higher representation cases by applying theT-system, the transfer matrix functional relations proposed recently. The eigenvalues are neatly described in terms of Yangian analogues of the semi-standard Young tableaux.     

Conformal blocks and generalized theta functions

LetSU _X r be the moduli space of rankr vector bundles with trivial determinant on a Riemann surfaceX. This space carries a natural line bundle, the determinant line bundleL. We describe a canonical isomorphism of the space of global sections ofL ^k with the space of conformal blocks defined in terms of representations of the Lie algebrasl _r (C((z))). It follows in particular that the dimension ofH ⁰(SU _X r,L ^k ) is given by the Verlinde formula.Both authors were partially supported by the European Science Project Geometry of Algebraic Varieties, Contract no. SCI-0398-C(A)     

CORAL: QSPR models for solubility of [C60] and [C70] fullerene derivatives

Quantitative structure–property relationships (QSPRs) between the molecular structure of [C₆₀] and [C₇₀] fullerene derivatives and their solubility in chlorobenzene (mg/mL) have been established by means of CORAL (CORrelations And Logic) freeware. The CORAL models are based on representation of the molecular structure by simplified molecular input line entry system (SMILES). Three random splits into the training and the external validation sets have been examined. The ranges of statistical characteristics of these models are as follows: n = 18, r ² = 0.748–0.815, s = 15.1 –17.5 (mg/mL), F = 47–71 (training set); n = 9, r ² = 0.806–0.936, s = 12.5–17.5 (mg/mL), F = 29–103 (validation set).     

Optical pumping of short lived Β-radioactive isotopes and the magnetic moment of37K

²¹Na (T _1/2=23 sec) and³⁷K(T _1/2=1.25 sec) have been produced in gas targets by (d, n) reactions and polarized by means of optical pumping or spin exchange scattering with optically pumped⁸⁷Rb. An asymmetry up to 3% in theΒ-decay of the polarized nuclei was found, which served to detect rf transitions between hfs levels of the atomic ground states of²¹Na and³⁷K.δF=0 andδF=1 resonances have been recorded, yielding spin, hfs separation and magnetic moment, especiallyI(³⁷K)=3/2,δW(³⁷K)=240.266 (3) Mc/sec andΜ _I(³⁷K)=0.02033(6) nm (diamagnetically corrected). For²¹Na earlier rf-spectroscopic data have been confirmed.     

核物质状态方程中动量相关作用可能的探针

研究了动量相关作用对于中子-质子比动能谱rb(Ek)的效应,发现rb(Ek)灵敏的依赖于动量相关作用而弱的依赖于介质中核子-核子碰撞截面和对称势.因此rb(Ek)是提取重离子碰撞中动量相关作用信息的可能探针.同时,对于丰中子弹核和相同质量稳定弹核在相同入射道条件下,丰中子碰撞系统明显加强了动量相关作用对rb(Ek)的效应.故两个碰撞系统rb(Ek)结果的比较为在重离子碰撞中提取动量相关作用的知识提供了另一个重要的判据。     

Free Energies of Dilute Bose Gases: Upper Bound

We derive an upper bound on the free energy of a Bose gas at density ϱ and temperature T. In combination with the lower bound derived previously by Seiringer (Commun. Math. Phys. 279(3): 595–636, 2008), our result proves that in the low density limit, i.e., when a ³ ϱ≪1, where a denotes the scattering length of the pair-interaction potential, the leading term of Δf, the free energy difference per volume between interacting and ideal Bose gases, is equal to 4pa(2r²-[r-r_c]²₊)4\pi a(2\varrho^{2}-[\varrho-\varrho_{c}]^{2}_{+}). Here, ϱ _c (T) denotes the critical density for Bose–Einstein condensation (for the ideal Bose gas), and [⋅]₊=max {⋅,0} denotes the positive part.     

Free-field realization of theWKP(N) algebra

TheW _KP ^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW _KP ^(N) can also be decomposed toN independent copies ofW _KP ⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW _KP ⁽¹⁾ . In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW _KP ^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R) _k algebras with levelk = 1. By reductions, we give similar results forW ^(N) andW ₃ ⁽²⁾ algebra.     

Photodisintegration of 4He and the Supermultiplet Potential Model of Cluster-Cluster Interactions

p+³H and p+³He elastic collisions are described in terms of a supermultiplet model with [ƒ]-dependent potentials. The phase shifts δ ^[ƒ] _L,t,S (E) with [ƒ] = [4], t = S = 0, L = even are reconstructed from the observable nuclear phase shifts δ _L,S (E) of the above collisions. So, the initial-state interaction V ^[4] _L,0,0 (R) of the ⁴He +Υ→³H +p(³He +n) reaction can be found unambiguously, while the final-state interaction V ^[31] _{L, 1, 0} (R) is defined by the observablesδ _L,0 (E) of p+³He scattering. The data on the proton momentum distribution in ⁴He and on the charge-exchange reaction ³H +p→³He +n confirm the model. In calculating the above photonuclear reactions, in addition to the initial-state and final-state antisymmetrizations, preserving the corresponding symmetry [ƒ], the nucleon-nucleon correlations in the ³H (³He) subsystem were also taken into account. The results are in good agreement both with recent experimental data and theoretical investigations by sofianos, Fiedeldey, and Sandhas, who followed a rather different approach. Received August 5, 1994; revised November 30, 1994; accepted for publication December 30, 1994     

A long-time tail for random walk in random scenery

Consider a simple random walk on ^d whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn _k be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let _k =E(n _k )–q ^–1. Our main result is a proof that (*) lim _k k ^d/2 _k = (1 –q)q ^{d/2 – 2}(d/2) ^d/2. Since it is known thatq ^{– 1} _k =E(n ₁ n _{k + 1} B) –E(n ₁ B)E(n _{k + 1} B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of _k (1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of _k for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of _k cannot be faster than (*).     

Specific heat of the harmonic oscillator within generalized equilibrium statistics

Summary Within the generalized equilibrium statistics recently introduced by Tsallis (p _n ∝[1−β(q−-1) _εn ]^1/(q−)), we calculate the thermal dependence of the specific heat corresponding to a harmonic-oscillator-like spectrum, namely ε _n ω(n−α) (∀ω>0,n=0,1,2,...). The influences ofq and α are exhibited. Physically inaccessible and/or thermally frozen gaps are obtained in the low-temperature region, and, forq>1, oscillations are observed in the high-temperature region. The specific heat of the two-level system is also shown.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum