Energy-level shifts of a stationary hydrogen atom in a static external gravitational field with Schwarzschild geometry

he first order perturbations of the energy levels of a stationary hydrogen atom in a static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, 4P, 4D, and 4F levels. The results show that the energy-level shifts of the states with total angular momentum quantum number 1/2 are all zero, and the ratio of absolute energy shifts with total angular momentum quantum number 5/2 is 145. This feature can be used to help us to distinguish the gravitational effect from other effects.

Gravitational corrections to energy-levels of a hydrogen atom

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.

Emittance estimation by an ion optical element with variable focusing strength and a viewing target

The emittance of an extracted ion beam can be estimated to first order by a series of three linear independent profile measurements. This estimation is restricted to the evaluation of an upper limit of the emittance value for a homogeneous, nonfilamented beam. The beam is assumed to be round, respectively elliptical, without any structure of the intensity distribution, no space charge has been assumed for the drifting beam, and the optics is assumed to be linear. Instead of using three different drift sections, a linear focusing element with three different focusing strengths can be used. Plotting the beam radius as function of focusing strength, three independent solutions can be used to calculate the Twiss parameters alpha, beta, and gamma and furthermore the emittance epsilon. Here we describe the measurements which have been performed with the SECRAL ion source at Institute of Modern Physics Lanzhou.

Chemisorption and reaction characteristics of methyl radicals on Cu(110)

Methyl radicals are generated by pyrolysis of azomethane, and the condition for achieving neat adsorption on Cu(110) is described for studying their chemisorption and reaction characteristics. The radical-surface system is examined by X-ray photoemission spectroscopy, ultraviolet photoemission spectroscopy, temperature-programmed desorption, low-energy electron diffraction (LEED), and high-resolution electron energy loss spectroscopy under ultrahigh vacuum conditions. It is observed that a small fraction of impinging CH3 radicals decompose into methylene possibly on surface defect sites. This type of CH2 radical has no apparent effect on CH3(ads) surface chemistry initiated by dehydrogenation to form active CH2(ads) followed by chain reactions to yield high-mass alkyl products. All thermal desorption products, such as H-2, CH4, C2H4, C2H6, and C3H6, are detected with a single desorption peak near 475 K. The product yields increase with surface coverage until saturation corresponding to 0.50 monolayer of CH3(ads). The mass distribution is, however, invariant with initial CH3(ads) coverage, and all desorbed species exhibit first-order reaction kinetics. LEED measurement reveals a c(2 x 2) adsorbate structure independent of the amount of gaseous exposure. This strongly suggests that the radicals aggregate into close-packed two-dimensional islands at any exposure. The islanding behavior can be correlated with the reaction kinetics and is deemed to be essential for the chain propagation reactions. Some relevant aspects of the CH3/Cu(111) system are also presented. The new results are compared with those of prior studies employing methyl halides as radical sources. Major differences are found in the product distribution and desorption kinetics, and these are attributed to the influence of surface halogen atoms present in those earlier investigations.

Kinetic study on the photo-catalytic degradation of pyridine in TiO2 suspension systems

It has been generally agreed that pyridine can be effectively mineralized in aerated TiO2 slurries using near-UV irradiation. The knowledge on the kinetics of the system possesses both practical and theoretical values. The present study, on the base of Langmuir-Hinshewood mechanism, illustrates a pseudo first-order kinetic model of the degradation with the limiting rate constant of 3.004 mg l(-1) min(-1) and equilibrium adsorption constant 2.763 x 10(-2) l mg(-1), respectively. The degradation efficiency in alkali is a little higher than that in acid with a minimum at about pH = 5, which is explained by the formation of acid-pyridine in acidic surrounding together with the amphoteric nature of the TiO2 surface. The promotion of H2O2 on the photo-degradation ties in its supplying proper amount of (OH)-O-. radicals for the inducement stage before surface redox reactions. (C) 2004 Elsevier B.V. All rights reserved.

Multipolar model for collisional quantum interference on rotational energy transfer

A theoretical model of collisional quantum interference (CQI) is developed in a diatom-diatom system based on the first-order Born approximation of time-dependent perturbation theory and the multipolar interaction potential. The transition cross section is obtained. The relations between the differential and integral interference angles are discussed. The key factors on the determination of the differential and integral interference angles are obtained. The changing tendency of the interference angles with the experimental temperatures is obtained.

基于一阶迁移系统的限界模型检测工具实现

为了简化在限界模型检测过程中模型的建立过程,给出了一种采用基于一阶迁移系统语言的模型建立方法,并在此一阶迁移系统语言中加入了通道的功能,增强了描述能力。然后在此基础上完成了一个以基于插值和k步归纳的限界验证算法为核心的模型检测工具(BMCF),最后利用该工具对常见的互斥协议,简单数据传输协议的性质进行了分析与验证。结果表明,利用该工具对系统进行建模具有方便直观的特点,并借助实现的验证算法能高效的检验性质的正确性,如果性质不成立工具还会给出反例提示。

AGET ATRP of acrylamide in aqueous media

The recently developed initiation system, the activator generated by electron transfer (AGET) was used in atom transfer radical polymerization (ATRP) to synthesize well-controlled polyacrylamide in aqueous media at 25 degrees C. The different reducing agents involved ascorbic acid and glucosa; well-controlled polymers were obtained when ascorbic acid was used as water-soluble reducing agent. The polymerizations targeted at degrees of polymerization in the range of 400 resulted in polymers with low polydispersity indices. Moreover, first order plots were linear.

Living polymerization of 1,3-butadiene by a Ziegler-Natta type catalyst composed of iron(III) 2-ethylhexanoate, triisobutylaluminum and diethyl phosphite

Living characteristics of facilely prepared Ziegler-Natta type catalyst system consisting of iron(III) 2-ethylhexanoate, triisobutylaluminum and diethyl phosphite have been found in the polymerization of 1,3-butadiene in hexane at 40 degrees C. The characteristics have been well demonstrated by: a first-order kinetics with respect to monomer conversion, a narrow molecular weight distribution (M-w/M-n = 1.48-1.52) of polybutadiene in the entire range of polymerization conversion and a good linearity between M-n and the yield of polymer. Feasible post-polymerization of 1,3-butadiene and block co-polymerization of 1,3-butadiene and isoprene further support the living natures of the catalyst bestowed with.

Monitoring catalytic degradation of dye molecules on silver-coated ZnO nanowire arrays by surface-enhanced Raman spectroscopy

Catalytic degradation of organic dye molecules has attracted extensive attention due to their high toxicity to water resources. In this paper, we propose a novel method for the fabrication of uniform silver-coated ZnO nanowire arrays. The degradation of typical dye molecule rhodamine 6G (R6G), as an example, is investigated in the presence of the as-prepared silver-coated ZnO nanowire arrays. The experimental results show that such composite nanostructures exhibit high catalytic activity, and the reaction follows pseudo-first-order kinetics. Furthermore, these nanowire arrays are desirable SERS substrates for monitoring the catalytic degradation of dye molecules. Compared with traditional UV-visible spectroscopy, SERS technology can reflect more truly the catalytic degradation process occurring on the surface of the catalysts.

A quantitative HPLC method for determining lactide content using hydrolytic kinetics

A new method for quantitative analysis of lactide has been developed by applying chemical kinetics to a HPLC system. The most important advance is its practical approach to the quantification of analytes that are unstable in the HPLC mobile phase. In HPLC analysis, anhydrous mobile phases cannot separate lactide from impurities, and only mixtures of water and organic solvent can achieve effective separation. By selecting conditions for testing and studying the kinetics of lactide hydrolysis, extensive experiments revealed that lactide degradation can be treated as a pseudo-first-order reaction under the given HPLC conditions, and lactide content or purity can be quantitatively determined. This method is practical for measuring the purity of the intermediate lactide in polylactic acid (PLA) production and the lactide content in PLA.

Polymerization of 2,2 '-Dimethyltrimethylene Carbonate by Lutetium Complexes Bearing Amino-Phosphine Ligands

A series of lutetium alkyl, amino, and guanidinato complexes based upon an amino-phosphine ligand framework had been prepared. These complexes were applied to initiate ring-opening polymerization of 2,2'-dimethyltrimethylene carbonate (DTC). The type of the initiator significantly influenced the catalytic activity of these complexes in a trend as follows: alkyl approximate to guanidinate > amide, whereas the complexes with flexible backbone between P and N atoms within the ligand exhibited higher activity than those with rigid backbone. The isolated PDTC had bimodal-mode molecular weight distribution. The molecular weights of each fraction increased linearly with the conversion, indicating that there might be two active species. This had been confirmed by analyses of oligomeric DTC living species and oligomer with NMR technique as the metal-alkoxide and the four-membered metallocyclic lactate. Kinetic investigation displayed that the polymerization rate was the first order with the monomer concentration.

Polymerization of 1,3-butadiene with VO(P-204)(2) and VO(P-507)(2) activated by alkylaluminum

The oxovanadium phosphonates (VO(P-204)(2) and VO(P-507)(2)) activated by various alkylaluminums (AlR3, R = Et, i-Bu, n-Oct; HAIR(2), R = Et, i-Bu) were examined in butadiene (Bd) polymerization. Both VO(P-204)(2) and VO(P-507)(2) showed higher activity than those of classical vanadium-based catalysts (e.g. VOCl3, V(acac)(3)). Among the examined catalysts, the VO(P-204)(2)/Al(Oct)(3) system (I) revealed the highest catalytic activity, giving the poly(Bd) bearing M-n of 3.76 x 10(4) g/mol, and M-w/M-n ratio of 2.9, when the [Al]/[V] molar ratio was 4.0 at 40 degrees C. The polymerization rate for I is of the first order with respect to the concentration of monomer. High thermal stability of I was found, since a fairly good catalytic activity was achieved even at 70 degrees C (polymer yield > 33%); the M-n value and M-w/M-n, ratio were independent of polymerization temperature in the range of 40-70 degrees C. By IR and DSC, the poly(Bd)s obtained had high 1,2-unit content (> 65%) with atactic configuration. The 1,2-unit content of the polymers obtained by I was nearly unchanged, regardless of variation of reaction conditions, i.e. [Al]/[V], ageing time, and reaction temperature, indicating the high stability of stereospecificity of the active sites.

Electrocatalytic reduction of 1,2-diiodoethane by anions of supramolecular complex of (beta-CD)(2)/C-60 in DMF solution

The homogeneous electrocatalytic reduction of 1,2-diiodoethane by anions of the supramolecular complex of (beta-CD)(2)/C-60 in DMF solution is reported. The results show that the trianion of (beta-CD)(2)/C-60 exhibits electrocatalytic behavior towards the reduction of 1,2-diiodoethane, whereas the diani on is unable to reduce the diiodoethane. The second-order catalytic rate constant in DMF solution was determined to be 3.1 x 10(5) M-1 s(-1) by analysis of voltammetric responses under pseudo-first-order conditions with respect to (beta-CD)(2)/C-60. The results suggest that the host beta-cyclodextrin molecules have little effect on the electrocatalytic ability of the encapsulated C-60 toward organic halides.

Polymeric pH indicators immobilized PVA membranes for optical sensors of high basicity based on a kinetic process

Two kinds of polymeric pH indicators PPF (phenolphthalein-formaldehyde product) and CPF (o-cresolphthalein-formaldehyde product) immobilized cross-linked poly(vinyl alcohol) membranes (PPF-PVA and CPF-PVA) for optical intermittent determination of high basicity ([OH-] = 1-8 M) based on a kinetic process were developed. In our previous work, we had demonstrated that PPF-PVA and CPF-PVA could perform the determination of high pH values from pH 10.0 to 14.0. Here the discoloring kinetic behaviors of PPF-PVA and CPF-PVA were compared with those of free phenolphthalein, o-cresolphthalein and thymolphthalein. Experimental results and theoretical analysis indicated that the response behaviors of the optodes' membranes in concentrated NaOH solutions were diffusion-independent and still complied with the pseudo-first-order kinetics. In addition, two data analysis methods for determination were presented. One was directly based on the reduced absorbance: the other was based on the discoloring kinetic constant. It was found that the latter could perform a rapid (60 s) and reliable (relative standard deviation: 2.6%) determination for high basicity.