WKB method for the Dirac equation with a scalar-vector coupling

We outline a recursive method for obtaining WKB expansions of solutions of the Dirac equation in an external centrally symmetric field with a scalar-vector Lorentz structure of the interaction potentials. We obtain semiclassical formulas for radial functions in the classically allowed and forbidden regions and find conditions for matching them in passing through the turning points. We generalize the Bohr-Sommerfeld quantization rule to the relativistic case where a spin-1/2 particle interacts simultaneously with a scalar and an electrostatic external field. We obtain a general expression in the semiclassical approximation for the width of quasistationary levels, which was earlier known only for barrier-type electrostatic potentials (the Gamow formula). We show that the obtained quantization rule exactly produces the energy spectrum for Coulomb- and oscillatory-type potentials. We use an example of the funnel potential to demonstrate that the proposed version of the WKB method not only extends the possibilities for studying the spectrum of energies and wave functions analytically but also ensures an appropriate accuracy of calculations even for states with n_r 1.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 83–111, April, 2005.     

Nuclear matter test for a separable non-localN-N interaction

A nuclear matter test has been conducted on a separable non-localN-N interaction proposed by Sirohi and Srivastava. The potential had been constructed by fitting the phase-shifts. The results obtained compare with those obtained by Tabakin in each partial wave. The binding energy per particle and the symmetry energy coefficient obtained are 19.4 MeV and 66.5 MeV respectively atk _F=1.65 fm⁻¹, while the best estimated values for these quantities are 16 MeV and 30–35 MeV atk _F=1.5 fm⁻¹. Single particle potential generated out of this NLSI has in general the same shape as the one obtained through Tabakin potential. Finally as a test of non-locality the integrated photoabsorption cross-section parameterh has been calculated and the value of 1.03 agrees with other reported values.     

Characteristic of the Ag(II)/Ag(I) system in the presence of 2,2′:6′,2″-terpyridine in acetonitrile

Summary Composition of complexes of Ag(II) and Ag(I) ions with 2,2:6,2-terpyridine (tp) have been established. It has been found that the Ag⁺ ion forms only one complex Ag(tp)⁺ withtp in acetonitrile; its conditional formation constant: ₀₁=6.6·10⁴ has been determined by the potentiometric method. Equilibria and redox systems formed in solutions due to the complexation of Ag⁺ and Ag²⁺ and oxidation of Ag(II) complexes are described. Their formal potentials have been found by coulometric and voltamperometric examinations. The presence of the Ag(tp) ₂ ³⁺ ion in the anodic oxidized solutions of the complexes Ag(tp)(NO₃)₂ and Ag(tp)₂(NO₃)₂ has been proved. Properties of the system Ag(II)/Ag(I) in the presence of terpyridine in water and in acetonitrile have been compared.

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Charakteristik der Systeme Ag(II)/Ag(I) in Gegenwart von 2,2:6,2-Terpyridin in Acetonitril

Zusammenfassung Die Zusammensetzung der Komplexe von Ag(I)- und Ag(II)-Ionen mit 2,2:6,2-Terpyridin (tp) wurde bestimmt. Das Ag⁺-Ion bildet mittp in Acetonitril nur einen Komplex-Ag(tp)⁺. Seine Konditionalbildungskonstante ₀₁=6.6·10⁴ wurde mit Hilfe der potentiometrischen Methode bestimmt. Es wurden die Gleichgewichte und Redoxsysteme als Resultat der Komplexbildung von Ag(II)- und Ag(I)-Ionen und der Ag(II)-Komplexoxidation charakterisiert und die Formalpotentiale mittels Voltametrie und Coulometrie bestimmt. Die Gegenwart der Ag(tp) ₂ ³⁺ -Ionen wurde in anodisch oxydierten Lösungen der Komplexe Ag(tp)(NO₃)₂ und Ag(tp)₂(NO₃)₂ nachgewiesen. Die Eigenschaften des Systems Ag(II)/Ag(I) in Gegenwart von 2,2:6,2-Terpyridin in Wasser und in Acetonitril wurden verglichen.

     

Random time change and recurrent boundary

The purpose of this paper is to study some properties of random time changes in recurrent potential theory. In particular we show that the Martin recurrent boundary is not invariant under a random time change. We then obtain a characterization of random time change destroying a boundary point. We also give some complement about the recurrent boundary connected with “special additive functionals”. We have for example a representation at the boundary of solutions of the Poisson's equation $\text{?(I-U}{}_1\text{)=-U}{}_1\text{(x,·)}$ by using local time at x.     

The ground state for sticky disks

It is proven that the ground state of the two-dimensional sticky potential is the triangular lattice.Research supported in part by NSF grant MCS 78-01520-A01.     

低能反质子的核散射与Glauber理论

运用Glauber多次散射理论,分析低能量反质子与⁴He核的弹性散射微分截面的实验结果.看到反质子能量低到19.6MeV时,多次碰撞的特征仍然是主要的.用光学模型的计算和比较,也得到相同的结论.     

利用Gupta势结合遗传算法研究ConCu55－n(n=0—55)混合团簇的结构演化及基态能量

采用半经验的Gupta多体势结合遗传算法对Co_nCu_55－n(n=0—55)混合团簇的基态结构和能量进行了研究,发现这些混合团簇的基态结构是在Co₅₅,Cu₅₅单质团簇(Mackay二十面体)的基础之上发生的畸变;从n=0(Cu₅₅)开始,Co原子从中心到表面,从棱到顶点依次、连续替换Cu原子;基态结构与键能较大键的数目及其平均键长有关;Co₁₃Cu₄₂具有最稳定的结构,13个Co原子全部位于团簇内部形成Mackay二十面体对整个团簇的稳定性有显著影响. 关键词： 团簇 结构和能量 Gupta势 遗传算法     

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。