Explicit spheroidal wave functions of the hydrogen atom

A simple and straightforward calculating scheme is suggested for finding wave functions of the hydrogen atom in prolate spheroidal coordinates. The wave functions are found in an explicit form by the direct solution of appropriate one-dimensional equations. The suggested calculating scheme allows us to carry out simple calculations and to obtain spheroidal wave functions in principle for arbitrary eigenstates of the hydrogen atom. Expansions are found for the obtained spheroidal wave functions over a spherical basis.     

椭球坐标下求解强磁场中的氢原子

在椭球坐标系下,采用B样条基组方法计算了磁场范围在0-1000 a.u.下氢原子低能态能量以及实验室磁场下(几个特斯拉)氢原子里德堡态的能级,并与文献中的精确结果进行了比较.对1s0态,磁场γ≤100 a.u.时,本文计算结果有12位有效数字的精度,γ=1000 a.u.时有11位有效数字的精度.对2p-1低激发态,γ≤100 a.u.时,能量至少有11位有效数字的精度;γ=1000 a.u.时,有9位有效数字的精度.对原子高激发态,我们计算了实验室磁场下(磁场为4.7特斯拉)氢原子里德堡态(主量子数n=23)的抗磁谱,得到了至少10位有效数字精度的能谱.本文方法既适用于超强磁场下低能态的计算,同样适合原子高里德堡态抗磁谱的计算,为精确计算强磁场下原子能谱提供了一个新的可行方案.此外,讨论了本文方法推广到平行及交叉电磁场下原子能谱计算的可行性.     

Hydrogen atom in strong magnetic field: a high accurate calculation in spheroidal coordinates

A B-spline-type basis set method for the calculation of hydrogen atom in strong magnetic fields in the frame of spheroidal coordinates has been introduced. High accurate energy levels of hydrogen in the magnetic field, with strength ranging from 0 to 1000 a.u., have been obtained. For the ground state, 1s₀, energies with at least 11 significant digits have been obtained. For the low-lying excited state, 2p₋₁, energies with at least 9 significant digits are obtained. The method has also been applied to the calculation of hydrogen Rydberg states in laboratory magnetic fields. Energy spectra with at least 10 significant digits are presented. A comparison with other results in the literatures has been performed. Our results are comparable to the most accurate one up to date. A possible extension to the cases of parallel and crossed electric and magnetic fields have been discussed.     

Cluster calculations of hydrogen in the grain boundaries of nickel

A series of self-consistent field, molecular orbital cluster calculations has been conducted to model the influence of hydrogen on certain structural units in the grain boundaries of nickel. The structural units considered were two Bernal polyhedra, namely the capped trigonal prism and the Archimedean antiprism. Other calculations were performed to simulate interstitial hydrogen and atomic hydrogen chemisorbed on the (111) surface. It was found that hydrogen causes local expansion as an interstitial impurity, in rough quantitative agreement with experiments on dilute solid solutions of hydrogen in nickel. In contrast, it was found that a single hydrogen atom causes a shrinkage of about 1.7% in the bond lengths of the capped trigonal prism and about 2.8% in those of the Archimedean antiprism. Similarly, a hydrogen atom chemisorbed above a nickel atom causes the nearest (111) surface bonds to shorten by about 1.7%. The shrinkage induced in the two Bernal polyhedra appears to be correlated to the low electron density at their centres, and the overall reduction of charge in the vicinity of certain nickel-nickel bonds upon the inclusion of the hydrogen atom.     

Semiclassical calculation of ionization rate for Rydberg hydrogen atoms near a metal surface

The ionization of Rydberg hydrogen atoms near a metal surface at different scaled energies above the classical saddle point energy has been discussed by using the semiclassical method. The results show that the atoms ionize by emitting a train of electron pulses. In order to reveal the chaotic and escape dynamical properties of this system in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed. As the scaled energy is close to the saddle point energy, the ionization process of the hydrogen atom is nearly the same as the case of hydrogen atom in an electric field. There is only a single pulse of electrons, with an exponentially decaying tail. With the increase of the scaled energy, the ionization rates are similar to the case of the hydrogen atom in parallel electric and magnetic field, a series of electron pulses appear in the ionization process. This is caused by classical chaos, which occurs for the metal surface. Our studies also suggest that the metal surface can play the role of both the electric and the magnetic fields. Our theoretical analysis will be useful for guiding experimental studies of the ionization of atoms near the metal surface.     

A quantum chemical study of tyrosyl reduction and O—O bond formation in photosystem II

Density functional theory has been used to study two of the main topics of oxygen evolution in photosystem II. The first concerns the reduction of the tyrosyl radical that occurs in every S-state transition. The two leading models, hydrogen atom transfer and electron transfer, have been investigated. In the present study, hydrogen atom transfer has the lower barrier. The second topic addressed is O—O bond formation in the S₃ to S₀ transition, where a Mn₃ complex including calcium and chloride cofactors was used as a model. The reaction is suggested to proceed from a bridging oxyl group to a radical hydroxyl, which combines to form the O—O bond with a hydroxide ligand of the Mn complex.     

EPR study of free radicals in γ-irradiated thiazide compounds

The aim of this paper was to identify the type of radicals formed by γ-irradiation in powdered chlorothiazide (CTZ), hydrochlorothiazide (HCTZ), althiazide (ATZ) and trichloromethiazide (TCTZ) on the basis of analysis of their electron paramagnetic resonance spectra with enhanced resolution. In TCTZ, HCTZ and ATZ the radical was formed by abstraction of a hydrogen atom from the carbon atom C-3, and in the case of CTZ by addition of a hydrogen atom to the nitrogen atom N-4. The hyperfine structure is found. The electron densities at nitrogen atom positions in the N-C-N group in HCTZ, ATZ and TCTZ depend on a single 3-position substitution and are in line with their diuretic potency.     

Resonant states for the scattering of slow particles by screened potentials

Partial resonant situations for the scattering of slow particles with nonzero angular momenta by short-range screened Yukawa and Buckingham potentials are considered. The problem of electron scattering by a hydrogen atom placed in a plasma medium is discussed. A general scheme of resonances has been constructed in the Pais approximation.     

Fractal Motion of Electrons with Variable Weak Memory and Nonlocality

Equations of fractal motion of electrons with variable weak memory and nonlocality are investigated. It is demonstrated that the fractal dimension of time changes by a harmonic law for stationary electron motion. The fractal nonlocality has been established for the free electron; it also changes by a harmonic law. The fractal nonlocality of the electron bound with the hydrogen atom nucleus differs radically. In this case, the fractal dimension of radial electron motion is everywhere less than unity. It can be greater than unity in regions well away from the nucleus. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 52–57, September, 2005.     

Electron Spin Resonance of Alkali Metal Contact Ion Pairs of 2,6-di-tert-Butylbenzoquinone in Non Polar Solvent

The question whether excited triplet states of quinones react with a number of substrates such as alcohols, phenols, and amines, via electron transfer mechanism has attracted much attention in recent years. The existence of some triplet exciplex was postulated by Kobashi et al¹ in their study of hydrogen atom abstraction by p-chloranil using laser flash spectrocopic detection. In some recent e.s.r. and CIDEP studies^2,3, however, there is no compelling evidence that the photoreduction of quinones and benzophenones undergoes an initial electron transfer mechanism. It should be noted that most of the e.s.r. studies of quinone radical anions had been carried out in polar solvents. In flash photolysis studies some evidence has indeed been obtained^1,4 in which the efficiency of hydrogen abstraction by excited triplet quinones increases with solvent polarity and therefore it is possible that the initial primary process involves electron transfer followed immediately by proton transfer. On the other hand, we     

CPT and Lorentz invariance violation in hydrogen-like atoms

We analyze an approximate solution to the Dirac equation for an electron in a central potential, in particular, in a Coulomb potential, when Lorentz invariance is violated. A quasi-relativistic approximation for the Dirac equation in an external field has been derived. The directivity pattern of spontaneous emission for a polarized hydrogen atom has been found to be asymmetric.     

氢原子波函数的经典极限分析

由电子绕原子核的经典轨道运动出发,对电子的椭圆轨道初始坐标参数求平均,得到空间密度分布。这分布与经典极限条件下氢原子中定态几率密度相同。类似的比较也推广到相空间进行。由这一比较得出结论:定态氢原子波函数不描述单个原子而描述一个系综。 关键词：     

Anisotropic features of two-dimensional hydrogen atom in magnetic field

The aim of this study is the numerical research of anisotropic characteristics of a two-dimensional (2D) hydrogen atom induced by a magnetic field. The ground state energy (GSE) of the 2D hydrogen atom and the corresponding wavefunction have been numerically calculated in the Born–Oppenheimer approximation and taking into account the finite proton mass. The nonlinear dependence of the GSE on angle α between the magnetic field vector and the normal to the electron motion plane has been found in a wide range of the magnetic field. The effect of a significant reduction of the GSE (up to 1.9-fold) is observed with increasing the angle α up to 90°. The agreement with experimental data has been demonstrated. The dependences of the GSE of a 2D exciton in GaAs/Al_0.33Ga_0.67As have been determined for various tilt angles and magnetic fields.     

核力和重子相互作用

本文评述了核力和重子相互作用研究的历程,取得的成就和存在的问题。     

Peculiarities of electron exchange between a negative hydrogen ion and atomic chains

This paper is dedicated to studying electron exchange between a negative hydrogen ion and an atomic chain with subsequent electron transport along the linear chain of hydrogen atoms. This process occurs after the electron transition from the negative hydrogen atom to the atomic chain. In our calculations, a method of wave packet propagation not using perturbation theory was applied. It is shown that the effectiveness of electron transport decreases uniformly as the distance from the ion to the chain increases. The electron propagates along the chain uniformly; in this case, the electron velocity is almost independent of the ion-chain distance.     

电子与氢原子碰撞激发（n=2,n=3态）微分散射截面理论计算

应用耦合通道光学势方法，计算了中等能量范围电子碰撞激发氢原子到ｎ＝２，ｎ＝３激发态以及弹性散射的微分散射截面，将计算结果同实验和其它理论方法进行了比较。     

Perturbation of the excited states of the hydrogen atom and hydrogen-like ions by a neutral atom

Owing to the degeneracy of the energy levels, the wavefunction of the electron in the excited states of the hydrogen atom and hydrogen-like ions perturbed by a neutral atom B is significantly different from the wavefunction of the unperturbed state. The perturbed function has a wide high maximum in the region of atom B, which is explained by multiple collisions of the electron with atom B, because the classical trajectories in the Coulomb field are closed and the size of atom B is much smaller than the size of the excited-state orbit. The radiative lifetimes of the excited states are much larger than those of unperturbed states. The orbital angular momentum L of the excited electron is strongly changed in collisions with atom B owing to the quantum interference or mixing of the temporal phases of adiabatic wavefunctions. The cross sections for such a change in the orbital angular momentum are several orders of magnitude larger than the cross sections found in early investigations in the approximation of the single collision of the electron with atom B.     

Interatomic potentials at short range using Madelung’s equations

Interatomic potentials at short range are investigated starting from the united atom electron density. Prior work has utilised time independent Rayleigh-Schr?dinger perturbation theory, adapted to overcome difficulties with convergence of the power series in internuclear distance, and has been confined to diatomic species. This work presents a time dependent approach, based on Madelung’s equations, in which the electron density evolves continuously from that of the united atom to the density of the polyatomic system; no power series is involved, there are no convergence difficulties and the approach is applicable to polyatomic systems. Electronic separation and interaction energies are calculated and compared to previous calculations. Some triatomic and tetratomic arrays of hydrogen atoms are examined and three and four body interaction terms estimated.     

低气压条件下氢气潘宁放电的模拟分析

为更好地理解低气压、弱电离条件下潘宁离子源放电过程中离子和电子的动力学行为, 通过建立二维轴对称模型, 采用粒子模拟与蒙特卡罗相结合(PIC/MCC)的方法, 考虑了电子与氢气之间的弹性碰撞、激发、电离以及氢原子、离子之间的弹性碰撞和电荷交换等过程, 对微型氢气潘宁离子源放电和引出过程进行了数值研究. 考察了磁场位形、壁面二次电子发射系数、引出电压和充气压力对放电过程的影响, 得到了实验中难以诊断得到的放电腔内电子与离子数密度分布, 阳极电流、引出极离子电流、单原子氢离子比例和双原子氢离子比例等宏观参数与实验结果相一致. 通过仿真使得对氢气潘宁放电机制的研究从定性过渡到定量, 这对于潘宁离子源的设计和改进具有重要意义. 关键词： 潘宁放电 氢气 粒子模拟 蒙特卡罗     

单轴应变对H在α-Fe中占位及扩散的影响

采用基于密度泛函理论的第一性原理方法,研究了H在不同单轴应变下α-Fe中的间隙占位,计算了H原子的溶解能、态密度、电荷差分密度和电荷布居.结果表明:不同单轴拉压应变作用下,H原子优先占据四面体间隙(Ts)位,且随着压应变减小、拉应变增加,H原子越易溶于α-Fe.压应变使得Ts位的H获得更多的电子,而拉应变减少了这种电荷转移.应用LST/QST过渡态搜索计算垂直应变方向的扩散.八面体间隙位是邻近Ts位H的扩散过渡态.扩散激活能与应变呈线性关系,且随着压应变的增加,扩散激活能降低,扩散更容易.