Notes on the nonrelativistic binding energy for neutral atoms

An analytical expression is obtained for the binding energy of a neutral atom within the statistical theory $\text{E = ? 0.76874 Z}{}^{\mathrm{<mtext>7</mtext><mtext>3</mtext>}}\text{+ 0.5 Z}{}^2\text{? 0.2699 Z}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$, which prefectly reproduces SCF binding energy for Z > 20. The oscillations of energy are discussed.     

The binding energy of electrons in supercritical atoms

In a supercritical atom, the most tightly bound electrons do not occupy bound-state eigenfunctions of the Dirac Hamiltonian. We discuss the binding energy of supercritical atoms in the light of this fact. We derive an expression for the binding energy which relates the supercritical and the undercritical cases in a smooth fashion.     

Core level binding energy shifts between free and condensed atoms

Assuming a fully screened final state (in the metallic case) and using the (Z + 1) approximation and a Born—Haber cycle we calculate the shift in the core level binding energy between the free atom and its metallic state. The agreement with known experimental shifts is shown to be very good. Utilization of the present method can for example give accurate core level binding energies for those free atoms where such data only exist for the metallic phase.     

Calculation of binding energy in negative ions of the alkaline-earth atoms Ca and Sr

The electron binding energy in negative ions of the alkaline-earth atoms Ca and Sr is calculated on the basis of the polarization-potential formalism and relativistic perturbation theory with a zeroth-order model potential. The results improve the data available in the literature for these negative ions. Odessa Hydrometeorological Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 27–31, September, 1996.     

三价原子的非相对论能级结构理论

本文以原子结构的拉卡方法为基础,从三价原子的拉卡基出发,反复利用三个角动量耦合的基本关系以及3j、6j、9j符号的性质,具体推导了(n1 l1)(n2 l2)(n3l3)和(n1 l1)2(n3l3)组态下三价原子非相对论哈密顿矩阵元的计算式,除径向部分用Slater-Condon径向积分表示以外,完成了所有的角向积分与自旋求和;简要举例说明了如何利用该矩阵元计算式推导三价原子非相对论谱项能量表达式以及利用变分原理确定其中的Slater-Condon径向积分,从而求出具体的谱项能量数值.可以说,本文已建立起三价原子非相对论性能级结构的一般理论.     

Fast-ion-beam laser probing of ion-source energy distributions and atomic structure

Collinear fast-ion-beam laser spectroscopy is a very high resolution probe for measuring ion-beam energy distributions and atomic structure parameters of interest in nuclear physics, atomic physics, and astrophysics. We have used offline 10-keV beams of atomic ions and a CW laser system to study the behavior of a Penning ion source and to measure hyperfine structure, isotope shifts, atomic lifetimes, spontaneous-emission branching fractions, oscillator strengths, and absolute wavelengths of a variety of atomic species from the lanthanide and transition-metal groups.     

Electron-electron correction to the chemical binding energy of hydrogen atoms in α-palladium hydrides

We show that the modification of the electron-electron term resulting from the binding of a pair of hydrogen impurities in α-palladium hydrides cancels the corresponding modification of the one-electron band energies.     

三价原子的非相对论能级结构

采用拉卡基函数并借助角动量耦合理论,导出了三价原子非相对论性哈密顿的矩阵元的一般表达式,完成了所有的角向积分和自旋求和计算,结果用3j、6j和9j符号表示,径向积分则表示为Slater-Condon参数.用相关结果对(n1p)2(n2p)组态的谱项结构进行了分析     

Non—conservation of energy arising from atomic dipole interactions and its effects on light field and coupled atoms

The interactions between coupled atoms and a single mode of a quantized electromagnetic field, which involve the terms originating from the dipole interactions, are discussed. In the usual Jaynes－Cummings model for coupled atoms, the terms of non-conservation of energy originating from dipole interactions are neglected, however, we take them into consideration in this paper. The effects of these terms on the evolutions of quantum statistic properties and squeezing of the field, the squeezing of atomic dipole moments and atomic population inversion are investigated. It has been shown that the coupling between atoms modulates these evolutions of fields and atoms. The terms of non-conservation of energy affect these evolutions of fields and atoms slightly. They also have effects on the squeezing of the field, the squeezing of atomic dipole and atomic population inversions. The initial states of atoms also affect these properties.     

On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

The exchange dispersion energy for the interaction of two helium atoms is expressed as a sum of multipole components. In contrast to the analogous expansion for the dispersion energy the derived series converges very slowly and the rate of convergence does not improve with an increasing interatomic distance. Numerical calculations show that at the van der Waals minimum the first term of the series, referred to as dipole-dipole exchange energy, represents merely 17 per cent of the exchange dispersion energy. Moreover, even the inclusion of dipole-quadrupole and quadrupole-quadrupole terms can account for only half of the total exchange dispersion interaction. The above difficulty can be avoided by expanding the dispersion pair function in terms of ionic type or explicitly correlated functions.     

A relation between the binding energy and the band-gap energy in semiconductors of diamond or zinc-blende structure

From an empirical calculation of bond energy, of semiconductors of diamond and zinc-blende structures, and of some wurtzite-type, it is revealed that between the gap energy E_g and single-bond energy E_s there exists a linear correlation which, for the different series of binary semiconductors of tetrahedral coordination taken into consideration here, can be expressed by a relation of the type : E_g = a(E_s−b) where a and b are characteristic constants of the series A^ivA^iv, AⁱⁱⁱB^v,AⁱⁱB^vi. The correlation found for the said semiconductors are not valid for the compounds AⁱB^vii of zinc-blende type structure and for the two oxides ZnO, CdO of wurtzite-type structure. This fact is attributed to the almost completely ionic character of the bond in these compounds, because of which the localization of the electrons along the valence bonds is negligible.     

Singular value decomposition of energy matrices in theoretical atomic structure calculations

The singular value decomposition, SVD, is applied to the linear eigenvalue problem in atomic structure calculations. By comparing with recent calculations of energy levels in neutral Ca, it is shown that the SVD can give quite accurate results and much faster than normal diagonalization techniques, even of the Davidson type. However, the energy levels calculated in this approach are more strongly bound than the real eigenvalues, and this is ascribed to an artefact of the SVD, caused by the use of a discretized continuum in the calculations. This effect can lead to fairly large errors if there is strong CI present. The property of the linear eigenvalue problem that the spectrum is unchanged when a constant is added to the diagonal does not apply to the SVD. This means that it is impossible to solve the problems connected with a discretized continuum simply by shifting the spectrum.     

Differential cross section surfaces for low energy scattering of electrons and positrons from rare gas atoms

The differential cross sections for scattering of electrons and positrons from He, Ne, Ar, Kr, and Xe at projectile energies below the inelastic thresholds are calculated using a model potential approach in which the interaction between the projectile and the target atom is partitioned into static, exchange (for electrons), and correlation-polarization parts. Two different forms of the parameter-free correlation-polarization potential are suggested; in both cases the correlation-polarization potential is determined by smoothly matching the asymptotic form of the polarization potential (1/r ⁴) to the correlation potential at the outermost orbital radius of the target atom. The results of angular distributions are presented in the form of contours of constant differential cross sections as well as in the form of differential cross section surfaces in three-dimensional plots. Both of these presentations display the locations of the principal maxima and minima of the differential cross sections as well as the critical points in a very useful manner.     

On the role of correlation energy produced by the spin-spin interaction in the formation of binding energy for two-electron atomic systems

An algorithm is proposed for computing the correlation energy produced by the spin-spin interaction V _SS of electrons in He-like atomic systems. The algorithm takes into account the singular nature of V _SS and the formation of a compact finite motion of electrons in the range of distances Ze ²/mc ² < r ₁₂ < ħ/mc between the electrons under the action of the magnetic fields of spins for a singlet ground state. Good agreement with experimental values of the ionization potential is attained for a wide set of two-electron atomic systems without resorting to variational procedures, but only using hydrogen-like wavefunctions and correctly taking into account the singular nature of the spin-spin interaction of electrons.