New summation rules for coulomb wave functions

Sums of products of the Coulomb wave functions over degenerate manifolds have been obtained in a closed form. These sums appear in many atomic and molecular problems. The sums have been obtained making use of the properties of the Coulomb Green's function G(r, r('),E), in the limit E-->E(n), where E(n) is the eigenenergy of the hydrogenlike atomic ion. The closed Hostler-Pratt form of G in the coordinate representation has been used. The sums calculated are a consequence of the n degeneracy of the Coulomb atomic energy levels. This itself, as is well known, follows from the four-dimensional symmetry of the Coulomb problem for the hydrogen atom.     

Nonrelativistic wave functions in relativistic physics

We explore the validity of using nonrelativistic wave functions for lightly-bound states in relativistic situations. This is shown to be acceptable for scattering problems, but not necessarily for those involving a decay. In the latter case the wave function would need to have special properties. These do not occur for a deuteron-like wave function but do occur for a positronium-like system, the crucial features being that positronium is bound by zero mass exchange.     

The dependence of exchange and coulomb energies on wave functions of the interacting systems

First-order energies have been calculated for the He₂ system using a number of He wave functions. The convergence to the Hartree-Fock limit has been studied and a two-term expansion in Slater orbitals gives about 98 per cent of this limit. The effect of correlation has been examined by adding s′² and p ² configurations to the wave function and a change of approximately 10 per cent in the effective first-order energy has been noted.     

高温等离子体相对论性平均原子模型中的半解析波函数

半解析求解平均原子模型方法充分利用了已知精确波函数的解析性质,通过对平均原子模型中势函数的数值拟合,就得到仅含一个数值因子的半解析波函数以及相应的能量本征值.本文列出了等离子体中相对论性平均原子模型的诸方程,特别注意方程求解技术和程序设计中的一些细节.与完全数值解以及其他类似模型得到的数值解进行的比较表明,在较高温度条件下半解析结果的精度是相当高的,求解的效率也很高.此外还对物理模型中某些缺陷进行了分析.     

A study of the relativistic coulomb problem in momentum space

The quantum-mechanical solutions of the operator equation corresponding to the classical equation $\text{[(p ? eA)}{}^2\text{+ m}{}^2\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? (E ? eU) = 0}$ are studied in the particular case of the one-dimensional Coulomb potential and compared to the standard solutions of the Klein-Gordon equation.     

On relativistic wave equations

A method is given for obtaining relativistic wave equations in matrix form for particles with higher spins. Values are given for the constants of the ^v matrices, the matrix of the inversion operator, and the scalar matrix which enters into the expression of the current for particles with spin 0, 1/2, 1, 3/2, or 2.     

Diraclike relativistic wave equation

It is proved that nondissociating P-invariant relativistic wave equations (RWE) for particles with maximal spin s_o whose matrices satisfy the commutative relations of Dirac matrix algebra contain all values of the spin from 0 (1/2) to s_o. Corollaries of the theorem are examined for certain of the existing approaches to the construction of a theory of RWE.     

Matrix relativistic wave equations

The matrix notation of paper I is extended to include first-rank spinors expressed as two-component spin-vectors. Well-known two-component and four-component spinor equations are expressed in this notation. In addition, it is shown how other covariant wave equations can easily be invented. A certain nonlinear equation is found to have only positive-energy solutions for particles and antiparticles.     

Exponential-trigonometric basis functions in the coulomb four-body problem

Basis functions of a new type—specifically, exponential-trigonometric functions depending on all six interparticle distances—have been proposed for the Coulomb four-body problem. A method has been developed for computing nine-dimensional integrals determining the matrix elements of the Hamiltonian for a four-body system and featuring these functions. The efficiency of the approach that relies on the proposed basis functions has been tested by calculating the e ⁺ e ^? e ⁺ e ^?, p ⁺μ^? p ⁺μ^?, μ⁺ e ^?μ⁺ e ^?, and p ⁺ e ^? p ⁺ e ^? molecules.     

Can the SCA with relativistic Hartree-Fock wave functions describe the high energy ionisation probability

Recently experimental data of the L-shell ionisation probability of Au in the impact parameter region around the L-shell radius have been reported with α-particle energies in the range of 12–50 MeV. A very large discrepancy growing with increasing energy was found between the experimental and theoretical values. Refined calculations using the semiclassical approximation (SCA) with hyperbolic projectile trajectories and relativistic Hartree-Fock electron wave functions show, that this discrepancy can still be explained unsufficiently.     

The generalised relativistic Lindhard functions

We present here analytic expressions for the generalised Lindhard function, also referred to as Fermi gas polarisation propagator, in a relativistic kinematic framework and in the presence of various resonances and vertices. Particular attention is payed to its real part, since it gives rise to substantial difficulties in the definition of the currents entering the dynamics.     

相对论行波管慢波结构几何参数研究

推导了无引导磁场下具有离子通道的波纹波导中的色散方程,并通过数值计算分析了该慢波结构的几何参数如波纹周期、波纹深度以及波导平均半径对相对论行波管的带宽及增益的影响,为相对论行波管的设计提供了一定的依据。     

相对论行波管慢波结构几何参数研究

 推导了无引导磁场下具有离子通道的波纹波导中的色散方程,并通过数值计算分析了该慢波结构的几何参数如波纹周期、波纹深度以及波导平均半径对相对论行波管的带宽及增益的影响,为相对论行波管的设计提供了一定的依据。     

Kinetic theory of a system of coulomb particles in the weakly relativistic approximation

An analysis is made of the connection between the relativistic analogs of the Vlasov and Landau equations obtained by Bogolyubov's method and the corresponding relativistic kinetic equations. The H theorem is considered in the weakly relativistic approximation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 99–101, May, 1980.We thank L. M. Kovrizhnykh, A. A. Rukhadze, I. P. Pavlotskii, and A. S. Sakharov for valuable discussions.     

Polarization symmetries of relativistic wave equations

Generators of the group invariance of polarization origin U(2s + 1) are constructed for relativistic wave equations (RWE), where s is the particle spin. Particular cases of the vector (mass) and Dirac fields are examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 74–77 November, 1982.     

Internal symmetry of relativistic wave equations

The properties are considered of the internal symmetry of first-order relativistic wave equations on the basis of the Gel'fand-Yaglom approach. A sufficient condition is established for the existence of such a symmetry for free fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 16–18, July, 1991.     

相对论行波管色散特性分析

 数值计算了一种填充等离子体的波纹波导结构的行波管，在强引导磁场下，被一环形相对论电子注驱动的小信号增益。详细地分析了等离子体的浓度、电子注的电压、电流及其在慢波结构中的传输位置对行波管的增益、带宽和中心频率的影响。