最弱受约束电子势模型散射态的精确解

研究了最弱受约束电子势模型的散射态性质，获得了扭曲库仑波的解析解．给出了精确的按“k/2π标度”归一化的散射态波函数及相移表达式．讨论了散射振幅的解析性质，给出了束缚-连续跃迁矩阵元的解析计算公式．结果可广泛应用于处理原子的散射问题 关键词：     

最弱受约束电子势模型中束缚-自由非相对论跃迁矩阵元的计算公式

研究最弱受约束电子势模型的散射态，获得了精确的按“ｋ／２π标度”归一化的散射态波函数以及相移表达式，给出了束缚—自由非相对论跃迁矩阵元的解析计算公式。这些结果可广泛应用于处理原子的散射问题之中。     

最弱受约束电子势模型中束缚—自由非相对论跃迁矩阵元…

研究最弱受约束电子势模型的散射态，获得了精确的按“ｋ／２π标度”，归一化的散射态波函数以及相移表达式。给出了束缚－自由非相对论跃迁矩阵元的解析计算公式。这些结果可广泛应用于处理原子的散射问题之中。     

相对论性无自旋氢原子的散射态

研究获得了相对论性无自旋氢原子散射态的精确解,给出了精确的相移表达式和按"k/2π标度"归一化的散射态的径向波函数,讨论了散射振幅的解析性质 .     

具有n维氢原子型标量势与矢量势的Klein-Gordon方程的束缚态

研究了具有n维氢原子型标量势和矢量势的Klein-Gordon方程的束缚态性质，获得了束 缚态的精确解-给出了精确的能谱方程和归一化的解析波函数，推导出径向平均值的两个递 推关系和部分低幂次径向平均值的解析表达式- 关键词： n维氢原子势 Klein-Gordon方程 束缚态 精确解     

新环形库仑势的束缚连续跃迁矩阵元

利用新环形库仑势的归一化的束缚态径向波函数和按“k/2π标度”归一化的散射态径向波函数,本文给出了新环形库仑势的任意幂次的束缚连续跃迁矩阵元的通项表达式.为了简化高幂次的束缚连续跃迁矩阵元的计算,我们还推导出了不同幂次的束缚连续跃迁矩阵元之间所满足的递推关系,并提出了计算径向波函数微商的矩阵元的计算办法.本文结果可广泛的用于原子与分子的散射问题特别是环形分子的散射问题之中.     

相对论性无自旋粒子在Hartmann势场中运动的精确解

在标量势等于矢量势的条件下,本文获得了具有Hartmann型势的Klein-Gordon方程的精确解.给出了束缚态的精确的能谱方程和归一化的径向波函数,对于散射态,获得了按“k/2π标度”归一化的径向波函数和相移的解析计算公式.讨论了散射振幅的解析性质和波函数、能谱方程以及相移的非相对论近似.     

一类n维非球谐振子势的精确解

严格求解一类n维非球谐振子势的定态薛定谔方程，获得了归一化径向波函数和能谱的 精确解.在此基础上导出径向矩阵元r,L_n｜r^s｜n′ ₄,L′_n>的通项公式. 关键词： n维非球谐振子 精确解 径向矩阵元 通项公式     

库仑波函数的束缚连续跃迁矩阵元的解析计算公式和递推关系

给出了库仑波函数的束缚连续跃迁矩阵元的解析计算公式,并获得了不同幂次矩阵元之间所满足的递推关系.这些结果可广泛的用于原子和分子的散射问题.     

在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.     

Electronic structure of hydrogen and muonium in Al,Mg and Cu

The electronic structure of hydrogen and muonium in simple metals is investigated. The spherical solid model potential is used for the discrete lattice and the Blatt correction for lattice dilation. The proton and muon are kept at the octahedral sites in the fcc and hcp lattices and self-consistent non-linear screening calculations are carried out. The scattering phase shifts, electronic charge density, effective impurity potential, self-energy, charge transfer, residual resistivity and Knight shift are calculated. The spherical solid potential changes the scattering character of impurity. The phase shifts are found slowly converging. The scattering is more prominent in Al than in Mg and Cu. The virtual bound states of proton and muon are favoured in all the three metals. The calculated value of residual resistivity for CuH is in good agreement with the experimental value. The results for Knight shift forμ ⁺ in Cu and Mg are in reasonable agreement with the experimental values while those forμ ⁺ in Al are lower than the experimental value. The analytical expressions for effective impurity potential and electronic charge density are suggested.     

Exact nonrelativistic expressions for the tensor for scattering of light by atoms

Exact nonrelativistic analytical expressions are derived for dipole two-photon transitions between arbitrary multiplets of the hydrogen atom and positive hydrogenlike ions. The result is expressed in terms of a single Gauss hypergeometric function and polynomials whose degrees increase linearly with the number of nodes of the bound states of the quantum system. The cross sections of elastic scattering of light by K-and L-shells of the hydrogen atom are given as an example. It is demonstrated that by expanding the discrete-spectrum wave functions in ultraspherical polynomials it is also possible to obtain analytical expressions of the cross sections of two-photon transitions between states described by the Simons model potential. The basis consisting of Chebyshev polynomials is shown to be the best expansion basis, and the coefficients of such an expansion are given for a broad range of parameters of the problem. Calculation of the polarizability of the 5S-state of the rubidium atom is chosen as an example. Finally, the results are compared with the experimental data and the theoretical results of other researchers. Zh. éksp. Teor. Fiz. 111, 816–830 (March 1997)     

Scattering-amplitude phase in spiderlike photoelectron momentum distributions

The spiderlike structures in the photoelectron momentum distributions of ionized electrons from the hydrogen atom are numerically simulated by using a semiclassical rescattering model(SRM) and solving the time-dependent Schrodinger equation(TDSE),focusing on the role of the phase of the scattering amplitude.With the SRM,we find that the spiderlike legs shift to positions with smaller transverse momentum values while increasing the phase.The spiderlike patterns obtained by SRM and TDSE are in good agreement upon considering this phase.In addition,the time differences in electron ionization and rescattering calculated by SRM and the saddle-point equations are either in agreement or show very similar laws of variation,which further corroborates the significance of the phase of the scattering amplitude.     

Bound states and scattering resonances induced by spatially modulated interactions

We study the two-body problem with a spatially modulated interaction potential using a two-channel model, in which the interchannel coupling is provided by an optical standing wave and its strength modulates periodically in space. As the modulation amplitudes increase, there will appear a sequence of bound states. Part of them will cause a divergence of the effective scattering length, defined through the phase shift in the asymptotic behavior of scattering states. We also discuss how the local scattering length, defined through short-range behavior of scattering states, modulates spatially in different regimes. These results provide a theoretical guideline for a new control technique in the cold atom toolbox, in particular, for alkaline-earth(-like) atoms where the inelastic loss is small.     

Proton polarizability and lamb shift in the muonic hydrogen atom

The corrections that the structure of the proton and its polarizability induce in the Lamb shift in the muonic and the conventional hydrogen atom are calculated on the basis of up-to-date experimental data on the structure functions in deep-inelastic scattering. Numerically, the contribution from proton polarizability to the 2P-2S shift in the muonic hydrogen atom is 4.4 GHz.     

Proton scattering by a hydrogen atom in an effectively two-body model

It is assumed that the total potential of proton interaction with a hydrogen atom is the sum of the short-range nuclear soft-core Reid potential and the long-range Thomas-Fermi potential. A quantum mechanical analysis of low-energy features of the phase shift and cross section for elastic proton scattering on a hydrogen atom is given for the case of zero total angular momentum. The calculations performed in the present study within a nonlinear version of the variable-phase approach ultimately revealed that, because of a long-range character of the asymptotic behavior of the Thomas-Fermi potential, the respective cross section at low energies oscillates but has a finite number of zeros.     

Elastic scattering of electrons by the metastable 2s state of atomic hydrogen

A two-potential approach is used to study the elastic scattering of electrons by the metastable hydrogen atom. The results or differential and total cross sections are presented at 200 and 400 eV energies and compared with the available calculations. Also a comparison between elastic scattering from 2s and 1s states of hydrogen is made.     

Features of the bremsstrahlung accompanying collisions with a hydrogen atom in an excited state

The features of the bremsstrahlung appearing during a collision of a fast charged particle with a hydrogen atom (or hydrogenic ion) in an excited state are investigated. It is shown that the emission spectrum of photons with energies greater than the ionization potential of a given excited state (except the 2s state) displays narrow lines, which are caused by de-excitation of the atom in an intermediate state. It is demonstrated that the scattering of a charged particle on an excited hydrogen atom produces a feature which is not observed in the case of scattering on a ground-state hydrogen atom. Expressions are obtained for the generalized dynamic polarizability of the hydrogen atom and hydrogenic ions in the 1s, 2s, and 3s states. A method is developed for deriving expressions for the generalized dynamic polarizabilities of other excited states through the use of the Coulomb Green’s function and representation of the electronic wave function in terms of the differentiation of the generating functions of Laguerre polynomials. The bremsstrahlung cross sections for electrons and positrons colliding with hydrogen atoms in the 1s, 2s, and 3s states are calculated. Zh. Tekh. Fiz. 69, 7–13 (October 1999)