氦原子和类氦离子基态能量的变分计算及相对论修正

采用一个包含坐标伸缩系数的简单有效的变分波函数,同时考虑到核的运动,利用Mathematic a语言开发了一个用变分法计算三体问题的程序,对氦原子和类氦离子(H^-,He,Li ⁺,Be⁺⁺,B³⁺,C⁴⁺,N⁵⁺,O ⁶⁺)的非相对论基态能量和解析波 函数进行了变分计算.在此基础上,对非相对论哈密顿量进行相对论和辐射修正,并考虑到有 限核电荷半径的影响,得到了氦原子和类氦离子高精度的基态能量值. 关键词： 氦原子 类氦离子 变分法 基态能量 相对论修正     

氦原子及类氦离子基态能量的经验公式

通过对氦原子和类氦离子电离能数据的分析 ,找到了一个能够快速计算类氦体系基态能量的经验公式 ,验算了一些类氦离子 (Z=2— 1 5 )的基态能量 ,与实验测量值符合得很好。除了 Li 和 Be 的基态能量的相对偏差为 0 .4 46 %外 ,其他的都低于 0 .4 %。     

类氦铝离子软X射线激光

通过一系列的数值计算，确定了实现类氦铝离子３ｄ＾１Ｄ２－２ｐ＾１Ｐ１跃迁激光增益的最佳等离子体条件，并提出了用辐射冷却的方法为实现所需的等离子体条件。     

类氦原子体系基态能量的变分法数值研究

选取由指数形式函数的线性组合所构成的试探波函数,利用变分法对类氦原子体系的基态能量进行了数值计算,计算中利用拟牛顿法求非线性方程组的一组实根,计算结果与实验值相当接近．计算表明：当n由1增大到2时,能量的计算值有较大的改进,但由于选取的变分波函数没有考虑到电子关联作用,所以计算只能达到一定的精确度．     

自由电子激光制备高强度亚稳态氦原子和类氦离子

在少电子原子精密光谱测量中,产生高强度、单一量子态的氦原子和类氦离子是实验研究的关键,也是改善实验测量信噪比的决定性因素.本文提出利用自由电子激光获得高强度亚稳态氦原子和类氦离子的实验方案.激光的制备效率可以通过求解光和原子相互作用的主方程获得,根据拟建设的深圳自由电子激光装置的设计参数和实验条件,计算得到亚稳态He, Li⁺和Be²⁺的制备效率分别可达3%, 6%和2%以上.与常见的气体放电和电子轰击等制备方法相比,激光激发产生亚稳态原子/离子不仅可以提高制备产率,也可以降低放电时产生的电子、离子以及光子等高能杂散粒子的影响.利用自由电子激光激发制备亚稳态氦原子和类氦离子有望应用于多个研究领域.     

氦原子及类氦离子基态的二参数变分法研究

提出了一种计算氦原子及类氦离子基态能量和波函数的二参数变分法,包括试探波函数的设计和基态能量表达式的推导,并用Mathematica 5.0软件的优化计算功能方便快捷地计算出基态能量,将计算结果与实验结果和部分所列文献的结果进行对比.结果表明,本文所得精度较高,变分参数个数较少.同时强调交换对称性和量子态的交缠在双电子原子体系问题中的重要性.     

类氦离子的电子碰撞电离微分截面

本文主要利用扭曲波玻恩交换近似方法(DBE)计算类氦离子在电子碰撞下,相应不同的末态电子能量分配的电离截面(能量微分截面)。发现对这些微分截面在不同靶电荷及入射能量下,都可用带两个参数的高斯函数αexp(β(x—0.5)²)很好地拟合。还给出两个拟合参数随靶电荷和入射能量的变化曲线,以及讨论了在库仑波玻恩交换近似(CBE)和DBE两种不同近似下所得参数值的差别。计算结果也表阴,在低靶电荷和低入射能量时用DBE计算的必要性。 关键词：     

类铍离子激发态的能量计算

采用多组态相互作用方法及Rayleigh- Ritz变分法,计算了类铍O4+离子1s22s2p3Po态的非相对论能量,并详细分析了如何选择质量最好的变分波函数.运用截断变分方法进一步饱和函数空间得到能量的改进量,并考虑相对论修正、质量极化效应等获得了相对论能量计算值.计算结果表明,此理论计算方法可得到高精度的能量计算值.     

类氦离子2p3p3Pe双激发态等电子系列的能级和精细结构

采用Rayleigh-Ritz变分法及组态相互作用,并考虑相对论修正和质量极化效应,研究了类氦离子等电子系列(Z=2～16)双激发态2p3p3Pe的相对论能量和辐射跃迁波长,并计算了该系统的精细结构.计算的结果与Drake等人的理论计算符合得很好.     

Two-body problem for Weber-like interactions

The problem of two moving bodies interacting through a Weber-like force is presented. Trajectories are obtained analytically once relativistic and quantic considerations are neglected. The main results are that in the case of limited trajectories, in general, they are not closed and in the case of open trajectories, the deflection angles are not the same for similar particles with given energies and angular momenta but opposite potentials. This last feature suggests the possibility of a direct verification of the validity of Weber's law of force for electromagnetic interactions.Departamento de Eletrônica Quântica/Grupo de Plasmas (on leave of absence from Comisión Nacional de Energía Atómica, Argentina).     

多包层光纤中的等效阶跃光纤方法

本文将等效阶跃光纤方法（ＥＳＦＭ）推广到多包层光纤,当已知多包层坯棒折射率分布,则利用这种方法可严格计算出核坯棒的等效阶跃光纤的等效折射率差,从而可方便地估算出该坯棒拉制出光纤的各种传输参数。文中以计算双包层椭圆光纤的截止波长为例作为部分验证。理论计算和实际测量的结果表明,除个别情况外,精度达到５％。因而,在工程解决了为确定多包层光纤的截止波长（或拉丝半径）,而必须进行重复凑试拉丝和测量的困难,大     

Helium-like recombination pumped soft x-ray lasers

Experimental studies on recombination pumped soft x-ray lasers with helium-like ions are presented. The four-beam multi-TW neodymium-doped phosphate glass laser system at the Institute for Solid State Physics of the University of Tokyo was used in this work. From simultaneous time- and space-resolved spectra of the resonance lines of helium-like aluminium ions, population inversions between the n=3 and 2 levels were observed. Details on the first observation of amplification in a recombination-pumped helium-like soft x-ray laser, exhibiting a time-resolved small-signal gain of 3.3±0.5 cm^-1 for the 3 ¹D-2 ¹P transition of helium-like nitrogen, are also given.     

Two-body methods for three-body problems

The “Equivalent two-body method” first introduced by Wigner for deriving triton wave functions is shown to be obtainable directly from the variation principle for the energy. It is extended to cover the general case of noncentral, hard core interactions, for both the bound state and for scattering states, including the breakup reaction. Methods are given for systematically improving the wave function.     

Fast-Beam Laser Spectroscopy of Helium-like Silicon

We have characterized a system of maghemite, γ-Fe₂O₃, nanosized particles prepared by a microemulsion method using an ionic surfactant. The Mössbauer spectra from 21 to 298 K evolve from a totally magnetically split signal at low temperatures to a single superparamagnetic (sp) doublet at 298 K with a blocking temperature of ≈150 K. The real component of the AC susceptibility (5≤ν≤10⁴ Hz) displays a behavior characteristic of a system of interacting particles. A broad distribution of the particle sizes is revealed by the much higher average energy barrier obtained by AC susceptibility than Mössbauer.

     

Elastic scattering of electrons from Helium-like positive ions

The adiabatic exchange method is used to calculate the elastic scattering phase shifts for electrons scattered from the positive ions Li⁺ to Ne⁸⁺ of the helium isoelectronic sequence for energies from 0 to 144 rydberg. Exchange is treated exactly and accurate dipole polarization potentials are included. Comparisons with previous work are given where possible.     

Two-body correlations in nuclear systems

Correlations in the nuclear wave-function beyond the mean-field or Hartree-Fock approximation are very important to describe basic properties of nuclear structure. Various approaches to account for such correlations are described and compared to each other. This includes the holeline expansion, the coupled cluster or “exponential S” approach, the self-consistent evaluation of Greens functions, variational approaches using correlated basis functions and recent developments employing quantum Monte-Carlo techniques. Details of these correlations are explored and their sensitivity to the underlying nucleon-nucleon interaction. Special attention is paid to the attempts to investigate these correlations in exclusive nucleon knock-out experiments induced by electron scattering. Another important issue of nuclear structure physics is the role of relativistic effects as contained in phenomenological mean field models. The sensitivity of various nuclear structure observables on these relativistic features are investigated. The report includes the discussion of nuclear matter as well as finite nuclei.     

Two-body and three-body halo nuclei

We have extracted the nuclear asymptotic normalization coefficients (ANC) for the virtual transitions B→A+N via some transfer reactions and the radioactive nuclear beam experiments. With these coefficients, root-mean-square (rms) radii for the valence particle in some possible halo nuclei have been calculated. The values of rms radii extracted with ANC approach are nearly model-independent, hence are a good quantity for the investigation of nuclear halo. In addition, we have also calculated the rms radii for the two valence neutrons in some three-body systems in terms of the relationship between the radii of valence particle, core nucleus and nuclear matter. With two conditions for nuclear halo formation, we have examined these extracted rms radii. The results show that 11Be(1/2+, g.s), 12B(1-, 2.621 MeV), 13C(1/2+, 3.089 MeV), 14C(0-, 6.903 MeV), 14C(1-, 6.094 MeV), 15C(1/2+, g.s) and 19C(1/2+, g.s) with the valence particle in the 2s ground or excited state are the neutron halo nuclei, whereas 17F(1/2+, 0.495 MeV) and 21Na(1/2+, 2.423 MeV) are the proton halo nuclei in the excited state. For three-body systems, except the well-established two-neutron halo nuclei 6He and 11Li, 14Be and 17B might be the two-neutron halo nuclei as well.     

Two-body density matrix for closed s-d shell nuclei

The two-body density matrix for ⁴He,¹⁶O and ⁴⁰Ca within the Low-order approximation of the Jastrow correlation method is considered. Closed analytical expressions for the two-body density matrix, the center of mass and relative local densities and momentum distributions are presented. The effects of the short-range correlations on the two-body nuclear characteristics are investigated. Received: 11 September 1999 / Revised version: 20 December 1999