Boundedness and convergence of perturbed corrections for helium-like ions in ground states

Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.

Non-sequential double ionization of helium-like atom

In this paper, author investigated the effect of the Coulomb potential of the core of atomic helium on the rescattering processes. Through the calculation author concluded that the Coulomb potential effect may not play an important role in causing the discrepancy between the experimental data and theoretical results of Kuchievs model, and the NS ionization is dependent on the frequency of the laser field. Furthermore, it is concluded that the strength of the laser field and the charge number of the core affect the frequency regime corresponding to the peak value of the NS ionization rate.

Nonvariational calculation of eigenenergies for ~3S states of helium-like systems

COMPARED with the popular hyperspherical coordinate scheme, the HHGLF method proposed by Deng and others has the advantages of rapid hyperradial convergence, analytical solution and huge basis set calculation. However, the problem of slow convergence in the hyperangle part still exists as other hyperspherical harmonics (HH) methods do. To solve the prob-

Variational Calculations for (ns2) 1Se, (np2) 1De and (nd2) 1Ge Resonance States for He Isoelectronic Sequences below the n = 2, 3 and 4 Hydrogenic Thresholds

This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed into three terms allowing to separate the kinetic energy, the electrons-nucleus interaction energy and the electron-electron interaction energy of the (2s2, 3s2 and 4s2) 1Se, (2p2, 3p2 and 4p2) 1De and (3d2 and 4d2) 1Ge resonance singlet states of the helium isoelectronic sequences. The states have been defined by using special forms of the Hylleraas type wave functions. The calculations have been carried out in the framework of the variational method using configuration interaction basis states with a real Hamiltonian. The agreement of the energy value of other states between the present theoretical values available in the literature is excellent. But as for the comparison of the kinetic energies, the electrons-nucleus energies interaction and the electron-electron interaction energies, we note a slight difference with the theoretical values common in literature.

基于参数微扰法精确计算类氦离子N^(5+)和O^(6+)的基态能量

在微扰论的基础上引入屏蔽参数σ,建立含有屏蔽参数σ的类氦离子N^(5+)和O^(6+)的哈密顿方程.以有效核电荷数为z*=z-σ的类氢原子基态1s和激发态ns(n=1,2,3,…)组合的双电子波函数,作为类氦离子N^(5+)和O^(6+)的基态近似波函数.根据类氦离子N^(5+)和O^(6+)的基态能量的实验值,通过求极值的方法确定合适的屏蔽参数σ,由此计算类氦离子N^(5+)和O^(6+)的基态能量.结果表明,应用参数微扰法计算类氦离子N^(5+)和O^(6+)基态能量的理论值与实验值的误差为ΔE≈10-4~10-5 a.u..

参数微扰法计算类氦原子基态能量

考虑类氦原子中电子对核的屏蔽效应,建立含有屏蔽效应参数的哈密顿算符,并作变换使得哈密顿算符中微扰项势能算符满足微扰法条件.通过参数微扰法计算类氦原子二级近似基态能量和有效核电荷,结果表明参数微扰法得到的类氦原子基态能量非常接近实验值.参数微扰法为研究多电子原子能级和原子能级精细结构提供了一种新的方法.

氦原子(n_1sn_2p)组态能级的相对论修正

本文采用拉卡基函数并借助不可约张量理论,导出氦原子(n1sn2p)组态的各种相对论效应的理论计算式,在这一过程中,完成了所有的角向积分和自旋求和计算,其结果用径向矩阵元形式来表示。

氦原子低激发态能量的变分计算

给出了一种用变分法计算氦原子低激发态 (电子组态为 1s2s,1s2p等 )能量的具体方法 ,计算过程中解决了激发态波函数与基态波函数的正交性 ,计算结果与实验值也相当接近.

奇性波函数及其在原子能量计算中的应用

讨论了波函数在原点的奇异性问题及其与势场的关系，指出在保证径向波函数平方可积，即积分∫｜Ｒｎｌ（ｒ）｜２ｒ２ｄｒ有限的前提下，出现Ｒｎｌ（０）＝∞的奇异性，在物理上是可以接受的。然后，将具有这种奇异性的波函数应用于类氦原子基态能量的计算，并通过对结果的分析指出，采用形如Ｒ１０（ｒ）＝Ｃｒｓ０ｅ－ｚ－β１＋ｓ０ｒ（０＞ｓ０＞－１／２）的奇性径向波函数，相当于将两电子间除屏蔽效应之外的关联作用，等效为中心场－｜γ｜／ｒ２的作用，从而使基态能量的计算结果比ｓ０＝０时的结果有所改进。

研究类氦原子基态能量的参数微扰法

考虑了类氦原子中电子对核的屏蔽效应,建立了含有屏蔽效应参数的哈密顿算符,并应用微扰理论研究了类氦原子基态能量.通过参数微扰法计算的类氦原子一级近似基态能量与变分法得到的能量完全相同,比无参数微扰法计算的能量更加接近实验值.参数微扰法为研究多电子原子能级和原子能级精细结构提供了一种新的方法.

He离子辐照金属钨引入缺陷的微结构研究

采用能量为100keV的He离子在室温下辐照金属钨,辐照注量范围为1.4×1017-3.5×1017/cm2,辐照后对样品进行了1100℃退火处理.利用X射线衍射、慢正电子多普勒展宽和扫描电镜技术研究了钨中He离子辐照引入的缺陷和注量之间的关系.研究结果表明辐照并退火后材料内部晶面间距增大,空位型缺陷浓度或尺寸随辐照注量的升高而增大,而高注量辐照的样品表面晶粒间连接疏松并存在孔隙,钨表层可能生成了大尺寸的He空位复合体或He泡.

类氦原子体系基态能量的双参数变分计算

采用包含了两电子之间关联坐标的双参数试验波函数,应用变分法计算了氦原子和类氦离子的基态能量,数值计算的结果与实验值相当吻合.计算表明,在变分波函数中显式地引入关联坐标可以有效地提高计算结果的准确度,同时电子之间的关联效应对氦原子基态能量的影响最为明显.

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.

基于相对论量子亏损理论的类氦离子电离能规律

依据离子能级的相对论量子亏损理论,给出了类氦离子电离能的一种表达式。根据原子序数6至15的类氦离子电离能的实验数据,对其电离能表达式中的量子数亏损及屏蔽电荷数进行了拟合,得到类氦离子电离能与原子序数的关系式,依据该关系式计算的电离能理论值与已有实验值符合得很好。推算了原子序数16至39的类氦离子的电离能,并与其他方法的计算结果进行了对比分析。

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 %。

Variational Calculation of the Doubly-Excited States Nsnp of He-Like Ions via the Modified Atomic Orbitals Theory

In this paper, we have declined the formalism of the method of the Modified Atomic Orbital Theory (MAOT) applied to the calculations of energies of doubly excited states 2snp, 3snp, and 4snp Helium-like systems. Then we also applied the variational procedure of the Modified Atomic Orbital Theory to the computations of total energies, excitation energies of doubly-excited states 2snp, 3snp, 4snp types of Helium-like systems. The results obtained in this work are in good agreement with the experimental and theoretical values available.

Modified atomic orbital theory applied to the calculation of high-lying ₂(K,T)_n^±1,3P°rydberg series of he-like ions

The 2(1,0)n-1P°, 2(1,0)n +3P°, 2(0,1)n+1P°, and 2(0,1)n-3P° intershell Rydberg series of the helium-like ions are investigated in the framework of the modified Atomic Orbital Theory (MAOT). High-lying energy resonances of He and excitation energy of the he- lium-like Li+ up to n = 10 are tabulated. In addition, total energy positions for low-lying states (n1,3P° autoionizing states of two-electron systems.

Energy Positions of the ^1,3D^eRydberg Series of the He-Like Ions Up to the <i>N</i>= 9 Threshold

The doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the β-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (N = 2 - 9) in He-like ions up to Z = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.

Calculations Energy of the (<i>nl</i>²) ¹<i>L^π</i>Doubly Excited States of Two-Electron Systems via the Screening Constant by Unit Nuclear Charge Formalism

In this work, the total energies of doubly excited states (ns2) 1Se, (np2) 1De, (nd2) 1Ge, (nf2) 1Ie, (ng2) 1Ke, and (nh2) 1Me of the helium isoelectronic sequence with Z ≤ 10 are calculated in the framework of the variational method of the Screening Constant by Unit Nuclear Charge (SCUNC). These calculations are performed using a new wavefunction correlated to Hylleraas-type. The possibility of using the SCUNC method in the investigation of high-lying Doubly Excited States(DES) in two-electron systems is demonstrated in the present work in the case of the (nl2) 1Lπ doubly excited states, where accurate total energies are tabulated up to n = 20. All the results obtained in this paper are in agreement with the values of the available literature and may be useful for future experimental and theoretical studies on the doubly excited (nl2) 1Lπ states of two-electron systems.

Classical Dynamics of Muonic-Electronic Helium and Heliumlike Ions: The Allowance for the Eccentricity of the Muon and Nucleus Orbits

In the previous paper by one of us (hereafter paper I), the author considered Rydberg states of the muonic-electronic helium atom or helium-like ion and used the fact that the muon motion occurs much more rapidly than the electron motion. Assuming that the muon and nucleus orbits are circular, he applied the analytical method based on separating rapid and slow subsystems. He showed that the electron moves in an effective potential that is mathematically equivalent to the potential of a satellite orbiting an oblate planet like the Earth. He also showed that the “unperturbed” elliptical orbit of the electron engages in two precessions simultaneously: the precession of the electron orbit in the plane of the orbit and the precession of the orbital plane of the electron around the axis perpendicular to the plane of the muon and nuclear orbits. The problem remained whether or not the allowance for the ellipticity of the orbit could significantly change the results. In the present paper, we address this problem: we study how the allowance for a relatively low eccentricity ε of the muon and nucleus orbits affects the motion of the electron. We derive an additional, ε-dependent term in the effective potential for the motion of the electron. We show analytically that in the particular case of the planar geometry (where the electron orbit is in the plane of the muon and nucleus orbits), it leads to an additional contribution to the frequency of the precession of the electron orbit. We demonstrate that this additional, ε-depen- dent contribution to the precession frequency of the electron orbit can reach the same order of magnitude as the primary, ε-independent contribution to the precession frequency. Therefore, the results of our paper seem to be important not only qualitatively, but also quantitatively.