Abstract

Atomic systems placed in external potentials manifest various characteristic features which provide useful knowledge about the surroundings. We have studied the structural properties of the ground state of different two-electron systems under isotropic harmonic confinement (IHC). In particular, we have considered negative hydrogen ion, neutral helium atom and positive singly ionized lithium ion to cover all types of charge states. In addition, we have also studied the system of two electrons inside IHC. The wave function is expanded in Hylleraas basis to incorporate the effect of electron correlation in an explicit manner and Ritz variational calculations are performed to obtain the energy eigenvalues and the relative wave functions. The energy levels become more positive with increasing strength of the confining potential. The results show that for ionic systems, the two-electron energy level crosses the respective one-electron threshold at a certain value of the potential beyond which the two-electron level becomes quasi-bound. In order to get deeper insight into such threshold ionization phenomenon, we have examined the contribution of the correlated energy \(E_\mathrm{corr}\) [sum of radial and angular correlation energy] and radial correlation energy \(E_\mathrm{rad.corr}\) to the total energy for different two-electron systems under IHC. The Hellmann–Feynman theorem and the virial theorem have been verified as a quantitative validation of the accuracy of our results. The one- and two-electron radial densities have also been analyzed to gain a physical insight into the structural changes of the two-electron systems under IHC. Moreover, the expectation values of different radial and angular variables are also reported which are important to estimate different geometrical and spectral properties.

Graphic abstract

中文翻译：

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各向同性谐波约束下双电子系统的结构修改

摘要

置于外部电位中的原子系统表现出各种特征，这些特征提供了有关周围环境的有用知识。我们研究了在各向同性谐波限制 (IHC) 下不同双电子系统的基态结构特性。特别是，我们考虑了负氢离子、中性氦原子和正单电离锂离子以涵盖所有类型的电荷状态。此外，我们还研究了 IHC 内部的两个电子系统。波函数以 Hylleraas 为基础展开，以明确的方式结合电子相关的影响，并执行 Ritz 变分计算以获得能量特征值和相对波函数。随着限制势的强度增加，能级变得更加正。结果表明，对于离子系统，两电子能级在一定的电位值时跨越各自的单电子阈值，超过该值，两电子能级变为准束缚态。为了更深入地了解这种阈值电离现象，我们检查了相关能量的贡献\(E_\mathrm{corr}\) [径向和角相关能之和] 和径向相关能\(E_\mathrm{rad.corr}\)与 IHC 下不同双电子系统的总能量。Hellmann-Feynman 定理和维里定理已被验证为对我们结果准确性的定量验证。还分析了单电子和双电子径向密度，以获得对 IHC 下双电子系统结构变化的物理洞察。此外，还报告了不同径向和角度变量的期望值，这对于估计不同的几何和光谱特性很重要。

图形摘要