中国物理B ›› 2008, Vol. 17 ›› Issue (5): 1720-1728.doi: 10.1088/1674-1056/17/5/031

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

海文华1, 赵云辉2, 赵乘麟3, 罗小兵4   

  1. (1)Department of Physics, Hunan Normal University, Changsha 410081, China; (2)Department of Physics, Hunan Normal University, Changsha 410081, China;Department of Physics, Shaoyang University, Shaoyang 422000, China; (3)Department of Physics, Shaoyang University, Shaoyang 422000, China; (4)Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2007-07-20 修回日期:2007-11-12 出版日期:2008-05-20 发布日期:2008-05-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10575034), and the Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics of China (Grant No T152504).

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

Zhao Yun-Hui(赵云辉)a)b), Hai Wen-Hua(海文华)a)†, Zhao Cheng-Lin(赵乘麟)b), and Luo Xiao-Bing(罗小兵)c)   

  1. a Department of Physics, Hunan Normal University, Changsha 410081, China; b Department of Physics, Shaoyang University, Shaoyang 422000, China; c Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2007-07-20 Revised:2007-11-12 Online:2008-05-20 Published:2008-05-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10575034), and the Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics of China (Grant No T152504).

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摘要： Applying the improved Rayleigh--Schr?dinger 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.

关键词: helium-like ion, perturbation correction, boundedness, convergence

Abstract: Applying the improved Rayleigh--Schrödinger 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.

Key words: helium-like ion, perturbation correction, boundedness, convergence

中图分类号:  (Electron correlation calculations for atoms and ions: ground state)

  • 31.15.ve
31.15.xp (Perturbation theory)