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)
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
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.
Received: 20 July 2007
Revised: 12 November 2007
Accepted manuscript online:
PACS:
31.15.ve
(Electron correlation calculations for atoms and ions: ground state)
Fund: 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).
Cite this article:
Zhao Yun-Hui(赵云辉), Hai Wen-Hua(海文华), Zhao Cheng-Lin(赵乘麟), and Luo Xiao-Bing(罗小兵) Boundedness and convergence of perturbed corrections for helium-like ions in ground states 2008 Chin. Phys. B 17 1720
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