中国物理B ›› 2008, Vol. 17 ›› Issue (8): 2783-2789.doi: 10.1088/1674-1056/17/8/006

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High-order perturbed corrections with scaling transformation

赵乘麟1, 赵云辉2   

  1. (1)epartment of Physics, Shaoyang University, Shaoyang 422000, China; (2)epartment of Physics, Shaoyang University, Shaoyang 422000, China;Department of Physics, Hunan Normal University, Changsha 410081, China
  • 收稿日期:2007-06-23 修回日期:2008-04-21 出版日期:2008-08-20 发布日期:2008-08-20
  • 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), and the Foundation of the Education Committee of Hunan Province of China.

High-order perturbed corrections with scaling transformation

Zhao Yun-Hui(赵云辉)a)b)† and Zhao Cheng-Lin(赵乘麟)a)   

  1. a Department of Physics, Shaoyang University, Shaoyang 422000, China; b Department of Physics, Hunan Normal University, Changsha 410081, China
  • Received:2007-06-23 Revised:2008-04-21 Online:2008-08-20 Published:2008-08-20
  • 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), and the Foundation of the Education Committee of Hunan Province of China.

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摘要： The performance of the so-called superconvergent quantum perturbation theory (Wenhua Hai {\em et al} 2000 \emph{Phys. Rev.} A {\bf 61} 052105) is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation $r\rightarrow r/Z$ applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge $Z$ (in atomic units). Using the improved Rayleigh--Schr\"{o}dinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.

关键词: integral equation, scaling transformation, higher-order perturbation

Abstract: The performance of the so-called superconvergent quantum perturbation theory (Wenhua Hai et al 2000 Phys. Rev. A 61 052105) is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation $r\rightarrow r/Z$ applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge $Z$ (in atomic units). Using the improved Rayleigh--Schrödinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.

Key words: integral equation, scaling transformation, higher-order perturbation

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

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