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.
Received: 23 June 2007
Revised: 21 April 2008
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), and the Foundation of the Education
Committee of Hunan
Province of China.
Cite this article:
Zhao Yun-Hui(赵云辉) and Zhao Cheng-Lin(赵乘麟) High-order perturbed corrections with scaling transformation 2008 Chin. Phys. B 17 2783
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