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Accuracy study for excited atoms (ions):A new variational method

Xiong Zhuang Wang Zhen-Xin Naoum C. Bacalis

Accuracy study for excited atoms (ions):A new variational method

Xiong Zhuang, Wang Zhen-Xin, Naoum C. Bacalis
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Publishing process
  • Received Date:  01 November 2013
  • Accepted Date:  22 November 2013
  • Published Online:  05 March 2014

Accuracy study for excited atoms (ions):A new variational method

  • 1. Space Science and Technology Research Institute, Southeast University, Nanjing 210096, China;
  • 2. Key Laboratory of Energy Thermal Conversion and Control, Ministry of Education, Southeast University, Nanjing 210096, China;
  • 3. Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vasileos Constantinou 48, GR-116 35 Athens, Greece
Fund Project:  Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91334205), and the Joint Funds of the National Natural Science Foundation of China (Grant No. 11178008).

Abstract: For the computation of excited states, the traditional solutions of the Schredinger equation, using higher roots of a secular equation in a finite N-dimensional function space, by the Hylleraas-Undheim and MacDonald (HUM) theorem, we found that it has several restrictions which render it of lower quality, relative to the lowest root if the latter is good enough. In order to avoid the variational restrictions, based on HUM, we propose a new variational function and prove that the trial wave function has a local minimum in the eigenstates, which allows to approach eigenstates unlimitedly by variation. In this paper, under the configuration interaction (CI), we write a set of calculation programs by using generalized laguerre type orbitals (GLTO) to get the approximate wave function of different states, which is base on the HUM or the new variational function. By using the above program we get the approximate wave function for 1S (e), 1P (o) state of helium atoms (He) through the different theorems, the energy value and radial expectation value of related states. By comparing with the best results in the literature, the theoretical calculations show the HUM's defects and the new variational function's superiority, and we further give the direction of improving the accuracy of excited states.

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