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Benchmark Calculation of Radial Expectation Value \(\varvec{\langle r^{-2} \rangle }\) for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillators

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An Erratum to this article was published on 31 August 2017

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Abstract

Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of \(\langle r^{-2} \rangle \) which is of practical importance in many applications has significant discrepancies among calculations by different methods. In this work we employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for \(\langle r^{n} \rangle \) was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies.

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  • 31 August 2017

    An erratum to this article has been published.

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Author information

Authors and Affiliations

  1. College of Physics, Jilin University, Changchun, 130012, People’s Republic of China

    Rong Mei Yu, Li Rong Zan & Li Guang Jiao

  2. College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang, 473061, People’s Republic of China

    Rong Mei Yu

  3. Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei, 106, Taiwan, Republic of China

    Yew Kam Ho

Authors
  1. Rong Mei Yu
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  2. Li Rong Zan
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  3. Li Guang Jiao
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  4. Yew Kam Ho
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Corresponding author

Correspondence to Li Guang Jiao.

Additional information

The original version of this article was revised: The table head of Table 6 was incorrectly published in the original article and the same is corrected here.

An erratum to this article is available at https://doi.org/10.1007/s00601-017-1316-0.

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Yu, R.M., Zan, L.R., Jiao, L.G. et al. Benchmark Calculation of Radial Expectation Value \(\varvec{\langle r^{-2} \rangle }\) for Confined Hydrogen-Like Atoms and Isotropic Harmonic Oscillators. Few-Body Syst 58, 152 (2017). https://doi.org/10.1007/s00601-017-1314-2

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