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Effect of nuclear motion on the critical nuclear charge for two-electron atoms

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posted on 2023-06-09, 01:34 authored by Andrew W King, Luke C Rhodes, Charles A Readman, Hazel CoxHazel Cox
A variational method for calculating the critical nuclear charge, Zc, required for the binding of a nucleus to two electrons is reported. The method is very effective and performs well compared to the traditional variational principle for calculating energy. The critical nuclear charge, which corresponds to the minimum charge required for the atomic system to have at least one bound state, has been calculated for helium-like systems both with infinite and finite nuclear masses. The value of $Z_C=$ 0.911 028 2(3) is in very good agreement with recent values in the literature for two-electron atoms with an infinite nuclear mass. When nuclear motion is considered, the value for Zc varies from 0.911 030 3(2) for that with a nuclear mass of Ne (the largest heliogenic system considered) to 0.921 802 4(4) for a system with the nuclear mass of a positron. In all cases the energy varies smoothly as $Z \rightarrow 0$. It is found that for the finite nuclear mass case, in agreement with previous work for the fixed nucleus mass system, the outer electron remains localised near the nucleus at Z = Zc. Additionally, the electron probability distribution is calculated to determine the behaviour of the electrons at low Z.

History

Publication status

  • Published

File Version

  • Published version

Journal

Physical Review A

ISSN

1050-2947

Publisher

American Physical Society

Issue

4

Volume

91

Article number

a042512

Department affiliated with

  • Chemistry Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-06-07

First Open Access (FOA) Date

2016-06-07

First Compliant Deposit (FCD) Date

2016-06-07

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