The spectral decomposition of the helium atom two-electron configuration in terms of hydrogenic orbitals

DOI10.1088/0143-0807/34/1/111zbMATH Open1266.81152arXiv1211.2109OpenAlexW1964776761MaRDI QIDQ4928977

Joel Hutchinson, Marc Baker, F. Marsiglio

Publication date: 19 June 2013

Published in: European Journal of Physics (Search for Journal in Brave)

Abstract: The two electron configuration in the Helium atom is known to very high precision. Yet, we tend to refer to this configuration as a

1 s u p a r r o w 1 s d o w n a r r o w

singlet, where the designations refer to Hydrogen orbitals. The high precision calculations utilize basis sets that are suited for high accuracy and ease of calculation, but do not really aid in our understanding of the electron configuration in terms of product states of Hydrogen orbitals. Since undergraduate students are generally taught to think of Helium, and indeed, the rest of the periodic table, in terms of Hydrogenic orbitals, we present in this paper a detailed spectral decomposition of the two electron ground state for Helium in terms of these basis states. The

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singlet contributes less than 93% to the ground state configuration, with other contributions coming from both bound and continuum Hydrogenic states.

Full work available at URL: https://arxiv.org/abs/1211.2109

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Atomic physics (81V45)