Benchmark calculations of the ³D Rydberg spectrum of beryllium

Abstract

High-accuracy calculations are performed for the four lowest ${}^{3}D$ states of the beryllium atom. All-electron explicitly correlated Gaussian (ECG) functions are employed to expand the functions and the non-relativistic internal Hamiltonian used in the calculations, which is obtained by rigorously separating out the centre-of-mass motion from the laboratory-frame Hamiltonian, explicitly depends on the finite nuclear mass of ${}^9$Be. The nonrelativistic wave functions of the considered states of ${}^9$Be are generated variationally with the nonlinear parameters of the Gaussians optimised using a procedure that employs the energy gradient determined with respect to these parameters. The nonrelativistic wave functions are used to calculate the leading relativistic corrections employing the perturbation theory at the first-order level. Only corrections that do not produce fine/hyperfine splitting of the energy levels are considered. The corrections are added to the nonrelativistic energies and the results are used to calculate the so-called ‘centre of gravity’ transition energies with respect to the ${}^9$Be ${}^{1}S$ ground state. A comparison with high-quality experimental results shows agreement to within about 0.6 cm${}^{-1}$.

GRAPHICAL ABSTRACT

KEYWORDS:

• High-precision calculations for few-electron (or few-body) atomic systems
• relativistic corrections
• electron correlation calculations for atoms and ions: excited states
• variational techniques
• explicitly correlated method

Acknowledgments

We dedicate this work to the memory of Professor Lutosław Wolniewicz. Throughout many years, he had been very supportive and helpful in our work. On numerous occasions he had shared with us his unpublished results and offered useful comments concerning our research.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has also been supported by a grant from the National Science Foundation; grant no. 1856702. L. A. also acknowledges the support of the Centre for Advanced Study (CAS), the Norwegian Academy of Science and Letters, in Oslo, Norway, which funds and hosts our research project titled: Attosecond Quantum Dynamics Beyond the Born–Oppenheimer Approximation, during the 2021–22 academic year. The authors are grateful to the University of Arizona Research Computing for providing computational resources for this work.