Benchmark calculations of the 3 D Rydberg spectrum of beryllium

Abstract

High-accuracy calculations are performed for the four lowest 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 Be. The nonrelativistic wave functions of the considered states of 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 Be ground state. A comparison with high-quality experimental results shows agreement to within about 0.6 cm.