The effects of the finite nuclear mass are investigated in high-accuracy calculations of the electronic spectra corresponding to the lowest ten ${}^{1}D$ states of beryllium $\left({}^9\mathrm{Be}\right)$. In the first step of the calculations, the nonrelativistic energies of the considered states are calculated using the standard variational approach with the Hamiltonian obtained by rigorously separating out the kinetic energy of the center-of-mass motion (CMM) from the laboratory-frame Hamiltonian. Large basis sets of up to $16200$ well-optimized all-particle explicitly correlated Gaussian functions are used to expand the nonrelativistic wave functions in the calculations. The wave functions are subsequently used to calculate the leading relativistic corrections using first order of the standard perturbation theory and the Breit-Pauli Hamiltonian (BPH). This Hamiltonian is derived by transforming the laboratory-frame BPH to the internal-coordinate system used to separate out the CMM in the nonrelativistic Hamiltonian. The results indicate that it is mandatory to include the finite-mass effects in the calculations to obtain the transition energies between ${}^{1}D$ states of beryllium with accuracy of below 1 ${\mathrm{cm}}^{-1}$. The major part of the effects comes from the nonrelativistic energy obtained within the finite-nuclear-mass approach.

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• Atomic, optical & lattice clocks
• Electronic excitation & ionization
• Electronic structure
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions
• Atoms
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• Perturbative methods
• Schroedinger equation
• Spectroscopy