Fine structure of the beryllium P3 states calculated with all-electron explicitly correlated Gaussian functions

Abstract

The recently presented general algorithm for calculating an atomic fine structure [K\ifmmode \mbox{\k{e}}\else \k{e}\fi{}dziorski et al., Chem. Phys. Lett. 751, 137476 (2020)] is employed to study the fine splitting of the lowest eight $^{3}P$ states of beryllium, i.e., the $1{s}^{2}\phantom{\rule{0.28em}{0ex}}2s\phantom{\rule{0.28em}{0ex}}np$, $n=2,\ensuremath{\cdots},9$, $^{3}P$ states. All-electron explicitly correlated Gaussian functions and a finite-nuclear-mass variational method are used in the calculations. The energies of the states are augmented with the leading ${\ensuremath{\alpha}}^{2}$ relativistic and ${\ensuremath{\alpha}}^{3}$ (and approximate ${\ensuremath{\alpha}}^{4}$) QED corrections ($\ensuremath{\alpha}=\frac{1}{c}$ is the fine-structure constant, and $c$ is the speed of light in atomic units). The calculated results are compared with the available experimental data.