Singlet and triplet bound state spectra in the four-electron Be-like atomic systems

A large number of bound singlet and triplet states in the four-electron Be-atom and Be-like ions B$^+$, C$^{2+}$, F$^{5+}$ and Mg$^{8+}$ are determined to milli-Hartree numerical accuracy ($1\cdot 10^{-3}$ a.u.). These states include the bound singlet and triplet $S$-, $P$-, $D$-, $F$-, $G$-, $H$-, $I$- and $K$-states. Based on computational results we analyze the singlet and triplet series of the Be atom bound state spectrum and some four-electron ions: B$^+$, C$^{2+}$, F$^{5+}$ and Mg$^{8+}$ (Be-like ions). The analogous study of the Be atom triplet states was the topic of our earlier study (A.M. Frolov and M.B. Ruiz, CPL 595-596, 197 (2014)). The computational data allowed us to draw the spectral diagram of the bound state spectrum of the Be-atom and other four-electron ions mentioned above. The Be-atom spectrum contains the two optical series of bound states: singlets and triplets.