The saddle-point variational method and restricted variational method are used to calculate energies of doublyexcited singlet states 1𝑠 2 3𝑙𝑛𝑙 ′ (𝑛 =3-5) 1 𝐷 𝑒 in Be-like O 4+ ions, including the mass polarization and relativistic corrections. The saddle-point complex-rotation method is used to compute the Auger widths and Auger transition rates. These results are compared with other theoretical and experimental data in the literature.

The Rayleigh-Ritz variational method is used with a multiconfiguration-interaction function to study the energies of singly excited and doubly excited Rydberg series in helium atom, including the mass polarization and relativistic corrections. The oscillator strengths, the transition rates, and the wavelengths are also calculated. The results are compared with other theoretical and experimental data in the literatures.