Based on a set of “quasicomplete bases,” using the large-scale multiconfiguration Dirac-Fock (MCDF) method, we calculate the forbidden electric quadrupole ($E2$) and magnetic dipole ($M1$) transition rates of the transitions ${}^2{D}_{5/2,3/2}^o\to {}^4{S}_{3/2}^o$ of the O ii ground state considering the quantum electrodynamics (QED) corrections. Our calculations demonstrate that the Breit interactions are most important among all the QED corrections. The calculated $E2$ and $M1$ transition rates converge in a systematical and uniform manner with the extending orbital basis and the calculation uncertainty of 2.5$\%$ is achieved by considering the valence- and core-excitation correlations totally. With the converged transition rates, a value of the intensity ratio between the two transitions in high-electron-density limit in planetary nebulas is given, that is, $r\left(\infty \right)=0.363\pm 0.009$, which is within the overlap of the different observations and with the least uncertainty up to now. In addition, the $E2$ and $M1$ transition rates of two transitions ${}^2{P}_{3/2,1/2}^o\to {}^4{S}_{3/2}^o$ of O ii ground state and the ratio between the two transition rates in high-electron-density limit are calculated and compared with the previous results.

• Received 23 February 2012

DOI:https://doi.org/10.1103/PhysRevA.85.062506