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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 o 5/2,3/2 → 4 S o 3/2 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(∞) = 0.363 ± 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 o 3/2,1/2 → 4 S o 3/2 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.

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An extended atomic data base with sufficiently high precision is required in astrophysics studies and the energy researches. For example, there are “infinite” energy levels in discrete energy region as well as overlapping resonances in autoionization region. We show in this paper the merits of our relativistic eigenchannel R-matrix method R-R-Eigen based on the analytical continuation properties of scattering matrices for the calculations of the energy levels, overlapping resonances and the related transitions. Using Ne+ as an illustration example, the scattering matrices of Ne+ in both discrete and continuum energy regions are calculated by our R-R-Eigen method directly. Based on our proposed projected high dimensional quantum-defect graph (symmetrized), one can readily determine the accuracies of the calculated scattering matrices using the experimental energy levels in a systematical way. The calculated resonant photoionization cross sections in the autoionization region are in excellent agreement with the benchmark high resolution experiments. With the scattering matrices checked/calibrated against spectroscopy data in both discrete and continuum energy regions, the relevant dynamical processes should be calculated with adequate accuracies. It should then satisfy the needs of the astrophysical and energy researches.

Low-energy electron-impact cross sections of helium among the ground and some low excited states are calculated using the R-matrix method. The convergences of the cross sections are checked systematically by using five sets of high-quality target states; i.e., including 5,11, 19,29, and 39 physical target states, respectively. Our calculated cross sections are in excellent agreement with the benchmark high-resolution experimental data. Compared with the recommended theoretical data, there is a deviation of about 6%, which suggests the recommended data may need a revision. Based on our calculation results, the influence of the Rydberg target states on the collision cross sections of the excited states is found to be similar to the case of the ground state; i.e., the amplitude of resonance structures will decrease with respect to the principal quantum number n of Rydberg target states. This result should be very useful for providing the cross-section data in the whole energy regions with high quality, which would be of great importance in related scientific fields.