Energy levels and radiative transitions of the core-excited high-spin states in boron atom (ion)

Abstract

Energy levels of the core-excited high-spin Rydberg states (4,5,6L, L = S, P) in boron atom (ion) are calculated by the Rayleigh-Ritz variation method with using large-scale multi-configuration wave functions. The important orbital-spin angular momentum partial waves are selected based on the rule of configuration interaction. The computational convergence is discussed by the example of the contribution from each partial wave in the non-relativistic energy calculations of the high-spin state 1s2s2p2 5Pe in B+ ion. To saturate the wave functional space and improve the non-relativistic energy, the restricted variational method is used to calculate the restricted variational energy. Furthermore, the mass polarization effect and relativistic energy correction are included by using a first-order perturbation theory. The quantum electrodynamic effects and higher-order relativistic contributions to the energy levels are also calculated by the screened hydrogenic formula. Then, the accurate relativistic energy levels of these high-spin states of B atom (ion) are obtained by adding the non-relativistic energy and all corrections. The fine structure splitting of these high-spin states is also calculated by the Breit-Pauli operators in the first-order perturbation theory. Compared with other theoretical results, our calculation results are in good accordance with the experimental data. The absorption oscillator strengths, emission oscillator strengths, absorption rates, emission rates, and transition wavelengths of the electric-dipole transitions between these high-spin states of B atom (ions) are systematically calculated by using the optimized wave functions. The oscillator strengths and transition rates are obtained in both the length and velocity gauges. By comparing the two gauge results of oscillator strength, we find that there is a good consistency between them when fl 0.3, and a reasonable consistency is obtained when fl 0.3. The accordance between the length and the velocity gauge results reflects that the calculated wave functions in this work are reasonably accurate. The calculated transition data are also compared with the corresponding experimental and other theoretical data. Good agreement is obtained except the wavelengths for two transitions: 1s2p4p 4Se1s2p3d 4P and 1s2p4d 4P1s2p3p 4Pe. The relative differences between our theoretical results and experimental data are 0.7% and 0.3%, respectively. They need to be verified by further theoretical and experimental studies. For some core-excited high-spin states, the related energy levels and transition data are reported for the first time. Our calculation results will provide valuable data for calculating the spectral lines in the relevant experiments.