Corrected fine-structure energy levels and oscillator strengths for Ne i–Si v in the neon sequence

The problem of calculating transition rates between atomic fine-structure levels is considered. Nonrelativistic configuration-interaction calculations of terms of interest are performed and the terms are then mixed by the relativistic couplings of the Breit-Pauli Hamiltonian. Frequently it turns out that the mixing components of the Breit-Pauli matrix are larger than the relative term energies. This leads to sensitivity of the level eigenvectors to small errors in the energies and thus to errors in the transition rates among the levels. A nonperturbative method for correcting the level vectors for cases involving any number of strongly mixed terms is developed. The method is based on solving the inverse eigenvalue problem for a matrix using the observed spectrum to correct the diagonal matrix elements of the Breit-Pauli matrix. It is applied in the present work to calculate level wave functions and transition rates for the 1$s^2$2$s^2$2$p^5$3s, 3p, and 3d levels of the Ne i–Si v ions of the neon isoelectronic sequence.