Theory of Atomic Structure Including Electron Correlation. IV. Method for Forbidden-Transition Probabilities with Results for [O I], [O II], [O III], [N I], [N II], and [C I].

Electric quadrupole transition probabilities for the oxygen atom auroral line ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ ($\lambda =5577\mathrm{}$ λ) and the ${}_{}{}^2{}_{}{}^{}P-{}_{}{}^2{}_{}{}^{}D$,${}_{}{}^1{}_{}{}^{}S-{}_{}{}^1{}_{}{}^{}D$ lines in CI, NI, NII, OII, and OIII, which are of atmospheric and astrophysical interest, are calculated. The nonclosed-shell many-electron theory (NCMET) of atomic structure developed by Sinanoğlu and co-workers, which treats electron correlation accurately in both ground and excited states, predicts novel correlation effects which are included in the wave functions used to calculate the transition probabilities. These are many-body calculations on "forbidden" lines, the first of their kind. We explicitly examine the effect of electron correlation on the quadrupole line strengths. It is found that the Hartree-Fock values are reduced by 13-17% when all the important correlation effects are included in the wave functions. In view of the accuracy of the wave functions and of the method of calculation, the results obtained are expected to be accurate with a less than 5% uncertainty. For the much discussed O I ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ (5577 Å) transition we find $A_Q=1.183\mathrm{}$ ${\sec }^{-1\mathrm{}}$. Comparison is made with previous experimental and theoretical work.