Coupling parameters and transition probabilities in P electron configurations.

Abstract

Transition probabilities for intermediate coupling cases have been calculated for atoms and ions from carbon to nickel whose ground configurations are p2 and p4. The work on p, p1, and p5 is in progress. The transitions involved are between levels of the same configuration and, hence, they are electric quadrupole and magnetic dipole transitions. Most of the lines observed in the solar corona and in gaseous nebulae are included in this work. The departures from (S,L) coupling are expressed in terms of the spin-orbit integral ~, and the electrostatic integral F2; ~ and F2 are calculated by equating the theoretical expressions for the energy levels with their observed values. The main feature of this work is the inclusion of the effects of mutual magnetic interactions. These interactions enter into the calculations of transition probabilities not only in so far as they introduce new terms in the theoretical expressions, but also indirectly through the revised calculations of ~. Aller, Ufford and Van Vleck1 have calculated transitions probabilities for OIl 2p1 4S-2D multiplet, taking only the direct effects of mutual magnetic interactions into account. The matrices of mutual magnetic interactions for p2 have been given by H. H. Marvin.2 The diagonal elements for p4 are found to be: 3P2: -17M0, 1P1: 25M0, 1P0: 10M0, 1D2,580 : 0, where M0 is the mutual magnetic interaction integral M0 = e2(h/2ir)2 f r>~1Rap2 (r i)Rnp2 (r1)dridr2. 40~2c2 For configurations with n = 2, it is shown that the effect of mutual magnetic interactions is much larger (10 to 15 times) than the second order effect of spin-orbit interaction. This is an interesting result since it shows that the mutual magnetic interactions have large effects on the patterns of energy levels. For configurations with n = 3, the effect of these interactions is much smaller but still not negligible. Calculations of ~ taking into account the effect of the mutual magnetic interactions were made and the results were found to differ by about 5 to 10 per cent from those of Robinson and Shortley.1 F2 is calculated from the term difference 1D-1P alone. This choice is made because 1D and 1P terms are displaced in a similar manner due to configuration interacti~n; while the ~8 term is displaced much more. Since for p4 configuration Robinso~ and Shortley have used the term difference `S-1D, their values of F2 differ from our values by more than 20 per cent. The direct effect of mutual magnetic interactions on transition probabilities is found to be quite large for p1, but is negligible for p2 and p4 configurations. I.Ap. J. 109, 42, 1949. 2.Phys. Rev. 71, 102, 1947. 3.Phys. Rev., 52, 713, 1937. Harvard College Observatory, Canipridge, Mass.