Coefficients of radial integral in the electrostatic interaction and their applications

We have derived the equations to calculate the electrostatic interaction energy and the coefficients of radial integrals between electrons ln or l1m and l′ of the atomic state |ln[S1L1]l1m[S2L2][ScLc]l′ SL >, where ln[S1L1], l1m[S2L2], and l′ are three open shells. The expressions have been checked against the formulas in the literature by reducing them to those for the case of atoms having two open shells. We demonstrate our formulas by evaluating the coefficients of the radial integrals in the interaction between the 2s or 2p4 and 3p electrons of the 2s2p4(2,4P)3p(3S,3P,3D) state of oxygen. Using these coefficients the wave functions and photoionization cross sections of oxygen 2s has been evaluated and compared with previous results. PACS Nos.: 31.15.Ne, 31.10.+z, 32.80.Fb

Transition rates in singly ionized titanium

Rates have been calculated for electric dipole transitions in Ti II between the fine structure levels of the terms 4p z 4Go, 4 Fo, 2Fo, 2Do, 4Do, and 2Go to the levels of the groundterm 4s a 4F and comparisons are made with the most recent available observations as well as with the calculations of Kurucz. These are the only other calculations available for this ion. To include certain configurations with more than two open shells, new approximations are necessitated by the complexity of the algebra. The approximations used are described and the results of calculations are given to demonstrate their effectiveness and accuracy. It will be shown that the CPU time reductions are very substantial, sufficient to make the inclusion of potentially important configurations feasible where it would not be so otherwise.The loss in accuracy in the situations examined is negligible. New results for transition rates that have not been measured are presented.PACS Nos.: 32.70.Cs, 32.70.Fw