Excitation energies, hyperfine constants, E1, E2, M1 transition rates, and lifetimes of $6s^2nl$ states in Tl~I and Pb~II

Energies of $6s^2np_j$ ($n$ = 6--9), $6s^2ns_{1/2}$ ($n$ = 7-- 9), $6s^2nd_j$ ($n$ = 6--8), and $6s^2nf_{5/2}$ ($n$ = 5--6) states in Tl~I and Pb~II are obtained using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 72 possible $6s^2nl_j-6s^2n'l'_{j'}$ electric-dipole transitions. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to obtain $6s^2np_{3/2} - 6s^2mp_{1/2}$ ($n,m=6,7$) transition rates. Hyperfine constants $A$ are evaluated for $6s^2np_j$ ($n$ = 6--9), $6s^2ns_{1/2}$ ($n$ = 7--9), and $6s^2nd_j$ ($n$ = 6--8) states in $^{205}$Tl. First-, second-, third-, and all-order corrections to the energies and matrix elements and first- and second-order Breit corrections to energies are calculated. In our implementation of the all-order method, single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. These calculations provide a theoretical benchmark for comparison with experiment and theory. Work was supported in part by National Science Foundation Grant No.\ PHY-01-39928 and DOE/NNSA under UNR grant DE-FC52- 01NV14050.