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

Energies of $6s^{2}n{p}_j$ $(n=6–9)$, $6s^{2}n{s}_{1∕2}$ $(n=7–9)$, $6s^{2}n{d}_j$ $(n=6–8)$, and $6s^{2}n{f}_{5∕2}$ $(n=5–6)$ states in $\mathrm{Tl}\mathrm{I}$ and $\mathrm{Pb}\mathrm{II}$ are obtained using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 72 possible $6s^{2}n{l}_j\text{−}6s^2{n}^{\prime }{l}_{j^{\prime }}^{\prime }$ electric-dipole transitions. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to obtain $6s^{2}n{p}_{3∕2}\text{−}6s^{2}m{p}_{1∕2}$ $(n,m=6,7)$ transition rates. Hyperfine constants $A$ are evaluated for $6s^{2}n{p}_j$ $(n=6–9)$, $6s^{2}n{s}_{1∕2}$ $(n=7–9)$, and $6s^{2}n{d}_j$ $(n=6–8)$ states in ${}^{205}\mathrm{Tl}$. 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.