Relativistic many-body calculations of the Stark-induced amplitude of the $6P_{1∕2}\text{−}7P_{1∕2}$ transition in thallium

Stark-induced amplitudes for the $6P_{1∕2}\text{−}7P_{1∕2}$ transition in $\mathrm{T}\mathrm{l}\mathrm{I}$ are calculated using the relativistic singles-doubles (SD) approximation in which single and double excitations of Dirac-Hartree-Fock levels are summed to all orders in perturbation theory. Our SD values ${\alpha }_S=368a_0^3$ and $\mid {\beta }_S\mid =298a_0^3$ are in good agreement with the measurements ${\alpha }_S=377\left(8\right)a_0^3$ and ${\beta }_S=313\left(8\right)a_0^3$ by D. DeMille, D. Budker, and E. D. Commins [Phys. Rev. A 50, 4657 (1994)]. Calculations of the Stark shifts in the $6P_{1∕2}\text{−}7P_{1∕2}$ and $6P_{1∕2}\text{−}7S_{1∕2}$ transitions are also carried out. The Stark shifts predicted by our calculations agree with the most accurate measured values within the experimental uncertainties for both transitions.