Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the $6p$, $7s$, $7p$, $8s$, $8p$, and $6d$ states and the dynamic dipole polarizabilities of the $6p$ and $7s$ states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the $7s_{1/2}$, $7p_{1/2}$, $8p_{1/2}$, and $8p_{3/2}$ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the $6p_{1/2}$–$7s$ and $6p_{3/2}$–$7s$ transitions in the range of 488–1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the $7s_{1/2}$–$7p_{1/2}$ and $7s_{1/2}$–$7p_{3/2}$ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the $6p_{1/2}$–$7p_{1/2}$ transition, are also evaluated and compared with available theoretical and experimental values.

• Received 21 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.062511