${\cal{P,T}}$-Violating and Magnetic Hyperfine Interactions in Atomic Thallium

We present state-of-the-art configuration interaction and coupled cluster calculations of the electron electric dipole moment, the nucleon-electron scalar-pseudoscalar, and the magnetic hyperfine interaction constants ($\alpha_{d_e}, \alpha_{C_S}, A_{||}$, respectively) for the thallium atomic ground state $^2P_{1/2}$. Our present best values are $\alpha_{d_e} = -559 \pm 28$, $\alpha_{C_S} = 6.77 \pm 0.34$ $[10^{-18} e$ cm$]$, and $A_{||} = 21172 \pm 1059$ [MHz]. These findings lead to a significant reduction of the theoretical uncertainties for ${\cal{P,T}}$-odd interaction constants but not to stronger constraints on the electron electric dipole moment, $d_e$, or the nucleon-electron scalar-pseudoscalar coupling constant, $C_S$