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A Reappraisal of the Electric Dipole Moment Enhancement Factor for Thallium

The electric dipole moment (EDM) enhancement factor of atomic Tl is of considerable interest as it has been used in determining the most accurate intrinsic electron EDM limit to date. However, the value of this quantity varies from $-179$ to $-1041$ in different approximations. In view of the large uncertainties associated with many of these calculations, we have employed the relativistic coupled-cluster theory with single and double excitations and a subset of leading triple excitations and obtained the EDM enhancement factor of Tl as $-466$, which in combination with the most accurate measured value of Tl EDM yields $2.0 \times 10^{-27}\,{\mathrm e\,cm}$ as the new upper limit for the EDM of the electron. The importance of all-order correlation effects is emphasized and their trends are compared with those of two other ab initio calculations.