Electric dipole moments due to nuclear Schiff moment interactions: A reassessment of the atoms ${}^{129}$Xe, ${}^{199}$Hg, and the molecule ${}^{205}$TlF

Abstract

We present relativistic many-body calculations of atomic and molecular Schiff-moment interaction constants including interelectron correlation effects using atomic Gaussian basis sets specifically optimized for the Schiff interaction. Our present best results employing a Gaussian nuclear density function are ${\alpha }_{\text{SM}}=(0.364\pm 0.025)\times 10^{-17}\frac{e\text{cm}}{e{\text{fm}}^3}$ for atomic ${}^{129}$Xe, ${\alpha }_{\text{SM}}=(-2.40\pm 0.24)\times 10^{-17}\frac{e\text{cm}}{e{\text{fm}}^3}$ for atomic ${}^{199}$Hg, and $W_{\text{SM}}=(39967\pm 3600)$ a.u. for the thallium nucleus in the molecule ${}^{205}$TlF. We discuss agreements and discrepancies between our present results and those from earlier calculations on the atoms ${}^{129}$Xe and ${}^{199}$Hg. Using the most recent measurements of $\mathcal{P},\mathcal{T}$-odd electric dipole moments and the present interaction constants reliable upper bounds on the Schiff moments of the ${}^{199}$Hg and ${}^{205}$Tl nuclei are determined in the context of a single-source assumption.

Comments: 24 pages, 1 figure