Hyperfine structure of hydrogenlike thallium isotopes

The hyperfine splitting of the $1s$ ground state of hydrogenlike Tl has been measured for the two stable isotopes using emission spectroscopy in the SuperEBIT electron-beam ion trap, giving $3858.22\pm 0.30\hspace{0.5em}\AA$ for ${}^{203}{\mathrm{Tl}}^{80+}$ and $3821.84\pm 0.34\hspace{0.5em}\AA$ for ${}^{205}{\mathrm{Tl}}^{80+}$ with a wavelength difference $\Delta \lambda =36.38\mathrm{}\pm 0.35\hspace{0.5em}\AA .$ This difference is consistent with estimates based on hyperfine anomaly data for neutral Tl only if finite size effects are included in the calculation. By using previously determined nuclear magnetic moments, and applying appropriate corrections for the nuclear charge distribution and radiative effects, the experimental splittings can be interpreted in terms of nuclear magnetization radii $〈r_m^2{〉}^{1/2}=5.83\mathrm{}\left(14\right)\mathrm{}\hspace{0.5em}\mathrm{fm}$ for ${}^{203}\mathrm{Tl}$ and $〈r_m^2{〉}^{1/2}=5.89\mathrm{}\left(14\right)\mathrm{}\hspace{0.5em}\mathrm{fm}$ for ${}^{205}\mathrm{Tl}.$ These values are 10% larger than derived from single-particle nuclear magnetization models, and are slightly larger than the corresponding charge distributions.