Changes in mean-square nuclear charge radii in Er from optical isotope shifts by laser-atomic-beam spectroscopy

High-resolution laser-atomic-beam spectroscopy has been applied to investigate transitions 4f ¹² 6s ²?4f ¹¹ 5d6s ² and transitions starting from metastable states of the configuration 4f ¹¹ 5d6s ² of Er I. Precise values for the transition isotope shifts and for the hyperfine constants of 10 levels belonging to the configuration 4f ¹¹ 5d6s² and 9 levels belonging to high lying even-parity levels have been determined. From the isotope shift data relative changes of mean-square nuclear charge radiiδ 〈r ²〉 for all the stable Er isotopes have been deduced: ¦168,170¦ 1, ¦166,168¦ 0.984(15), ¦164,166¦ 0.984(15), ¦162,164¦ 1.198(18), ¦166,167¦ 0.3357(50). Absoluteδ 〈r ²〉 values have been obtained by calibrating the optical data with a value from muonic x-ray spectroscopy: ¦168,170¦ 0.121 (10) fm². The odd-even staggering parameter for¹⁶⁷Er has been determined: 0.683(10). Our results are compared with experimental data from electronic x-ray spectroscopy and data from calculations with the extended liquid-drop and the droplet model.