Finestructure, hyperfine structure and isotope shift of 4f

The isotope shift (IS) and hyperfine structure (hfs) of nine levels (31720 to 38921 cm-1) assigned to the configuration $4f^{12}6s7s$ in neutral erbium have been determined experimentally using Doppler-reduced saturation absorption spectroscopy in a gas discharge. We performed a fine structure analysis in the SL-coupling scheme of the single configuration $4f^{12}6s7s$, confirming and extending the classification of even parity Er I levels. We discriminated the different hfs contributions of the $4f^{12}$ core and the (6s+7s) outer electrons of the shell in a non-relativistic JJ-coupling approach and in the relativistic effective tensor operator formalism in SL-coupling. The relativistic one-electron parameters of the hfs for 167Er were fitted to the experimental data by a least squares fit procedure: 0pt[0pt] MHz, 0pt[0pt] MHz, 0pt[0pt] MHz. The level dependencies of the isotope shift were evaluated based on crossed second order (CSO) effects. We obtained the following results for the CSO parameters for the isotope pairs 170-168Er: $d_{6s7s}=-740(30)$ MHz, $z_{4f}= 0(5)$ MHz, $(g_{3,6s}(f, 6s)+g_{3, 7s}(f, 7s))= -24(15)$ MHz and for 170-166Er: $d_{6s7s}=-1500(50)$ MHz, $z_{4f}=0(10)$ MHz, $(g_{3,6s}(f,6s)+g_{3,7s}(f+7s))=-50(29)$ MHz. The resulting parameters for the hfs are compared with those known for other configurations of the Er atom and ion