Fig. 5

Molecular g factors, \(g_\text{mol}\) as defined in the text, (a) and transition magnetic moments (b) as functions of \(\Omega\) for DyOH (orange filled circles) and ErOH (grey filled circles) at their linear equilibrium geometries along the body-fixed Ln-O axis. G-factors of the pseudo-spin are defined in the text. The DyOH and ErOH molecules are in their \(\hbox {4f}^9\hbox {6s}^2\)+\(\hbox {2p}^6\) and \(\hbox {4f}^{11}\hbox {6s}^2\)+\(\hbox {2p}^6\) ground-state configuration, respectively. In panel (a) the dashed orange and grey lines are the experimental g factors of the \(j=15/2\) level of the \(\hbox {4f}^9\hbox {6s}^2\) and \(\hbox {4f}^{11}\hbox {6s}^2\) configurations of \(\hbox {Dy}^+\) and \(\hbox {Er}^+\), respectively. In panel (a) the solid black curve is a polynomial in \(\Omega ^2\) found from a fit to the data for DyOH, while the solid black curves in panel b) correspond to a fit to adjustable parameter \(g_1\) times matrix elements of the angular momentum raising operator \(j_{+1}/\hbar\).