Line shape of three-level ions in Paul traps

A cloud of three-level ions (${\mathrm{Ba}}^{+}$) confined in a Paul trap was illuminated with two lasers and the resulting fluorescence was observed as a function of the laser detunings from the ionic resonance. The observed spectra show features due to the oscillatory motion of the trapped ions. In order to describe the observed line shapes, calculations are presented in which the ion ensemble is separated in classes of velocity amplitudes of the oscillatory motion rather than velocity classes.