New method for determining relative oscillator strengths of atoms through combined absorption and emission measurements: Application to titanium (Tii)

The authors introduce a procedure that combines measurements of absorption and emission by atoms to obtain relative oscillator strengths that are independent of temperature determination in the sources and of assumptions regarding local thermodynamic equilibrium. The experimental observations are formed into sets of transitions and required to satisfy defined ratios. The screened data are adjusted with a least-squares program to obtain optimized relative oscillator strengths and constants relating the observations to these values. With appropriate choices of input observations, the constants are proportional to upper-level lifetimes and lower-level populations. The procedure is illustrated by the published data of Whaling et al. and Smith and K\"uhne for 16 transitions in Tii. The relative oscillator strengths resulting from this procedure have calculated uncertainties between 5 and 17% ({~} 95% confidence level). Evidence is presented to suggest that these uncertainties have been overestimated. Calculated oscillator strengths are normalized to the atomic-beam absorption measurements of Bell et al. and to the experimental lifetimes of Roberts et al. and Whaling et al. The absolute oscillator strengths are determined with an uncertainty of 7-18%. The results indicate that the published lifetime for the level y³D₂⁰ of Tii should be increased by 24%.