# Laser Induced Breakdown Spectroscopy of Er II for Transition Probability Measurements
## 3 Results and Discussion  
Figure 2a shows the LIBS spectrum for the whole spectrometer region (200-1080 nm) obtained by about 1000 shot accumulations. Close-up views of the 300-400 nm, 330-340 nm and 390-400 nm regions are also shown in Figure 2b-d, respectively. In addition to the emission lines of Er, lines from Ar (atmospheric gas) and Al (the main content of the target alloy) were also confirmed, including strong lines of Al I [5] at around 310 nm and 395 nm. Among the observed Er lines, 30 Er II lines in Lawler2008 were found to have enough intensity to analyze. All of them, which are listed in Table 1, were concentrated in the 300 nm range shown in Figure 2b. For example, in the 330-340 nm range shown in Figure 2c, eight lines from Er II were observed, as indicated by the red arrows. They are well represented by a Gaussian line shape, as shown in the inset for the 337.271 nm line as an example. The peak area of each observed line was thus obtained by fitting a Gaussian function, and the relative intensity \(I\) was obtained, as listed in Table 1, by correcting the peak area with the response function obtained with the calibration light source. Figure 1: Schematic diagram of the experimental setup. The self-absorption effect can be estimated from the line intensity ratio between the intense transitions with the same upper level [23,24]. When the thin condition is valid, the intensity ratio of such a transition pair should be equivalent to the branching ratio determined only by the transition probability ratio. On the other hand, when the thin condition is not valid, the intensity ratio of such a pair tends to deviate from the branching ratio, as the self-absorption effect decreases the observed intensity more significantly for the transition with a larger transition probability. In the present spectrum, the ratio between the 389.623 nm and the 383.048 nm lines, which are relatively intense and have the same upper level with an energy of 3.236 eV, is a suitable probe for the self-absorption effect. The sensitivity corrected experimental intensity ratio for those lines was 1.2 \(\pm\) 0.2, which is in good agreement with the branching ratio 1.23 \(\pm\) 0.09 [10] within the uncertainties. We also measured this ratio using a target with twice the content (10 wt%\(\sim\)1.8 4%) of Er. Although consistency with the branching ratio was also confirmed for the higher content target, we used the lower content (5 wt%\(\sim\)0.8 at%) target to ensure the thin plasma condition more certainly. Figure 2: LIBS spectrum obtained for an Al-5 wt% Er alloy target in an Ar atmosphere for the (**a**) whole spectrometer (200–1080 nm), (**b**) 300–400 nm, (**c**) 330–340 nm, and (**d**) 390–400 nm regions. It is noted that the sensitivity correction is not applied. It is also noted that the undulated baseline of the spectrum reflects the response of each diffraction order of the Echelle grating. The lines indicated by the red arrows represent those given in Lawler2008 [10]. The blue arrow indicates the 393.863 nm line listed in the NIST database without a transition probability. The left side values of Equation (2) obtained from the experimental intensity \(I\) and the \(gA\) values in Lawler2008 are plotted in Figure 3 as a function of the energy \(E\) of the upper level of the transition. The error bars represent the uncertainty obtained considering four contributions: (i) the fitting error, (ii) the statistical uncertainty of the photon counts estimated from the conversion factor from the digital counts to the photon number, (iii) the uncertainty in the radiometric data of the calibration light source, and (iv) the uncertainty in the \(A\) values. The linear function corresponding to Equation (2) was obtained by weighted fitting to the data, as shown by the solid line. The 68.3% confidence interval is also shown by the dashed curves.