# Laser Induced Breakdown Spectroscopy of Er II for Transition Probability Measurements
## 3 Results and Discussion
From the gradient of the fitted linear function, the plasma temperature is derived to be 6700 \(\pm\) 400 K.  
As seen in the figure, the Boltzmann plot shows rather a good linearity although some of the data are scattered from the fitted linear function. In general, the linearity in the Boltzmann plot ensures the LTE condition of the plasma and the reliability of the \(gA\) values. In other words, the deviation of the data from the linear dependence should be attributed to the deviation from the LTE condition or the error in the \(gA\) value (or both). We consider that the scattering is due to an incomplete LTE condition in the present experiment, as the reliability of the data in Lawler2008 was confirmed through comparison with the transition \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Lower**} & \multicolumn{3}{c}{**Upper**} & \multicolumn{3}{c}{\(A\)} \\ \cline{2-9} \(\boldsymbol{\lambda}\) **(nm)** & **Parity** & **2_J_** & **\(E\) (eV)** & **Parity** & **2_J_** & **\(E\) (eV)** & **(10\({}^{6}\) s\({}^{-1}\))** & **\(I\)** \\ \hline  
ven & 9 & 0.892110 & odd & 11 & 4.214012 & 19.5 \(\pm\) 1 & 0.08 (1) \\
373.816 & odd & 13 & 1.619322 & even & 15 & 4.935095 & 46.8 \(\pm\) 2.5 & 0.06 (1) \\
374.264 & even & 9 & 0.636362 & odd & 9 & 3.948168 & 20.6 \(\pm\) 1.1 & 0.11 (1) \\
383.048 & even & 13 & 0.000000 & odd & 13 & 3.235860 & 19.4 \(\pm\) 1.0 & 0.49 (6) \\
385.839 & even & 9 & 0.892110 & odd & 11 & 4.104563 & 18.5 \(\pm\) 0.9 & 0.08 (1) \\
388.061 & even & 9 & 0.636362 & odd & 7 & 3.830423 & 31.3 \(\pm\) 1.6 & 0.15 (2) \\
388.289 & even & 11 & 0.886441 & odd & 9 & 4.078630 & 31.6 \(\pm\) 1.6 & 0.12 (2) \\
389.623 & even & 11 & 0.054607 & odd & 13 & 3.235860 & 23.9 \(\pm\) 1.2 & 0.59 (6) \\
390.631 & even & 13 & 0.000000 & odd & 11 & 3.173046 & 48.2 \(\pm\) 2.4 & 1.00 (10) \\
393.863 & even & 13 & 0.00000 & odd & 11 & 3.147014 & 12 \(\pm\) 2 & 0.26 (3) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Transitions used in the present analysis. Wavelength (\(\lambda\)), parity, 2\(J\) value, level energy (\(E\)), and transition probability (\(A\)) are taken from Lawler2008 [10] except for the 393.863 nm line. For the 393.863 nm line, wavelength, parity, 2\(J\) value, and level energy taken from the NIST database [5] and the transition probability obtained in the present measurement are listed. The sensitivity-corrected relative intensities \(I\) in the present LIBS spectrum, normalized to the 390.631 nm line, are listed for all the lines. probability data independently obtained by a different method from another group [12], as described in Introduction. However, the large deviation for the data at \(E\) = 4.85 eV may imply an underestimation of the \(gA\) value for the corresponding transition (359.950 nm). If the data is applied to the obtained linear function, an \(A\) value of \(1.5(2)\times 10^{8}\) s\({}^{-1}\) is obtained, whereas it is \(5.22(27)\times 10^{7}\) s\({}^{-1}\) in Lawler2008. In the NIST database, there is one transition at 393.863 nm for which the lower and upper level energies are given but the transition probability is not given. The transition probability of this line is not included either in Lawler2008. As listed in the last line in Table 1, the angular momentum and the parity of the upper level are defined as \(J=11/2\) and odd in the NIST database, but the electron configuration is not given. According to [PERSON] and [PERSON] [13], \(4f^{11}5d\)s is assigned to the corresponding level although \(4f^{11}6s^{2}\), \(4f^{12}6p\), and \(4f^{11}5d^{2}\) are mixed with a mixing coefficient of 0.37, 12.55, and 2.71 %, respectively. This 393.863 nm line was observed in the present LIBS spectrum, as indicated by the blue arrow in Figure 2d, and the intensity was obtained from the peak area of the fitted Gaussian function shown in the inset. By applying this line to the linear function in Figure 3, as plotted by the blue square, the transition probability \(A\) is obtained as 1.2(2) \(\times 10^{7}\) s\({}^{-1}\).