# Laser-Induced Breakdown Spectroscopy for Determination of Spectral Fundamental Parameters
## 5 Experimental Determination of Spectral Parameters by LIBS
### Determination of Transition Probabilities  
In some papers, the oscillator strength \(f\) of the transition is obtained, instead of the transition probability. The two parameters are equivalent, since:  
\[f=1.499\times 10^{20}\ \lambda_{0}^{2}\ \frac{\delta k}{g_{i}}A_{ki} \tag{32}\]  
where \(\lambda_{0}\) is the peak wavelength of the transition (nm), \(A_{ki}\) is the transition probability (\(10^{8}\) s\({}^{-1}\)) and \(g_{i}\), \(g_{k}\) are the degeneracies of the lower and the upper level of the considered transition, respectively. [PERSON] et al. in 1993 [96], calculated transition probabilities of 38 Na II lines from measurements of emission-line intensities in a laser-produced plasma. The authors evaluated the effects of self-absorption by calculating the optical depth for the most intense Na II line (309.273 nm), showing that the plasma could be considered optically thin in their experiment. The same group in 1994 [97] used the optical emission from a laser-produced plasma to measure the relative transition probabilities of 43 lines arising from the 3d\({}^{4}\)4p configuration of Cr II. Measurements were carried out with Al-Cr alloys with a Cr content of about 0.1%, to have an optically thin plasma. Transition probabilities were placed on an absolute scale by using, where possible, accurate experimental lifetimes from the literature and line-strength sum rules. The authors estimated the effects of self-absorption by calculating the absorption coefficient of the intense Cr II 206.542 nm line, demonstrating that for this line, self-absorption effects were negligible. [PERSON] et al. [98] in 1995 determined the absolute transition probabilities of 28 Si II lines measuring the intensities of spectral lines from LIPs generated on a Silicon sample in Ar and Kr atmospheres. In this way, branching ratios of spectral lines arising from the 3s\({}^{2}\)4p levels were utilized to determine the transition probability values. Authors also calculated absolute transition probabilities of 23 Si II spectral lines using the Boltzmann plot method, under the assumption of local thermodynamic equilibrium (LTE). A direct calculation indicates that self-absorption effects were below 3% for the strongest lines. In the same year, [PERSON] et al. [99] calculated the transition probabilities of 36 lines of Ag II using spectral lines emitted by a laser-induced plasma of pure silver sample. An estimation of the absorption coefficient was carried to verify that self-absorption was negligible. The authors found the absorption effects to be lower than 5% for the most intense lines. [PERSON] et al. [100] in 1996 calculated the for the first time the absolute transition probabilities for 10 In II lines from branching-ratio measurements. In their experiments, the Indium sample was located inside a vacuum chamber, which was filled with argon at a pressure of 6 Torr. They found that the self-absorption corrections were below 1% for the strongest 468.11 nm line. In 1997, [PERSON] et al. [101] calculated the experimental transition probability values for 59 spectral lines of Ni II by measuring the emission line intensity of laser-produced plasmas of alloys of nickel and aluminum with low nickel content. To determine the transition probability values, branching ratios for the 3p\({}^{6}\)3d\({}^{8}\)4p to 3p\({}^{6}\)3d\({}^{8}\)4s lines of Ni II were measured. Some other transition probabilities were calculated by comparing their intensities with those of neighboring lines whose transition probabilities were previously determined. Relative values of transition probabilities were put on an absolute scale by using the lifetimes values. It was calculated that in their measurements, self-absorption effects were lower than 2.5% for the most intense lines. In the same year, [PERSON] [102] used the laser-produced plasma of a lead target with 99.9% purity, to measure transition probabilities for 30 lines of Pb II. For nine of them, the results reported were the first experimental data obtained.