# Laser-Induced Breakdown Spectroscopy for Determination of Spectral Fundamental Parameters
## 5 Experimental Determination of Spectral Parameters by LIBS
### Determination of Transition Probabilities
The authors calculated the transition probabilities by plotting the intensities of the Pb II emission spectrum lines on a Boltzmann plot, assuming local thermodynamic equilibrium (LTE). To assess the effect of self-absorption, they calculated values of the optical depth not over 2%, thus confirming the optical thin hypothesis in their measurements. [PERSON] et al. [103] also in 1997 determined the experimental transition probabilities for 32 lines from the 5p\({}^{2}\)6s configuration of neutral Sb. All measurements were carried out with several Sn-Sb alloys were the Sb content was lower than 2% to have an optically thin plasma. The authors measured the emission intensities of lines arising from the same upper level to determine the relative transition probabilities and corresponding branching ratios. The results were placed on an absolute scale by using experimental lifetime values from the literature. To test the laser-produced plasma results, branching ratios have been obtained, where possible, by using a hollow-cathode lamp as a light source. It was found that the effect of self-absorption in the measurements for all spectral lines was lower than 4%. In 1999, [PERSON] et al. [104] determined the first experimental values of the atomic transition probabilities for ten spectral lines of Pb III from the measurement of emission-line intensities in an optically thin laser-produced plasma of Pb. Authors calculated relative transition probability values for lines of a given atomic species by measuring relative intensities, while absolute transition probabilities were obtained from relative line strength measurements by comparison with the relative line strength of the 560.89 nm Pb II transition in the Saha equation. They also considered the self-absorption effects in all measurements and determined that it affected their calculation for less than 3%. [PERSON] et al. [105], in the same year, used a laser-produced plasma to measure the experimental transition probabilities for 103 lines from the 3s\({}^{2}\)3p\({}^{2}\)4p configuration of S II. The experiment was carried out with samples of zinc sulfide (ZnS) and antimony sulfide (Sb2S3) in a controlled atmosphere of pure argon. The authors obtained relative values from the measurement of emission-line intensities and the results were placed on an absolute scale by using line-strength sum rules and lifetime values. Moreover, they reported that the effects of self-absorption in their measurements were lower than 1.2%. By using temporal spectra from a laser-induced plasma, [PERSON] et al. [106] in 2000 made an experimental and theoretical investigation on the transition probabilities of Xe II. They measured transition probabilities for eighteen lines by means of the Boltzmann plot method. The authors evaluated the effects of self-absorption by calculating the intensity ratio between the Xe II lines at 424.5 and 458.5 nm as a function of time. They found that the ratio remains almost constant about the mean value and thus, in that range, the plasma can be considered optically thin. Furthermore, in 2000, [PERSON] and [PERSON] [107] determined the transition probabilities values for 36 lines of Sn II by measuring the emission line intensity of a laser-produced plasma of lead and tin alloys. The transition probabilities were determined through the Boltzmann plot method and branching ratios measurements. The authors evaluated the effects of self-absorption on the measured lines by calculating the absorption coefficient and they demonstrated that for the most intense line, the self-absorption effect is less than 3%. The authors used the Boltzmann plot method to obtain absolute values of the transition probabilities. In the same year, transition probabilities for 26 lines with origin from the 5s\({}^{2}\)(6p, 6f, 6d, 7s and 5g) configurations of Sb III were determined by [PERSON] et al. [108]. They used the branching ratios method and put the data on an absolute scale using calculated lifetimes and lines strengths.