# Laser-Induced Breakdown Spectroscopy for Determination of Spectral Fundamental Parameters
## 5 Experimental Determination of Spectral Parameters by LIBS
### Determination of Transition Probabilities
Measurements were carried out at different delays after the laser shot. The authors demonstrated that the effect of self-absorption is below 1%. [PERSON] et al. [109] also in 2001 calculated the transition probabilities of 24 Si II lines. Measurements were done in air at atmospheric pressure by focusing a 10 ns laser beam (\(\lambda\) = 1064 nm, \(E\) = 140 mJ) on a silicon target, in a xenon and hydrogen atmosphere. In that work, the transition probabilities were deduced either from relative intensity ratios or by the branching ratio method. For correcting self-absorption effects, the authors used adapted numeric methods. [PERSON] et al. [110] calculated the transition probability for the line 220.353 nm of Pb II and the transition probabilities for 39 lines of Pb I. In this case, they used Boltzmann plot method and branching-ratio measurements. To avoid self-absorption effects, the authors used Sn-Pb alloys with a lead content lower than 0.5%, in Argon atmosphere. They found that self-absorption effects were lower than 1% for the most intense lines; thus, the plasma could be considered optically thin. In 2004, [PERSON] et al. [111] used LIBS for determining the transition probabilities of 20 Ag II and 3 Cu II lines from the branching-ratio measurements obtained in the experiment. The measurements were carried out in a controlled Argon atmosphere (\(\sim\)8 Torr). The authors found a good agreement between the measured and the calculated transition probabilities values. In another work, the same year [PERSON] et al. [112] determined by LIBS the transition probabilities of 120 emission lines of Zr III with 4d5p and 4d5d electron configurations. Their analysis was performed experimentally and theoretically on Cu-Zr alloy with a Zr concentration lower than 13% for maintaining an optically thin condition of plasma. Transition probabilities were estimated from branching ratio measurements and calculated lifetime magnitudes. [PERSON] et al. [113] reported the experimental transition probabilities for Ag II spectral lines with electron configurations 4d\({}^{9}\)6s and 4d\({}^{9}\)5d, and as well for Cu II lines from 3d\({}^{9}\)4d electron configurations. The authors used a Nd:YAG laser at 1064 nm wavelength to irradiate a silver or cooper target with 99.9999% purity in a controlled argon atmosphere (\(\sim\)8 Torr). The theoretical values of the transition probabilities were calculated by the Relativistic Hartree-Fock method considering configuration interaction and core-polarization influences. The absolute transition probabilities were measured taking into account the branching ratio and theoretical data related to radiative lifetimes. [PERSON] et al. [114] determined the transition probabilities and different plasma parameters (including temperature, composition and spectral self-absorption) of Cd II and Zr III, using a temporal and spatial resolved LIBS analysis. Relative transition probabilities for 38 transitions arising from the 4d\({}^{10}\)(6p, 7p, 8p, 4f, 5f) and 4d\({}^{9}\)5s5p electron configurations of high lying states of Cd II were calculated by [PERSON] et al. [115] exploiting a LIBS plasma in LTE conditions. The experiment was performed on pure cadmium sample as well as on some Zn-Cd alloys, at Cd concentrations lower than 10%. The experimental transition probabilities were measured from branching ratios, which were converted to absolute values using theoretical data on the radiative lifetimes of corresponding states. LIBS was used by [PERSON] et al. [116] in 2007 for the experimental determination of the transition probabilities of 16 Au II (all of them measured for the first time) with 6p configuration. The experiment was done on Cu-Au alloy with 10% Au content for achieving to the optically thin condition of plasma. Transition probabilities were evaluated experimentally by utilizing the theoretical lifetimes calculated in the same study.