## 2 Plasma Emission and Multi-Element Detection
The number of photons emitted from a laser-induced plasma per atom in the plasma and per time can be calculated considering the spectroscopic parameters of the involved atomic transition and the plasma temperature [51]. From Equation (1) this element-specific emission rate (EMRA) is calculated by [Equation (3)]:  
\[\rm{EMRA}=(\Delta n_{\rm{ki}}/\Delta t)/N=A_{\rm{ki}}\,g_{\rm{k}}\,exp[-E_{\rm{ k}}/k_{\rm{B}}\,T_{\rm{e}}]/Z(T_{\rm{e}}). \tag{3}\]  
Figure 1 shows the calculated emission rate of most chemical elements for a homogeneous and optically thin plasma in (local) thermodynamic equilibrium at T\({}_{\rm{e}}\) = 10,000 K.  
Figure 1: Number of photons emitted per atom and second for optically thin and homogeneous LTE plasma at temperature T\({}_{\rm{e}}\) = 10,000 K. This emission rate of atoms EMRA is calculated for most chemical elements using the most intense emission lines of neutral species (upper part). The ionization energy of neutral atoms versus the atomic number of elements (lower part). The sign ”**” stands for multiplication. For each element, the most abundant isotope is selected and at least the two most intense emission lines of neutral atoms are evaluated [52; 53]. Ions are not considered here as most species are neutrals in LIBS plasma measured at longer delay times with respect to the laser pulse. The emission rate varies by almost 12 orders of magnitude for the different elements. The temperature T\({}_{\rm e}\) = 10,000 K is typical in LIBS measurements employing nanosecond laser pulses with energy density (fluence) \(\Phi\) = 1\(-\)100 J/cm\({}^{2}\) for ablation. At very high nanosecond laser fluence of \(\Phi\) \(\sim\) 10\({}^{4}\)\(-\)10\({}^{5}\) J/cm\({}^{2}\) the plasma species can have high ionization stages (e.g., Ti\({}^{12+}\) and Sn\({}^{11+}\)). The corresponding plasma temperatures are around 10\({}^{5}\)\(-\)10\({}^{6}\) K and plasma emission is obtained in the extreme UV and soft X-ray spectral ranges. This regime has so far not been explored for technical applications in analytics. The lower part of Figure 1 displays the ionization energy of neutral atoms. The plasma emission and the ionization energies of elements are correlated. High energy levels are sparsely populated and atoms with high excited state and ionization energies have relatively weak emission. In Figure 2 the emission rate of atoms in ideal plasma is presented according to the group of chemical elements in the periodic table. The numbering of groups follows the scheme of the International Union of Pure and Applied Chemistry [54]. In group 1, the alkali metals (lithium to francium) show intense emission (EMRA \(\approx\) 10\({}^{6}\)\(-\) 10\({}^{7}\) photons/atom \(\times\) sec), whereas the hydrogen emission lines are weak in comparison (EMRA \(\leq\) 10\({}^{4}\) photons/atom \(\times\) sec). The alkaline earth metals (beryllium to radium, group 2), the transition metals (group 3 including lanthanoids and groups 4\(-\)12), and the elements in group 13 (boron to thallium) have rather intense emissions. From group 14 to 18 the emission rates show a trend to lower values and much larger variations for different elements within the same group. For halogens (group 17) and noble  
Figure 2: Emission rate EMRA of atoms in ideal plasma for most chemical elements in groups 1 to 18 of the periodic table (T\({}_{\rm e}\) = 10,000 K). Groups are numbered according to the IUPAC scheme [54]. The sign “**” stands for multiplication. gases (group 18) the lightest elements have the faintest emissions with EMRA \(\approx\) 100 and 10\({}^{-3}\) photons/atom \(\times\) sec for fluorine and helium, respectively. Elements with high plasma emission intensities such as alkali metals, alkaline earth metals, and lanthanoids are measured with low LOD values, for example -10 ppm for Mg and Na and -2 ppm for Y. For halogens, on the other hand, the emission intensity is much lower and the reported LOD values are much higher, for example \(\sim\)300 ppm for F, \(\sim\)1000 ppm for Cl, and \(\sim\)5000 ppm for Br.