# Laser Induced Breakdown Spectroscopy of Er II for Transition Probability Measurements
## 1 Introduction  
Spectroscopic data of rare-earth elements are important for several fields, especially in astrophysics. For example, data of transition wavelength and probability are essential to estimate the amount of these elements in the stellar atmosphere [1, 2]. In addition, such atomic data sets are needed for the accurate radiative transfer simulation for kilonovae produced by neutron star mergers [3, 4]. Er is one of the most important among rare-earth elements. In the NIST atomic spectra database (ASD) [5], 285 lines of Er II are registered on the basis of the data compilation by [PERSON] et al. [6] in 1975. Among them, only 11 lines are listed with energy level classifications and transition probabilities. [PERSON] and [PERSON] [7] measured relative transition probabilities of 101 lines by arc plasma spectroscopy. By normalizing the relative data to the experimental radiative lifetime by [PERSON] and [PERSON] [8], absolute values were determined. [PERSON] et al. [9] measured radiative lifetimes of 30 excited levels by time-resolved laser-induced fluorescence (LIF). By using theoretical branching fractions, transition probabilities of 32 lines were obtained. Significant progress was made by [PERSON] et al. [10] (this paper is referred to as Lawler2008 hereafter), who determined the transition probabilities of 418 lines from their branching fraction measurements with a combination of radiative lifetimes measured by [PERSON] et al. [11]. Some of the transition probability data in Lawler2008 were evaluated in a recent experimental study by [PERSON] et al. [12] using a time resolved laser induced fluorescence method. Good agreement in the \(gA\) values found between their data implies the reliability of the transition probabilities in Lawler2008. [PERSON] and [PERSON] [13] extended the study with the aid of theoretical analysis, using the Cowan code [14], and 130 levels of even parity and 230 levels of odd parity were summarized with configuration mixing coefficients. [PERSON] and [PERSON] [15] estimated the isotope shift between \({}^{166}\)Er and \({}^{170}\)Er, using the mixing coefficients derived by [PERSON] and [PERSON], and found that the estimated shifts were consistent with the experimentally measured shifts. In this paper, we present an emission spectrum of Er II, obtained by laser induced breakdown spectroscopy (LIBS), where the emission from plasma produced by an intense laser pulse is observed. LIBS has been mainly developed for element analysis in industrial manufacturing [16], environmental monitoring [17; 18], geological studies [19] including planetary exploration [20], and many other applications. On the other hand, LIBS is one of the most powerful methods for the determination of fundamental atomic properties, such as transition probabilities (see the review paper [21] in this Special Issue and references therein). In order to determine transition probabilities properly, a local thermal equilibrium (LTE) condition should be realized. Although the temperature of the plasma varies with time, instantaneous observation of the plasma with a time-resolved intensified camera can ensure the LTE condition. Since the emission intensity \(I\) in the LTE condition is proportional to the product of the transition probability \(A\) and the Maxwell-Boltzmann population determined by the temperature \(T\) and the upper level energy \(E\), the logarithm of \(1/gA\), where \(g\) is the statistical weight, should have a linear dependence on \(E\) (see Section 2). The linearity can be used to confirm the reliability of the \(A\) values used. Once the linearity is confirmed, unknown \(A\) values can be obtained by applying the experimental intensity to the linear function obtained. LIBS is a simple method for evaluating or accumulating transition probability data, compared with other methods such as LIF. It also has the advantage that many transitions can be evaluated at the same time and that metal targets can be used as is, without vaporization.