New Energy Levels of Neutral Lanthanum Derived from an Optogalvanic Spectrum between 5610 and 6110 Å

: In Atoms 2020 , 8 , 23; doi:10.3390 / atoms8020023, we reported on a complete optogalvanic (OG) spectrum of a discharge burning in a La–Ar gas mixture, in the spectral range 5610–6110 Å (17,851 to 16,364 cm − 1 ). Now we are able to communicate further new energy levels, found via searching for laser-induced ﬂuorescence lines when exciting unclassiﬁed lines from the OG spectrum. We were able to ﬁnd 17 new levels, and for two further levels, the line list has extended. With the help of these 19 levels, we could classify 132 spectral lines.


Introduction
Lanthanum (La, Z = 57) has the electron ground state configuration [Xe] 5d6s 2 and an empty 4f shell. The electronic structure and the spectrum of Lanthanum is of special interest, not only for practical reasons but also for the theoretical description of it.
As reported in reference [16], we were able to record a complete optogalvanic (OG) spectrum of Lanthanum between 5610 and 6110 Å (17,851 to 16,364 cm −1 ), consisting of more than 1900 overlapping laser scans. In [16], the discovery of 12 even-parity levels and one odd-parity level was reported. Continuing the analysis of the spectra, we found a further 17 new energy levels with even parity. Further analysis of the spectrum is in progress. Two additional levels at 41,465.181 and 41,681.602 cm −1 were published earlier [14]. In the OG spectrum treated here, we found additional lines in which these levels are involved, confirming their existence. Thus, we give now a list of all lines classified by these two even-parity levels. Altogether, 132 spectral lines can be classified as transitions in which these 19 levels are involved. For checking the existence of the levels, we also set the laser wavelength to some lines in the ranges 6900-6110 and 5610-5550 Å, and observed OG and laser-induced fluorescence (LIF) signals.
For classification of the lines observed in our investigations, we used the program "Elements" [12,19], which shows classification suggestions together with proposed hyperfine structure (hf) patterns, calculated from already known energy levels and their hf constants. For some lines, up to 10 suggestions are found in a wavenumber interval of ±0.5 cm −1 around the wavenumber of the treated line. If for a line under investigation, no suggestion fits to the wavenumber and the observed Atoms 2020, 8, 88 2 of 12 hf pattern, we had to conclude that a new energy level is involved in the observed transition. The fit of the hf patterns was performed using the program "Fitter" [20]. Methods for finding new energy levels are described in references [12,14]. Some information we could obtain from an available Fourier transform spectrum [21,22].

Experiment
As reported in reference [16], the source of free La atoms was a discharge, burning in a La-Ar plasma. We used, as in several works before (e.g., [5]), a see-through hollow cathode lamp. The cylindric cathode had a length of 20 mm and was made from copper, the inner wall bushed with La, with an inner diameter of 3 mm. The discharge was started in Ar buffer gas of ca. 0.1 mbar pressure. After some minutes, a sputtering process began and the discharge was carried mainly by a La plasma. The color of the discharge changed during this process from grey-blue with moderate intensity (Ar) to white, emitting then very bright light. In order to enhance the sputtering process and to lower the Doppler width of the lines, the discharge housing was embedded in liquid nitrogen (see sketch in reference [16]). The discharge was operated in constant current mode at ca. 90 mA.
Tunable laser light was generated by a homemade continuous wave, actively stabilized ring dye laser, operated with R6G, pumped by a frequency-doubled Nd:YAG-laser (Coherent Verdi). A line width as low as ca. 1 MHz was obtained and the scanning range was 45 GHz (1.5 cm −1 ). Scan velocity was about 250 MHz/s, and we stored 50 data points per second. For additional wavelength regions, we also used the dyes DCM and R110. The frequency scale was generated using the transmission intensity of a temperature-stabilized confocal Fabry-Perot cavity (free spectral range 367.33(2) MHz).
The detected OG signal is proportional to the change of the power supply voltage in dependence on the laser wavelength. Since this change is very small compared to the applied voltage (some mV against ca. 350 V), detection is possible only when applying quite sensitive methods. Thus, before entering the discharge region, the laser light was intensity modulated by means of a mechanical chopper and the voltage change was amplified by means of a Lock-In amplifier, synchronized with the chopper.
The structures in the recorded OG spectra show all possible transitions independently of which energy states are involved. These lines can be classified due to their wavelength and their characteristic hf patterns. However, if an observed line cannot be explained as the transition between already known energy levels, we have to conclude that a new level is involved and we need information of at least one of the combining energy levels. For this purpose, we apply detection of LIF. We focused the discharge light by means of quartz lenses to the entrance slit of a monochromator and detected the transmitted light by means of a photomultiplier and a Lock-In amplifier. By tuning the monochromator, we could find LIF lines, which intensities are modulated with the chopper frequency, and were able to determine their wavelength. The combination of all information (LIF and laser wavelengths and hf pattern of the investigated transition) allowed us to discover up to now unknown energy levels, as described in references [12,14]. A sketch of the apparatus used can be found e.g., in reference [11]. Besides lines of La I, we also found lines belonging to La II and to the carrier gas of the discharge (Ar I, Ar II).
Since, meanwhile, a huge number of La I energy levels are known, we await to find new levels in the energy range between 40,000 cm −1 and the ionization limit of 44,981 cm −1 [23]. Taking into account the exciting photon energy (17,851 to 16,364 cm −1 ), the lower energy levels of the excited, not classifiable transitions must have energies above 22,000 cm −1 and below 29,000 cm −1 . A schematic level scheme of La is shown in reference [16].
Let us assume that an odd-parity level in this energy range, sufficiently populated by the discharge, can be excited by the chopped laser light to a new, previously unknown even-parity level. This odd-parity level can also decay to low-lying even-parity levels. Since the odd-parity level is excited periodically, its population and thus, the intensities of its decay lines are also modulated by the chopper frequency. This gives the possibility to find the wavelengths of LIF lines by tuning the monochromator transmission wavelength and to identify via this way the odd-parity level. The phase of the detected LIF lines is opposite to the detected laser stray light and to the OG signal.
If the excited medium-energy level has even parity, the situation is in principle the same, but the lowest odd-parity level has an energy of 13,260 cm −1 . Thus, no decay to lower odd-parity levels is possible in the visible or near ultraviolet region, and excited even-parity levels cannot be identified by this method. Indeed, only a very small number (ca. 5) of high-lying odd-parity levels were found by laser spectroscopy.
In principle, the new, high-lying level can decay and lead to LIF lines. However, as our experiments show, laser excitation leads to a high OG signal (mirroring the ionization probability) but only in very few cases to a detectable LIF signal. Thus, we have to conclude that the ionization probability in the discharge plasma is much higher than the probability of radiative decay.

Results
The levels found during this investigation are listed in Table 1 and all have even parity. Additionally, the levels 41,465.181 and 41,681.502 cm −1 , published in reference [14], are listed with all classified lines.
In columns 1 to 3, J-value, energy E and hf constants A of the discovered levels are given. Due to the limited signal-to-noise-ratio (SNR) of the records, no values for the constants B could be determined. The levels are ordered by energy. The uncertainty of the energies of the levels is dependent on the number of lines classified by the level and by the accuracy of their wavelengths (given in col. 4). For lines in which center of gravity (cg) wavelength was determined by our lambdameter (uncertainty ±0.01 Å), two digits are given. For several excited lines, other, well classified lines showed up in the same laser scan due to the high line density (confer Figures 1 and 2). In such cases, we could determine the cg wavelength with lower uncertainty. For the well-known classified lines, we could calculate their cg wavelengths from updated level energies [24]. For the conversion from wave number to wavelength, the formula given by Peck and Reeder [25] for the dispersion of air was applied. A common fit of all lines in the record allowed us to determine the spacing between the cg frequencies of the lines and to calculate the wavelength of the line classified by the new level. Wavelengths determined in this way are given in Table 1 with three digits (uncertainty ±0.003 Å). In Figures 1 and 2, typical OG records are shown. Classification of the visible lines is given in Table 2.  Table 1).  Table 1).  Table 1).  Table 1). The line at 5909.966 Å had much higher intensity than the others, thus at a frequency offset of 12,000 MHz, the amplification was increased by a factor of 10. This also increased the OG background, thus a jump of the signal occurred.  Table 1). The line at 5909.966 Å had much higher intensity than the others, thus at a frequency offset of 12,000 MHz, the amplification was increased by a factor of 10. This also increased the OG background, thus a jump of the signal occurred.
The line on which the corresponding level was discovered is marked in Table 1 by an asterisk. For all lines classified by the corresponding new level, J-values, energies, and constants A and B of the combining level are given in columns 5 to 8. In column 9, the source of the A and B values in columns 7 and 8 is given. Column 10, comments, contains: nf means observation of LIF on a decay line of the lower level ("negative" LIF line), nf+ a strong LIF signal. Decay lines of the upper levels are marked with f. The wavelength of the LIF line is given without decimal places. For lines appearing in the FT spectra, the remark FT is given, followed by the SNR in the FT spectrum. Lines without comment are observed in the OG spectrum only and classified due to wavelength and hf pattern.
As can be noticed from Table 1, we confirmed the existence of the discovered levels also using laser wavelengths in the red region of the spectrum (6900-6100 Å). Of course, not all excitations of the predicted transition wavelengths were successful. However, sometimes due to such experiments, we discovered other new levels, which are also published in this work.
In Figures 1 and 2, typical OG records are shown. Classification of the visible lines is given in Table 2. Table 1. New La I energy levels and lines classified by these levels. E-energy; wl-wavelength; tw-this work. OG observation of only the OG signal. FT-wavelength determined from the Fourier transform spectrum with given SNR. nf-LIF line (phase opposite to the OG signal, "negative" LIF); nf+-strong LIF signal. f-LIF line (in phase with the OG signal). Wavelengths in column 10 are given without digits after decimal point.

Upper Even-Parity Level
Line Lower Odd-Parity Level  [27] nf 4800 nf 4887 nf+ 5173 nf 3641 + these levels were reported already in reference [14], but without list of all classified lines. The laser scan started in Figure 1 at 5858.68 Å. The high peak at ca. 4000 MHz frequency offset is the last hf component of a widely split line (5857.767 Å, cg frequency at −6945 MHz). The next weak structure belongs to a line at 5858.596 Å. Both these lines are transitions between well-known levels and thus, their wavelengths can be calculated from the level energies, using recently improved energy values [24]. The hf structure of the line at ca. 23,000 MHz frequency offset can be nicely fitted, assuming the hf constants and J-values given in Table 2, but we were not able up to now to classify the line. The last hf pattern at 5858.224 Å was also not classified. The wavelength of the last two lines was determined from the differences of the cg frequencies. After excitation with laser light at the wavelength of the highest peak of the last line, we observed strong LIF at 4494 Å, with an opposite phase relative to the OG signal, identifying the level at 24,910.373 cm −1 as the lower level of the excited transition. This line did lead to the discovery of the new level at 41,975.663(10) cm −1 , even parity, J = 3/2, A = 140(3) MHz. Z. Figure 2 shows a record in which we have changed the amplification of the OG signal by a factor of 10 after ca. 12,000 MHz scan offset, since we noticed in another scan, starting at the same wavelength of 5910.07 Å, that after the strong line at 5909.966 Å, there might be some structures. Indeed, two weak lines are now clearly visible. The line at 5909.870 Å could not be classified, but their cg wavelength could be easily determined from both other classified lines, using the differences of the cg frequencies.
Excitation of the unclassified line led to the observation of LIF at 4137 and 5639 Å, identifying the odd-parity level at 25,218.264 cm −1 as the lower level of the laser-driven transition, and finally, to the new even-parity level at 42,134.425(10) cm −1 , J = 5/2, A = 209.9(20) zMHz. MHz.
As can be seen from the figures, the separation of the hf components of some lines is quite small and certainly much smaller than the resolution of the experiment, in which the FWHM of the line components is limited mainly by Doppler broadening (about 800 MHz) and additional collisional broadening. These effects are treated in more detail in reference [11]. Thus, we cannot fit each hf component separately. Instead, for each line, a start envelope curve is generated by a simulation of the observed hf pattern, using features contained in "Elements" [12,19]. For already classified lines, J-values and hf constants are known, and the FWHM is adapted to obtain agreement between the recorded and simulated curve. For unclassified lines, as mentioned before, J-value and hf constants of the lower level are known, and we vary the A-factor of the new level and FWHM until we obtain agreement. These values are then the start values of the program "Fitter" [20], which minimizes the deviation between the simulated and observed hf pattern with a least squares procedure. The program allows us to determine which parameters are set to be fixed and which ones are treated as free parameters (e.g., A-factor of the new level, FWHM). Moreover, up to five spectral lines contained in one laser scan can be fitted simultaneously, even if their hf patterns are overlapping, and the program gives their cg frequency positions in the scan

Conclusions
This paper reports 17 previously unknown energy levels of La I, having even parity. For two further levels, reported in reference [14], the full list of classified transitions is given. These 19 levels made it possible to classify altogether 132 spectral lines. The discovery of the new levels can be seen as a contribution to find more and more energy levels of La, enabling a future theoretical description of the energy levels.