Experimental Investigation of the Hyperfine Structure of Neutral Praseodymium Spectral Lines and Discovery of New Energy Levels

Experimental investigations of Pr I spectral lines were performed by means of laser induced fluorescence spectroscopy, using a hollow cathode discharge lamp as source of free atoms. The wavelengths for the laser excitation were found by the help of a highly resolved Fourier transform spectrum. Altogether we excited 236 unclassified lines and analysed their hyperfine structure, which led, together with the measured wavelengths of the observed fluorescence lines, to the discovery of 32 new even parity and 38 odd parity fine structure energy levels. These levels allow to classify more than 670 spectral lines of Pr I. The wave number calibrated Fourier transform spectrum allowed us to determine the energies of most of these newly discovered levels with an uncertainty of 0.015 cm -1 . Angular momenta, parity, and magnetic and electric hyperfine interaction constants (A and B) of the new levels were also determined.


Introduction
Praseodymium is a rare earth element belonging to the lanthanides group.Its atomic number is 59, and it has naturally occurring only one stable isotope 141 Pr with nuclear spin quantum number I = 5/2.The ground state 4 I °9/2 belongs to the electronic configuration [Xe] 4f 3 6s 2 , having five valence electrons outside a Xenon-like electron core.Its nuclear magnetic dipole moment amounts to µ I = 4.2754(5) µ N (Macfarlane, Burum & Shelby 1982) and its nuclear electric quadrupole moment is Q = -0.0024b(Böklen, Bossert & Foerster 1975).Due to the five valence electrons, praseodymium has a very large number of fine structure (fs) levels and consequently an extremely line rich spectrum.
The first investigation of hyperfine (hf) structure in the spectrum of praseodymium can be traced back as early as 1929, when H.E. White (White 1929) investigated the wave number separation of hf structure components of 173 spectral lines.He was the first in determining the nuclear spin quantum number of 141 Pr.Since 1929 and over the span of five decades, several authors investigated the spectrum of praseodymium and discovered several electronic levels which were then collected and published in 1978 (Martin, Zalubas & Hagan 1978).A major contribution to the understanding and development of the spectrum of praseodymium (atom and singly charged ion) came from A. Ginibre (Ginibre 1981, Ginibre-Amery 1988, Ginibre 1989a, Ginibre 1989b).Her published (and also not yet published) work is based on the study of the fine and hyperfine structures in the configurations 4f 2 5d6s 2 and 4f 2 5d 2 6s of neutral praseodymium.In this work, she calculated the wave numbers for a large number of new fs levels and also determined their hyperfine interaction constants.In 1981, Childs and Goodmann, using an atomic-beam -laser-rf double-resonance technique, determined the hyperfine (hf) constants of several low-lying metastable electronic levels with high accuracy (Childs & Goodman 1981).Kuwamoto et al. (Kuwamoto et al. 1996) investigated the hf structure of Pr I lines by using an atomic beam of neutral praseodymium, crossed perpendicular with an exciting laser beam, and determined A and B constants for 57 levels.The energies of 11 fs levels were determined for the first time.Krzykowski et al. (Krzykowski, Furmann, Stefanska, Jarosz & Kajoch 1997) accurately determined the values of the hf structure constants of some lower levels belonging to the configuration 4f 3 5d6s and for the upper levels of the investigated Pr-I lines, excited by laser light.The group of G. H.
Guthöhrlein (Guthöhrlein 2005) investigated a big number of Pr I lines using laser-induced fluorescence spectroscopy.Unfortunately, most of the results are still not published.Based on the available experimental results, in 2003 J. Ruczkowski et al. applied a semi-empirical method to describe configuration and designation of the known Pr I levels (Ruczkowski, Stachowska, Elantkowska, Guthöhrlein & Dembczyński 2003).In 2006 Furmann et al. (Furmann, Krzykowski, Stefańska & Dembczyński 2006) reported hf structure investigations of Pr I lines and the discovery of 57 new electronic levels with odd parity.
Since 2004, the group in Graz is concerned with experimental investigations of the hf structure of praseodymium lines using laser induced fluorescence (LIF) spectroscopy (Uddin 2006).In parallel to the laser spectroscopic work highly resolved Fourier-transform spectra were also recorded.These spectra led to the discovery of more than 9000 previously unknown Pr I and Pr II spectral lines, from which more than 1100 could been classified (Gamper et al. 2011).Later on, we focused on searching for new fs levels of praseodymium and were able to discover a significant number of levels, some of which have already been published, see refs.(Uddin et al. 2012a, Shamim, Siddiqui & Windholz 2011, Syed et al. 2011, Uddin et al. 2012b, Siddiqui, Shamim & Windholz 2014, Uddin et al. 2012c, Uddin 2014, Gamper, Khan, Siddiqui & Windholz 2013, Siddiqui, Shamim & Windholz 2016, Uddin, Siddiqui, Tanweer, Jilani & Windholz 2015).
The present investigation of the spectrum of praseodymium not only broadens the understanding of the Pr I level scheme but is also of interest to astrophysicists (Ryabchikova, Savanov, Malanushenko & Kudryavtsev 2001, Dolk et al. 2002) in analysing the Pr abundance in various stars.
All wavelengths given in this paper are in Å in standard air.Conversion from wavelength to wave number was performed using the formula given by Peck and Reeder (Peck & Reeder 1972) for the refractive index of air.

Experimental Setup
A laser-induced fluorescence (LIF) technique in combination with Fourier transform (FT) spectroscopy is used for the investigation of the hf structure of lines in the spectrum of praseodymium.The experimental setup is shown in Fig. 1, and a detailed description of each component used is given in ref. (Shamim, Siddiqui & Windholz 2011).Excitations of Pr lines were performed by means of a tunable ring dye laser, pumped by a single frequency semiconductor diode pumped Nd-Vanadate (Verdi V-18) laser.The investigations were carried out in the spectral regions of the dyes Rhodamine 6G (5700-6100 Å) , Sulforhodamine B (6100-6300 Å), DCM (6300-6800 Å) and Stilbene 3 (4200-4700 Å).The source of free praseodymium atoms is a dc hollow cathode discharge lamp (HCL), filled with Ar as buffer gas, in which free praseodymium atoms were produced by cathode sputtering.One of the advantages of using a HCL is, that, as a result of collisional processes within the Ar-Pr plasma, free Pr atoms are not only produced in its ground state but also in high lying excited states up to about 25000 cm -1 .
Of course the HCL emits all spectral lines of Pr and Ar (and their first ions).In order to distinguish the light emitted from the HCL from LIF intensity, the exciting laser beam is modulated with the help of a mechanical chopper 1 (see Fig. 1).The light emitted by the discharge is dispersed by a monochromator whose output is detected by a photomultiplier.Only lines influenced by the laser light show the same modulation and are detected with the help of Lock-In amplifier 1.The LIF signal together with the transmission signal of a temperature-stabilized marker etalon are digitally stored in a computer for further analysis.
The investigation of a line begins by tuning the laser light wavelength into resonance with the wavelength of a hf component of the investigated line.This wavelength is extracted from the FT spectrum.As a result of the excitation one expects laser-induced fluorescence lines, which are then detected.If the upper level of the excited transition is known, the monochromator transmission wavelength can be set to an expected decay line of this level and the hf structure of the line can be recorded by scanning the laser light frequency over the transition.If the upper level is previously unknown, we first have to set the laser frequency to a strong hf component of the line (wavelength known from the FT spectrum) and to search for LIF lines by tuning the transmission wavelength of the monochromator.The function of chopper 2 and Lock-In amplifier 2 will be explained when discussing the discovery of the level at 19111 cm -1 .

Data evaluation and Analysis
The analysis of the recorded hf pattern can lead to the knowledge of parameters of the combining fs levels such as total angular momentum J and magnetic dipole and electric quadrupole hf constants A and B, respectively.In case of praseodymium, which has a very small nuclear quadrupole moment, the value of B is very small for most of the levels and is often neglected.Exceptions are high precision Doppler free laser spectroscopic methods like experiments on an atomic beams, where the hf constants can usually be determined with high precision, and so also small B factors are determined reliably (Krzykowski, Furmann, Stefanska, Jarosz & Kajoch 1997, Childs & Goodman 1981).The evaluation of the recorded hf patterns also gives an estimated center-of-gravity (cg) wave number of the excited line.Together with the values of J and A (and sometimes B) and the wavelengths of the experimentally observed fluorescence lines, the identification of the involved fs levels is possible.Of special interest is the excitation of lines which cannot be classified as transitions between already known energy levels.
In such cases the wavelengths of the fluorescence lines are previously unknown and have to be found by tuning the monochromator which disperses the light emitted by the discharge.
If now one of the combining levels is already known, let us say, the lower level, the energy of the upper combining unknown level is determined by adding the cg wave number of the line to the energy of the lower level.On the other hand, if an upper level is already known, the energy of lower combining unknown level is determined by subtraction of the cg wave number from the energy of the upper level.In the worst case, where both the combining levels are not known, only the observed fluorescence wavelengths can be used for the determination of the energies of the combining levels.For a detailed description of the method see ref. (Uddin et al. 2012a).
In an otherwise slightly simpler situation, where one (or several) of the observed fluorescence lines are in the wavelength range of our laser, laser excitation of a former fluorescence line can be performed and the hf pattern can be recorded on the previously excited line.Since the probability that a previously unknown energy level decays to an already known level is high, the energy of the new upper level can be determined.In each case, at least one of the levels involved in the excited transition must be identified.

Discovery of the New Level at 19111.80 cm -1 , Even Parity, J = 13/2, A = 762 MHz
A quite prominent line at 5636.940 Å, appearing in the FT spectrum with a high signal-to noise-ratio (SNR) of 140, was experimentally investigated using laser spectroscopy.The line exhibits a well-defined hf structure with clearly visible hf pattern, but with unresolved hf components, see Fig. 1.The line could not be classified using already known level energies, thus we had to assume that a previously unknown energy level is involved in the transition.
Laser excitation was performed by tuning the laser wavelength to the highest peak of the pattern at 5636.92 Å.A single fluorescence line at 5228 Å was observed when tuning the transmission wavelength of the monochromator from 3000 Å to 7000 Å. Observation of only one LIF line can happen when the upper level has only a few number of decay channels or has a very low transition probability for the other lines.The hf structure of the line was recorded by scanning the laser frequency across the line.The LIF spectrum had a good signal-to-noise ratio and showed the hf structure pattern as appearing in FT spectrum, but with higher resolution (Figure 2).
The recorded hf structure was then fitted assuming different pairs of J-values for upper and lower level.For this, the program "Fitter" was used (Guthöhrlein 1998) which minimizes the sum of the squares of the differences between measured and calculated intensity values (ESS).The best fit situation with the lowest ESS value was obtained for J up = 13/2, J lo = 11/2, A up = 762 MHz and A lo = 733 MHz, see Figure 3.The cg wavelength obtained from the fitting procedure was 5636.940Å.First we assumed that an unknown upper level is involved in the excitation of the investigated line.Therefore we searched in our database of known energy levels for a level having J = 11/2 and approximately the A-value from the fit.Several levels, having both even or odd parity, fulfilled these requirements (see Table 1).Hypothetical new levels were calculated by adding the cg wave number of the excited line at 5636.940 Å (17735.198cm -1 ) to the energies of these levels.Then we calculated possible decay lines of the hypothetical levels, but none of them could explain the observed LIF line at 5228 Å.Thus we repeated the procedure assuming that a new lower level is involved, but still without any success.Next we thought about a possible scenario in which both the lower and upper of the combining levels are not known and were yet to be discovered.But to solve such a situation the wavelengths of at least two LIF lines have to be determined with high precision.The method is described e.g. in ref. (Windholz 2016).But here we obtained only one LIF line, so this scenario cannot be resolved.
Nevertheless, we tried to find a more accurate value of the fluorescence wavelength.The light emitted by the HCL was modulated using a second mechanical chopper, working with much higher frequency than the first chopper, modulating the intensity of the exciting laser light.The output of the photomultiplier was given now to two Lock-In amplifiers, one set to the chopping frequency of the laser light and the second one to that of the light emitted by the HCL.The laser frequency was fixed to the strongest hyperfine component of the line 5636.940Å and the monochromator transmission wavelength was tuned around the line 5228 Å (from 5210 to 5240 Å).Both output signals of the LI-amplifiers were recorded simultaneously (see Figure 4).One trace now shows the LIF signal, obtained when the transmission wavelength of the monochromator agrees with the LIF line.The second trace shows the emission spectrum of the HCL.This spectrum now can be wavelength calibrated with help of the FT spectrum.In this way the high wavelength precision of the FT spectrum can be used to determine the LIF wavelength with an uncertainty of lower than 0.1 Å, despite of the fact that the monochromator used has a resolution of only 1 Å.The determined value of the fluorescence wavelength was 5227.97(10)Å.
In the FT spectrum there is a very strong line (SNR = 5300) at 5227.968 Å, see figure 5.This line is already classified as a transition from the ground level to a known low lying upper level at 19122.567 cm -1 , even parity, J = 11/2.Thus we had to believe that the observed LIF line is this strong line.
Thus again we came back to searching for a new lower energy level.But a fit of the recorded structure (Figure 2) is not possible with low ESS taking the hf constants of the level 19122.567cm -1 as fixed values in the fitting procedure.This suggested that the upper level involved in the excitation of line at 5636.940 Å is not 19122.567cm -1 .Thus we had to conclude that the observed LIF line at 5636.940 Å is not a direct decay line of the new energy level.In this case we have to assume that the new level has an energy close to 19122.567cm -1 and that the laser-induced enhancement of the population of the new level is (at least partly) transferred to 19122.567cm -1 by collisions.
We now treat again the list of lower levels having J = 11/2 and A close to 733 MHz as determined by the fit procedure.For the energy of the level we expect 19122 ± 1000 cm -1 due to the assumed collisional coupling.The wave number of the excited line is 17735 cm -1 .This gives 19122 ± 1000 -17735 = 1387 ± 1000 cm -1 for the lower level of the excitation.Indeed, as can be seen from Table 1, only one level, 1376.602cm -1 , even parity, is located in the estimated energy region.
Moreover, when fitting the pattern shown in Fig. 2 with A-and B-values for the lower level, the best fit (lowest ESS) is obtained for 1376.602cm -1 as lower level.
The odd parity level at 1376.602 cm -1 , J lo = 11/2 and A lo = 730.393MHz, B lo = -11.877MHz is the lowest metastable level of Pr I, the nearest neighbour of the ground level.Taking now this level as the lower one of the laser excitation, we obtain a new even parity level at 19111.80 cm -1 , having J = 13/2, A = 762(2) MHz.B is assumed to be zero.
The newly calculated hypothetical level was then confirmed by a second laser excitation.First we calculated possible decay lines of the newly introduced level to lower levels.From this list we tried to excite lines in the wavelength range of our lasers.We were successful with the line 6146.45Å, which appears in the FT spectrum with SNR = 24.Again we observed a strong LIF signal at the collisionally coupled line 5228 Å.The correct cg wavelengths of both excited lines were determined from the FT spectrum, i.e. 5636.940Å and 6146.447Å.The energy of the lower levels were already corrected earlier, therefore the energy of the newly discovered level could be determined with less uncertainty to be 19111.800(10)cm -1 .The magnetic and electric hf constants for the lower combining levels 1376.605cm -1 and 2846.741cm -1 were determined with high precision using laser-atomic beam spectroscopy [31,9], therefore from a repeated recording of both laser-excited lines, the electric quadrupole hf constant for the newly discovered upper level could also been determined.Therefore the hf constants of the new upper level are finally A = 760(1) MHz, B = -20(10) MHz.
Table 1 shows the energies of all the possible combinations of known lower levels and calculated upper levels for the line 5636.940Å.It also displays the ESS value of the best fit situation for each combination of J-and A-values of the combining levels (A-and B-values of the lower levels fixed during the fitting procedure).With the help of a calculated list of decay lines of higher lying odd levels to the new level we could classify two further lines in the FT spectrum (7586 and 9632 Å, see Table 2).One additional excitation was also successful (at 7086.57Å, transition to the upper level 32289.455cm -1 , odd parity).The complete scheme of all transitions in which the new level is involved is shown in Figure 7.

Results and Discussion
In similar way as decribed for the level 19111 cm -1 in chapter 4, or using methods described in ref. (Windholz 2016), we found altogether 70 previously unknown energy levels of Pr I.
The data of all newly discovered levels are given in Table 2.The levels are listed separately for even and odd parity and are sorted by their value of J and their energy.In col. 1 the value of J is given, in col. 2 the level energy together with its estimated uncertainty (one standard deviation) is given.In col. 3 the magnetic dipole hf constant A is given.With the exception of the level at 19111 cm -1 , the electric quadrupole hf constant B could not be determined reliably and therefore was assumed to be zero.In the next column the cg wavelengths at which laser excitation was performed, are given.Values having three figures after the decimal point are determined with help of the FT spectrum, the other values with help of the lambdameter measuring the laser wavelength (uncertainty  0.01 Å).Wavelengths of observed fluorescence lines are given in Col. 5. Lines in the FT spectrum classified due to their cg wavelength and hf pattern are given in col.6.Some levels were discovered as lower levels of the excited transitions, and their existence was detected by decay lines of the combining upper levels.In such cases one finds in col. 5 the entry "see Table 3".In Table 3 all lines classified by new levels, which were discovered as lower levels of the excited transitions, are listed.
Once such (hypothetical) level was introduced, its existence was checked by trying excitation from this level to other known upper levels.In such case we expect laser-induced decay lines from the known upper level.Thus in Table 3 also the observed fluorescence channels are mentioned.In cols.1-3 the data from Table 2 are repeated (J, energy and A).In cols.4-6 the excited line is given.If the line appears in the FT spectrum, the cg wavelength is given with three figures after the decimal point, and in col.6 the SNR is given.If the cg wavelength is given with only two figures after decimal point, the cg wavelength is determined with the lambdameter measuring the laser wavelength, and in col.6 SNR is set to 1.In col. 5 (C.) a comment is given: nl means a previously unknown spectral line not contained in commonly used spectral tables (e.g.Harrison 1969), cl means that the line was already known (in most cases from the work of A.Ginibre (Ginibre-Amery 1988)), but not classified.e means the line was excited by laser light.The data of the combining upper level are given in cols 7-9.Some of these are previously unknown levels but discovered within this work.If a decay of the upper level was observed, wavelength and SNR in the FT spectrum are given.nl means again a previously unknown line.
If in col.12 SNR = 1 is given, the LIF on this line was observed, but the line does not show up in the FT spectrum.In cols.13 and 14 J and energy of the lower levels of the LIF lines are given.Finally in col.15 a reference to the source of hf constant A (given in col.9), used when determining the A-value of the new level (given in col.3), is given.
Table 4 contains the lines classified by the newly found even levels, which were discovered as upper levels of the investigated lines.The structure of the table is similar to Table 3.A comment (C.) f means the line was observed as LIF line.The lines classified by the discovered upper odd levels are given in Table 5.

Conclusion
Experimental investigation of the hyperfine structure of Pr I lines is reported in this paper.The investigation resulted in the discovery of 70 Pr I fs levels having even and odd parity.The magnetic dipole interaction constants A of all new levels could be determined, and for one level also the very small electric quadrupole interaction constant B. The investigation is carried out in the spectral regions of Rhodamine 6G, Sulforhodamine B, DCM and Stilbene 3. Furthermore the discovery of these levels led to the classification of ca.670 praseodymium spectral lines.
Appendix: Full versions of Tables 4 and 5 Table 4. Lines classified by the newly discovered even levels.

Figure 2 .
Figure 2. Line 5636.940Å in the FT spectrum of Praseodymium

Figure 4 .
Figure 4. Best fit situation of the recorded hyperfine structure of line 5636.940Å.The lower trace shows the residual between experimental and fitted hf pattern (x 0.5)

Figure 7 .
Figure 7. Level scheme of all observed lines classified by the new level at 19111 cm -1 .Laser excitations are shown as arrows; lines classified in the FT spectrum as thin full lines.The observed LIF at 5228 Å is an indirect line caused by collisionally induced population transfer.Wave numbers in cm -1

Table 1 .
All the possible combinations of known lower levels and calculated upper levels for the line 5636.940Å

Table 2 .
Previously unknown energy levels of Pr I discovered within this work

Table 3 .
New energy levels discovered as lower levels of the excited transitions

Table 4 .
Lines classified by the newly discovered even levels