Experimental Branching Fractions, Transition Probabilities, and Oscillator Strengths in Sm ii

Branching fractions (BFs) of Sm ii for 71 lines from 12 excited levels ranging from 31,638.79 to 35,463.91 cm−1 were determined for the first time based on the Fourier transform spectra available from the National Solar Observatory database. New transition probabilities and oscillator strengths for these lines were derived by combining the determined BFs with reliable lifetimes measured using a time-resolved laser-induced fluorescence technique. Furthermore, BFs for 38 lines from five levels included in earlier studies were also determined for comparisons. The new results reported in this work will be useful in many fields, especially for astrophysics.


Introduction
The knowledge of accurate experimental radiative parameters such as radiative lifetimes, branching fractions (BFs), transition probabilities, and oscillator strengths for rare-earth (RE) elements plays an important role in a variety of scientific fields and applications (Weeks et al. 2021).For example, in theoretical research, RE atoms and ions are characterized with open 4f shells causing strong relativistic effects and configuration interactions that make it difficult to construct reasonable theoretical models.Accurate experimental parameters are critical for checking and perfecting these models (Yu et al. 2019).In plasma characterization, the oscillator strength of a spectral line is the necessary parameter to obtain the Boltzmann factor and the line width (Aragón & Aguilera 2008).In lighting applications, the rich optical spectra of RE elements make them increasingly used in metal-halide arc lamps.Transition probability data are the basic parameters for modeling and diagnosing these lamps (Biémont & Quinet 2003).
Radiative parameters are also essential for the determination of elementary abundances in stellar atmospheres (Geng et al. 2022;Irvine et al. 2022).Recently emerged new detection technologies have made it possible to record stellar spectra with a high resolution and high signal-to-noise ratio, in particular for singly ionized RE elements because their rich visible spectra are easily accessible from ground-based observatories.The recorded spectra have greatly increased opportunities for elemental abundance study, which is particularly important for testing and refining the s-, r-and p-processes in nucleosynthesis.Radiative parameter determinations, particularly for singly ionized samarium (Sm II), have been investigated by several groups with the Sm II lines being observed in many different stellar objects like the Sun, Ap, Am, or Bp stars, Ba stars, and C-or S-type stars (Xu et al. 2003).
In the period from 1975 to now, radiative lifetimes were measured using the beam-foil technique, delayed-coincidence technique, beam-laser technique, time-resolved laser-induced fluorescence (TR-LIF) technique, and other techniques (Andersen et al. 1975;Blagoev et al. 1978;Vogel et al. 1988;Biémont et al. 1989;Scholl et al. 2002;Xu et al. 2003;Lawler et al. 2006;Zhang et al. 2011).Among these, TR-LIF is regarded as the most reliable technique (Wang et al. 2021).For BFs, the most frequently used method is analyzing the emission spectrum from a hollow-cathode lamp (Saffman & Whaling 1979;Lawler et al. 2006).In addition, Rehse et al. (2006) measured BFs of 69 Sm II levels using the spectrum of laserinduced fluorescence from a velocity-modulated 10 keV ion beam.In theoretical research, Xu et al. (2003) calculated BFs for 162 transitions with the relativistic Hartree-Fock (HFR) method.Transition probabilities and oscillator strengths for Sm II were determined with two methods; one of them was using optical nutation with a fast Doppler-switching technique (Kastberg et al. 1993), the other was to combine lifetimes with BFs, which is generally considered to be a more accurate method (Saffman & Whaling 1979;Xu et al. 2003;Lawler et al. 2006;Rehse et al. 2006).
Although radiative parameters for Sm II have been reported by several groups, the available data remain insufficient, because for some levels whose lifetimes were reported in the literature, corresponding BFs, transition probabilities, and oscillator strengths have not been investigated.Thus, this work is focused on the determination of radiative parameters for Sm II to meet the needs in many fields including astrophysics.Specifically, BFs were determined based on emission spectra recorded using a Fourier transform (FT) spectrometer.Moreover, we also deduced corresponding transition probabilities and oscillator strengths by combining our BFs and reliable lifetimes published in the literature.

Branching Fraction Determinations
The BF R ki for the transition λ ki is defined as where A ki is the transition probability from the upper-level k to lower-level i and the sum in the denominator includes all The Astrophysical Journal Supplement Series, 271:51 (7pp), 2024 April https://doi.org/10.3847/1538-4365/ad2f32 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.electric-dipole-allowed transitions.The transition probability A ki can be expressed as where I ki is the spectral intensity, in units proportional to photons per second, and N k and g k are the population and statistical weight of the upper level, respectively (Jiang et al. 2012).Then, by combining Equations (1) and (2), the BF R ki can be given as In this work, the intensities were obtained from the spectra available from the digital library of the National Solar Observatory (NSO) in Kitt Peak, USA1 and listed in Table 1.These spectra were emitted from hollow-cathode discharge (HCD) lamps operating at both high and low currents and recorded with an FT spectrometer that has a high spectral resolution, excellent wavenumber accuracy, and broad spectral coverage from UV to IR.The spectra with indexes from 1 to 7 whose carrier gas was Ar were used in our BF determinations, and index 8 recorded with Ne as the carrier gas was only used to separate possible blends between Sm II and Ar lines.These spectra cover from 7929.160 to 34,997.638cm −1 and have a limit of resolution of 0.053 cm −1 .The spectrum with index 5 was recorded with 50 coadds to obtain a high signal-to-noise ratio for weaker lines.
The naturally occurring Sm isotopes include five even (nuclear spin I = 0) isotopes: 144 Sm (abundance 3.1%), 148 Sm (abundance 11.3%), 150 Sm (abundance 7.4%), 152 Sm (abundance 26.7%), and 154 Sm (abundance 22.7%); and two odd (nuclear spin I = 7/2) isotopes: 147 Sm (abundance 15.0%) and 149 Sm (abundance 13.8%).Thus, several Sm II lines have hyperfine structures and show some broadening.This being the case, observed line intensities were obtained via the integral areas under the line profiles.However, these intensities cannot represent the intrinsic line intensities I ki because the instrument system and any other components in the light path or any reflections can cause the recorded spectra to have wavelengthdependent optical properties.The determinations of spectral responses at different wavelengths were indispensable.According to Equation (3), the BFs depend on the ratio of line intensities.Therefore, we just need to determine relative spectral response as the function of wavelength to put the spectra on the same relative intensity scale.A reliable method to obtain the relative spectral response function is a comparison of branching ratios for Ar I and Ar II lines, which have been accurately reported in the literature (Hashiguchi & Hasikuni 1985;Whaling et al. 1993), to the intensity ratios determined for the same lines.Then by dividing the observed line intensities with a spectral response function the I ki values were determined, from which the BFs were derived.The BF uncertainties arise from the observed line intensity uncertainties and the calibration uncertainties.The former were determined using the function which had been described in detail by Sikström et al. (2002), while the latter depend on branchingratio uncertainties and intensity uncertainties of the chosen of Ar lines.
In the spectral calibration and BF determinations, the used spectra were recorded with both high and low currents.Therefore, we need to consider the influence of self-absorption because if the spectrum is recorded with a higher current, the density of atoms and ions is sufficiently high, which may result in the reabsorption of emitted photons within the emitting plasma (Sikström et al. 2002).Since the self-absorption depends on the atom and ion density, it is more likely to affect stronger lines.This self-absorption reduces the apparent intensity of the line, thereby changing the branching ratios relative to other lines from the upper level.In spectral calibration and BF determinations, we compared the intensity ratio of two lines originating from the same upper level as the function of current in the light source.If this ratio remains constant, it indicates that neither of the lines is affected by it, and vice versa.The spectra with indexes 2, 3, 6, and 7 recorded with low currents have this effect significantly reduced, but some of the weaker lines are missing in them.In this work, we have verified that there is no noticeable self-absorption in the used spectra, and at the same time, the spectra recorded at high currents ensured the appearance of weaker lines.Although the high spectral resolution helps to avoid most blends from the carrier Ar gas, an additional spectrum with index 8 emitted from a Ne-filled Sm HCD lamp was also used to make sure that the investigated Sm II lines were correctly identified.For some levels having branches blended with Sm I lines, we compared branching-ratio data, which were determined based on the spectra recorded at different currents, to judge whether blends exist or not.Similarly, some Sm II lines of interest are blended with other Sm II lines.If the blended lines are weak branches, they have been kept in the BF normalization, but dropped from Table 2 and considered as residuals.Otherwise, the levels have   been omitted from the BF determinations.A similar approach was used for very weak branches with large uncertainties.

Results and Discussion
In this work, we determined BFs of Sm II for 12 excited levels ranging from 31,638.79 to 35,463.91 cm −1 .These results are listed together with the standard uncertainties in Table 2.For strong branches (R ki > 0.2), the BF uncertainties are within ±15% and the vast majority are within ±10%.Besides, Table 2 also lists the deduced weighted transition probabilities, gA, and oscillator strengths on a logarithmic scale, log(gf ).The radiative lifetime τ k of the upper-level k is expressed as the inverse sum of transition probabilities of all lines from this level, Then, according to Equation (1), the transition probability A ki can be derived by combining the radiative lifetime and BF, The relationship between the oscillator strength f ik and transition probability A ki is given as follows: where σ is the wavenumber of the transition in cm −1 and g k and g i are the statistical weights of the upper and lower levels, respectively (Martin et al. 2023).We can see clearly that the transition probability and oscillator strength values can easily be derived by combining lifetimes and BFs, and the corresponding uncertainties also depend on these two parameters, which have been described in detail by Sikström et al. (2002).
In addition, in order to verify the correctness of the procedure used in this work, Table 2 also includes published gA and log(gf ) for the levels at 21,655.42, 25,304.09, 25,980.32, 27,063.30, and 33,598.70cm −1 , as determined by Lawler et al. (2006) using some of the same spectra as utilized in this work.Good agreement can be seen between our results and those by Lawler et al. (2006).Take the gA values as examples: using our data as a reference, the mean difference between our and their values is −0.53% and the rms difference is 8.32%.Figure 1 shows the comparison of gA values between  (This table is available in machine-readable form.)these two works.The good agreement in gA values also indicates concordance in the BF results, since both sets of gA values were derived by combining lifetimes and BFs, and we adopted their lifetimes.It is worth noting that the FT spectrometer, which recorded the spectra for both studies, has been used in BF determinations for many atoms and ions, particularly for complex rare-earth atoms and ions (Lawler et al. 2013;Den Hartog et al. 2015;Yu et al. 2022).Furthermore, for the three levels at 21,655.42, 25,304.09, and 25,980.32cm −1 , Rehse et al. (2006) also measured BFs in a fast-ion-beam laser-induced-fluorescence experiment.They used these data together with previously published lifetimes to infer gA and log(gf ).We see that there is some weaker but still acceptable agreement for the two levels at 21,655.42 and 25,980.32cm −1 .The gA differences lie within 20% with the exception of very weak branches (R ki < 0.1).However, a serious discrepancy is found for the level at 25,304.09cm −1 .This serious discordance is mainly caused by the transition at 732.705 nm, which was determined to have a BF of 0.013 in this work and of 0.43 by Rehse et al. (2006).The BF for this line reported by Rehse et al. (2006) in their Table 3, 0.43, is likely a technical error.According to Equation (2) provided by Rehse et al. (2006) and the relative intensity values listed in their Table 2, the BF value should be 0.32.Nevertheless, the serious discrepancy remains.A comprehensive analysis of the discrepancy with the results of Rehse et al. (2006) has already been extensively addressed by Lawler et al. (2008), and we will not delve into it here.In this work, we carefully analyzed this line and made sure that it was correctly assigned.
For the odd-parity level 27,063.30cm −1 , gA and log(gf ) values were also reported by Xu et al. (2003) and Saffman & Whaling (1979).Figure 2 is a comparison of our gA values with those determined by Xu et al. (2003) and by Saffman & Whaling (1979).The extremely weak line at 410.147 nm (R ki = 0.004) for which our results disagree with Xu et al. (2003) by roughly a factor of 10 is not included in Figure 2. Xu et al. (2003) gave two sets of gA and log(gf ) values.One set is their calculated results based on the HFR method and the second one is the corrected values determined by combining the HFR BFs and measured lifetimes.Considering the better reliability of theoretical BFs as compared to gA values, we used the second set for comparison.However, a larger discrepancy still appears between our results and those of Xu et al. (2003), not only for the weak lines but also for some strong lines.In the paper of Xu et al. (2003), the authors pointed out that a large number of calculated odd-parity levels mixed with each other, making it difficult to establish an unambiguous correspondence between the calculated and the experimental values.In view of this, we speculate that the results given by Xu et al. (2003) could be less accurate for odd-parity levels such as the level at 27,063.30cm −1 .A poor agreement is also seen between our results and those by Saffman & Whaling (1979), as shown in Figure 2. The gA values reported by Saffman & Whaling (1979) were computed from their measured BFs and estimated lifetime based on the data given by Andersen et al. (1975).Considering the inaccuracy of the estimated lifetime, we combined the BFs from Saffman & Whaling (1979) with the lifetimes measured using the reliable TR-LIF technique reported by Lawler et al. (2006) to derive corrected gA and log(gf ) values and found a respectable agreement with our data, except for the weaker line at 501.661 nm (R ki = 0.043).The comparisons are also presented in Figure 2. Thus, we can conclude that disagreements with Saffman & Whaling (1979) are mainly due to inaccurate lifetimes used by them.
In conclusion, this paper is devoted to determination of radiative parameters for Sm II levels to meet the needs in astrophysics and other fields.Specifically, BFs of Sm II for 71 lines from 12 excited levels have been determined for the first time by using archival FT spectra.Based on these data, new transition probabilities and oscillator strengths have been derived by combining the determined BFs with reliable lifetimes measured in other works using the time-resolved laser-induced fluorescence technique.

Figure 1 .
Figure 1.Comparison of A values from Lawler et al. (2006) to our A values as a function of our gA values.The error bars correspond to the greater of the two reported uncertainties due to strong correlation between the two data sets.The dashed line corresponds to the equality between them.

Figure 2 .
Figure 2. Comparison of A values from references to our A values as a function of our gA values.Specifically, the open triangular symbols represent the natural logarithm of the ratios A Xu et al. (2003) /A TW .The open circle symbols represent the natural logarithm of the ratios A Saffman & Whaling (1979) /A TW .The filled circle symbols represent the natural logarithm of the ratios A SL /A TW , while A SL values are derived by combining BFs from Saffman & Whaling (1979) and reliable lifetimes from Lawler et al. (2006).The error bars correspond to uncertainties combined in quadrature.The dashed line corresponds to the equality between them.

Table 1
Parameters of the FTS Spectra Used in this Work All spectra are publicly available from the digital library of the NSO on Kitt Peak, USA (https://nispdata.nso.edu/ftp/FTS_cdrom/).

Table 2
Branching Fractions (R kj ), Transition Probabilities, Oscillator Strengths of Sm II Levels, and Comparison with Previous Results