Experimentally determined oscillator strengths in Rh II

This paper presents new experimentally determined branching fractions and oscillator strengths (log gf) for lines originating from 17 levels belonging to 5 terms of the first excited odd configuration 4d7(4D)5p in Rh II. The intensity calibrated spectra of Rh II have been recorded with a Fourier transform spectrometer between 25000 and 45000 cm−1 (2200–4000 Å). In this region, 49 lines have been identified and measured. By combining the branching fractions obtained from the spectra with previously measured lifetimes, log gf values are reported. The new results are compared with previous theoretical work.


Introduction
Rhodium is one of the most expensive metals on earth and finds its use in the automotive industry as a catalyst. Of more scientific interest is the fact that rhodium has been detected in the spectra of many astrophysical objects e.g. the sun [1], and the HgMn-type stars χ Lupi [2], HD 65949 [3] and HD 175640 [4]. The need for accurate and reliable atomic data in order to investigate high-resolution spectra from objects such as these is significant, and to the best of our knowledge no experimental oscillator strengths are available for Rh II. In a recently published study, Quinet et al [5] combined measured lifetimes with theoretical branching fractions (BFs) and derived semiempirical oscillator strengths. The lifetime measurements were performed on ions in a laser-generated plasma employing the time-resolved laser-induced-fluorescence technique, and the calculations were performed with a relativistic Hartree-Fock model with core-polarization (HFR+CPOL). This paper aims Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. to experimentally evaluate the reliability of these oscillator strengths and further enhance our knowledge of Rh II.
A schematic drawing of the lower part of the energy level structure of singly charged rhodium can be seen in figure 1. When measuring BFs, extensive knowledge of the energy level structure of the system of interest is necessary since accurate values require the measurements of all lines originating from an upper level. The line list used in this work was compiled by Kramida et al [6] and based on earlier work by Sancho [7]. In this study, BFs for transitions from terms belonging to the first excited d 7 ( 4 D)5p configuration are measured and combined with previously published experimental lifetimes [5]. More specifically, levels belonging to the terms z 5 F o , z 5 D o , z 5 G o , z 3 F o and z 3 G o are investigated.
The main decay channel for the quintet terms in the 4d 7 ( 4 D)5p configuration is to levels in the a 5 F term belonging to the configuration 4d 7 ( 4 F)5s. However, they also decay by inter-combination transitions to states in the ground configuration (4d 8 a 3 F). The latter transitions fall in the vacuum UV, and cannot be measured in the present experiment. This is a potential problem in the BF determinations for these levels. However, in most cases, the inter-combination lines  are weak and their influence can be estimated from these theoretical calculations.

Experiment
To determine the oscillator strengths, it is necessary to measure the lifetime of the upper level as well as the relative intensities of all lines originating from that level. The branching fraction, BF, is defined as where u labels the upper and l the lower level, respectively. A is the transition probability and I is the measured intensity in units of number of photons per second on an accurately calibrated scale over the whole wavelength range. Combining the BFs with the lifetime defined as allows for the extraction of the individual A ul -values as The oscillator strength, f lu , is then derived through the formula where g is the statistical weight and λ ul is the wavelength (in A) of the transition in question.

Determination of branching fractions
A hollow cathode (HC) discharge was used as the emission light source. The HC has a hollow iron core where a thin foil, 0.125 mm thick and 25 × 25 mm wide, was inserted. The foil consisted of 99.9% rhodium. The HC was operated at currents between 0.1 and 1 A and neon was used as a carrier gas. The typical pressures during the measurements were around 1.6-1.8 torr. The light emitted from the cathode was analysed by an FTS instrument (Chelsea Instruments FT500). The instrument itself restricts the wavelength region to be covered in the spectra since it has a beamsplitter which cuts off at 1850Å. However, this was not the main limitation since the optical path between the HC and the FTS instrument was in air, hence no wavelengths below 2000Å could be measured. Another restriction posed on the obtained spectra is the sensitivity of the detectors used when recording the spectra. To cover the region of interest, two different detectors were used. In the region between 25000 and 40000 cm −1 , a Hamamatsu 1P28 photo multiplier tube (PMT) was used, whereas the region between 35000 and 45000 cm −1 was covered by a Hamamatsu R166 PMT. To avoid the aliasing inherent in the FTS method, a standard UG5 coloured glass filter (cutoff around 6500Å) was used in combination with the 1P28 detector to limit the aliasing with longer wavelengths where the detector is sensitive. In figure 2, two complete spectra recorded with the two different detector setups are shown, displaying their sensitivity, as well as their relative strengths in the overlapping region.
Promptly after measuring a series of rhodium spectra, a spectrum of a calibrated deuterium lamp was recorded. The deuterium spectrum was then used to determine the response of the detectors. For the determination of BFs, no absolute calibration is necessary; only the relative intensities are of interest. However, the spectra recorded with the different detectors have to be brought to a common scale. This was done by comparing the intensities of lines recorded by both detectors in the overlapping region. Thus, the scaling factor between the two regions was determined by taking the ratios  [5]. b The wavelengths are from Sancho [7] except the starred ones which are calculated from the energy levels. between a number of lines recorded by both detectors. The variation of this ratio gives an uncertainty in the detector response determination. The wavenumber scale is given by an internal laser in the FTS controlling the sampling rate. The relative uncertainty in the wavenumber scale is around 10 −6 and allowed us to unambiguously identify all the lines of interest.

Results
Rhodium has only one stable isotope which makes the interpretation of the spectra easier with no isotope shift present. Furthermore, it has a nuclear spin of I = 1/2 so at most two possible hyperfine components of each level are possible. However, this splitting was too small to be resolved. For all the observed lines, the GFit [8] software was used to fit Gaussian line shapes to determine line positions as well as to obtain the area of the peaks. The fits were in general good and the result of one particular fit can be seen in figure 3. The line in the figure has a full-width at half-maximum of 0.155(2) cm −1 at 31643.9 cm −1 . For some of the strongest lines (with A-values around 10 9 s −1 ), a small asymmetry was observed which affected the goodness-of-fit, but to a lesser extent the uncertainty in the area determination. The reason for this asymmetry is most likely imperfections in the alignment of the optical path of the FTS instrument. In the determination of the oscillator strengths, there are several uncertainties contributing to the final uncertainty stated in table 1: the uncertainty in the area determination, the intensity calibration of the spectra (with the use of the deuterium lamp) and the lifetime. These are then added quadratically to obtain the total uncertainty. A detailed description of the uncertainty analysis can be found in [9]. In general, the main contributor to the uncertainty budget is the previously measured lifetimes, which in some cases have uncertainties around 15%. Whether a line is observed or not is due to the combination of the sensitivity of the detection setup at the wavelength of the line and the intrinsic line strength. In general, lines weaker than A ≈ 4 × 10 7 s −1 [5] were not observed or the signalto-noise ratio was too low to provide a satisfactory fit of the observed line. Contributions from lines not measurable in the spectra or outside of the range of the detectors are summed up using the theoretical BF from Quinet et al [5] into a residual. The experimental BFs are then adjusted to accommodate the missing branches, i.e. they are scaled down to make the sum of all measured-and estimated-residual branches equal to 1. The main decay channel for some of the triplet terms is to the ground configuration. The estimation of the missing branches for these levels can therefore be up to around 50%.
The result can be seen in table 1. The log(gf ) values ordered by wavelength can also be found in table 2. The agreement between the theoretical and experimental BFs is in general good. The ratio between the experimental and theoretical BFs plotted against the experimental BFs can be seen in figure 4 and against the wavenumbers in figure 5.
In figure 4, it can be seen that the weaker lines have larger uncertainties, originating primarily from the uncertainty in the area determination of the peaks. It can also be seen that the ratios form two groups, one which is centred slightly above and the other slightly below. When looking in more detail, it is found that spin-forbidden lines from the quintet to triplet states  Figure 5. Ratio between our measured branching fractions, BF exp , and the theoretical branching fractions from Quinet et al [5], BF theory , plotted against wavenumber.
(e.g. b 3 F 4 -z 5 F o 4 ) are seen below one group and spin-allowed (e.g. a 5 F 3 -z 5 F o 3 ) lines are seen in the other group. This trend suggests that the mixing of levels in the calculations could be overestimated, resulting in stronger spin-forbidden lines. The same trend can be seen in figure 5 where the spin-forbidden lines, with in general lower wavenumbers due to the energy level structure, can be seen to the left in the picture and the allowed to the right, indicating as in figure 4, that the mixing is overestimated in the calculation.

Conclusions
Branching fractions for 49 Rh II lines were measured for the first time using an FTS instrument and an emission source. The BFs have been combined with previously measured lifetimes by Quinet et al [5], to yield oscillator strengths for these transitions. The deviations between our measured and the theoretical BFs are mostly within the uncertainty limits. However, our data suggest a slight overestimation of the mixing leading to higher theoretical BFs-and thus log(gf )for the spin-forbidden lines.