Fe i Oscillator Strengths for Transitions from High-lying Odd-parity Levels

Iron is one of the most-studied elements within the field of astronomy due to its important presence in stellar spectra. With a very complex spectrum, neutral iron presents thousands of transitions across a very wide spectral range, from the ultraviolet to the infrared. A very comprehensive study of its spectrum was undertaken by Nave et al. (1994), which provides an extremely useful guide for the identification of Fe i spectral lines in astronomical spectra. However, of the 6758 lines included in the National Institute of Standards and Technology (NIST) atomic database (Kramida et al. 2011) in the spectral interval ranging from 200 to 1050 nm, only a small percentage possess accurate values of transition probabilities.

Atomic oscillator strengths (transition probabilities, log $({gf})$) are essential to model stellar line intensities and to calculate not only chemical abundances, but also other stellar parameters. In particular, the iron spectrum is of the utmost importance to obtain stellar metallicities, as this property is directly linked to the iron abundance. However, the quantity and quality of the existing data lies far from the current needs of the astronomical community, remaining the Achilles' heel of the field of Galactic archeology (Bigot & Thévenin 2006). Several attempts have been made to assemble comprehensive line lists with reliable atomic data (Heiter et al. 2015b) that can be used as a standard input for the different local thermodynamic equilibrium (LTE) and non-LTE models used to determine chemical abundances.

Several studies regarding the measurement of oscillator strengths of neutral iron have been conducted over the last 50 years. A very detailed review of the situation was carried out 11 years ago by Fuhr & Wiese (2006), who presented the most comprehensive compilation of Fe i transition probabilities to date, which states clearly the need for new studies that complete and improve the quality of thousands of spectral lines in the database of Fe i log $({gf})$ values. Among all the works whose values are included in Fuhr & Wiese (2006), two deserve special attention due to the quality of their results and their coverage: the experiments conducted by Blackwell et al. (1979a, 1979b, 1980, 1982a, 1982b, 1986) and O'Brian et al. (1991).

Very accurate absorption oscillator strengths were obtained by Blackwell et al. from a very stable light source in an absorption experiment, with estimated uncertainties lower than ±4% on an absolute scale. Their values are generally considered as the most reliable ones by Fuhr & Wiese (2006), who rated them as "A" in their compilation. The comprehensive work from O'Brian et al. (1991) provides accurate transition probabilities for 1814 spectral lines of neutral iron obtained in an emission experiment by using two different methods. One method combines radiative lifetimes of 186 energy levels with measurements of branching fractions yielding 1174 absolute transition probabilities. The other method used by O'Brian et al. interpolated the populations of energy levels using those with known lifetimes in an inductively coupled plasma source, producing 640 extra transition probabilities with uncertainties that they estimated to be lower than ±10%. Within the spectral range included in our new study, the majority of the log $({gf})$-values available for comparison belong to O'Brian et al. (1991).

The present work is the third in a series of articles published as a result of the collaboration between the Fourier Transform Spectroscopy laboratory at Imperial College London (IC) and the University of Wisconsin-Madison (UW). It completes the previous works on log $({gf})$ for Fe i lines of interest in the Gaia-ESO survey (Ruffoni et al. 2014) and oscillator strengths for transitions coming from high-lying even-parity Fe i levels (Den Hartog et al. 2014). In this paper, we focus on the log $({gf})$ values for transitions coming from high-lying odd-parity upper energy levels, four of which contain spectral lines of particular interest for the Gaia-ESO survey. We provide new radiative lifetimes for 60 high-lying odd-parity levels obtained at the UW, 39 of which are measured for the first time. Fe i emission spectra were recorded with the Fourier transform spectrometers (FTSs) at IC and at the NIST. Measurements of branching fractions were completed for 15 of the previously mentioned odd-parity levels, and were combined with the new lifetimes to obtain 120 accurate values of oscillator strengths (and transition probabilities). Comparison with previous experiments shows that 22 of the analyzed transitions have no earlier log $({gf})$-values and for 63 transitions the accuracy of the log $({gf}){\rm{s}}$ are improved compared with existing measurements in the literature.

Oscillator strengths, or absorption f-values, are obtained experimentally from the measurement of atomic transition probabilities, A_ul, where the subscript ul refers to the transition from a given upper energy level, u, to a lower level, l. Transition probabilities and absorption f-values are related by (Thorne et al. 2007)

$$\begin{eqnarray}&&\mathrm{log}({g}_{l}f)=\mathrm{log}[{A}_{{ul}}{g}_{u}{\lambda }^{2}\times 1.499\times {10}^{-14}]\end{eqnarray} \tag{ 1 }$$

where g_l and g_u are the statistical weights of the lower and upper energy level, respectively, and λ is the wavelength of the line expressed in nm.

The transition probability of a given atomic transition can be obtained spectroscopically, because in the case of an optically thin plasma, it is proportional to the area under the profile of the corresponding spectral line. The integrated area of each intensity calibrated spectral line, I_ul, is proportional to its intensity in photons per second (Pickering et al. 2001a).

So-called branching fractions (Huber & Sandeman 1986) are given by

$$\begin{eqnarray}&&{\mathrm{BF}}_{{ul}}=\displaystyle \frac{{I}_{{ul}}}{{\displaystyle \sum }_{l}{I}_{{ul}}}=\displaystyle \frac{{A}_{{ul}}}{{\displaystyle \sum }_{l}{A}_{{ul}}},\end{eqnarray} \tag{ 2 }$$

and for a particular upper energy level, the lifetime ${\tau }_{u}$ is

$$\begin{eqnarray}&&{\tau }_{u}=\displaystyle \frac{1}{{\displaystyle \sum }_{l}{A}_{{ul}}}.\end{eqnarray} \tag{ 3 }$$

As long as the sum of the A_ul includes all branches to the lower energy levels, we can combine expressions (2) and (3) to obtain the transition probability of a given transition as

$$\begin{eqnarray}&&{A}_{{ul}}=\displaystyle \frac{{{\rm{BF}}}_{{ul}}}{{\tau }_{u}}.\end{eqnarray} \tag{ 4 }$$

As can be seen, this method of measuring A_ul has the advantage that no assumption needs to be made regarding the thermodynamic equilibrium of the plasma used as a light source.

2.1. Branching Fraction Measurements

Two different sets of spectra were used to obtain the log $({gf})$ values included in this work. Spectrum A was measured on the 2 m FTS at the NIST, and it covers the spectral range between 8000 and 26,000 cm⁻¹. An iron cathode mounted in a water-cooled hollow cathode lamp (HCL) was used to generate the plasma used as light source. The HCL was run in Ne at a pressure of 2.1 mbar and a current 2 A. Detailed descriptions of this measurement can be found in Ruffoni et al. (2014) and Den Hartog et al. (2014). The response function of the spectrometer, shown in Figure 1 for Spectrum A, was obtained by using a calibrated standard tungsten (W) halogen lamp in the spectral range between 250 and 2400 nm. To verify that this spectrometer response was stable over time, spectra of this tungsten lamp (whose radiance is known to ±1.1%) were measured before and after acquiring iron spectra with the HCL.

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Spectra B, C, D, and G were measured on the 0.2 m VUV FTS at Imperial College, and they cover the spectral range between 20,000 and 62,000 cm⁻¹. The resolution, detector, and filter used to record each spectrum, as well as the experimental conditions, are included in Table 1. The Fe i emission spectra were produced in a water-cooled HCL filled with Ne at a pressure ranging from 1.3 to 1.4 mbar and with a 99.8% pure iron cathode operated as the source. Currents of 700 or 1000 mA (see Table 1) were selected depending on the signal-to-noise ratio (S/N) of the spectral lines of interest. These conditions were optimized to obtain the highest S/N for the weaker lines, while avoiding self-absorption effects for the stronger lines.

Table 1.  FTS Spectra Used for the Branching Fraction Measurements

Spectrum	Wavenumber	Resolution	Detector	Filter	P Gas	I Lamp	Spectrum
	Range Used (cm−1)	(cm−1)			(mbar)	(mA)	File Namea
A (NIST)	9600–26000	0.02	Si diode	None	2.1	2000	Fe0301to0403_Calib
B (IC)	21000–33000	0.037	R11568 PMT	Schott BG3	1.3	700	F130610.002.047_Scaled
C (IC)	23000–41000	0.037	R11568 PMT	UG5	1.4	700	Fe130624.011.039_Scaled
D (IC)	31000–47000	0.037	R7154 PMT	None	1.3	1000	Fe130603.021.059_Calib
G (IC)	20000–35000	0.037	R11568 PMT	Schott BG3	1.3	1000	Fe130604A.007.034

Note.

^aSeveral spectra were coadded to improve the S/N of the spectral lines.

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Two standard intensity calibrated lamps were used to obtain the response function of the IC VUV spectrometer for these four spectra: a deuterium lamp (D₂) in the spectral interval ranging from 200 to 350 nm and a tungsten lamp (W) for longward of 300 nm. Spectra from these two lamps were measured before and after each of the runs recorded with the HCL lamp and using the same measurement conditions. The uncertainties of the relative spectral radiance of the W lamp, calibrated by the UK National Physical Laboratory (NPL), were lower than ±1.4% between 410 and 800 nm, increasing to ±2.8% at 300 nm. The deuterium lamp, calibrated by the Physikalisch-Technische Bundesanstalt in Germany, has a relative spectral radiance with an uncertainty of ±7% between 170 and 410 nm. The response functions of the different spectra, shown in Figure 1, were obtained by combining the response functions found using both lamps, W and D₂.

The Fe spectra were fitted by using Voigt profiles with the XGREMLIN package (Nave et al. 1997). Once fitted and intensity calibrated, the spectra were used to obtain the branching fractions of all the transitions coming from the upper energy levels of interest by using the FAST software package (Ruffoni et al. 2013b). The calculated branching fractions of Kurucz (2007) were used to define the transitions to be included, and to estimate the completeness of the set of transitions from each upper level considered, as described in Pickering et al. (2001a, 2001b). Final results for new log $({gf}){\rm{s}}$ were also obtained using the FAST software to combine the branching fractions with the new experimental upper energy lifetime values described in Section 2.2.

All of the fitted spectral lines were checked for possible self absorption by carefully examining the residuals from the line fits. Possible cases of blended lines were also analyzed by checking the Fe i line list of Nave et al. (1994) and Fe ii line list of Nave & Johansson (2013), as well as the theoretical log $({gf}){\rm{s}}$ of Kurucz (2007).

For most of the cases, more than one spectrum from Table 1 was necessary to encompass all the transitions coming from a given upper energy level. In these situations, all of the lines were put on a common relative intensity scale by calculating the ratio in the intensity of several lines from that particular upper energy level which were measured in the overlapping region of the pairs of spectra. A detailed description of this method can be found in Pickering et al. (2001a, 2001b).

We paid special attention to the calculation of the experimental uncertainties introduced in our BF measurements by taking into account all the different sources of error, such as the uncertainty in the S/N of the observed Fe i spectral line and the standard calibration lamp spectra, as well as the spectral radiance uncertainty of these standard light sources. A detailed description can be found in Ruffoni et al. (2013b) and Ruffoni (2013a), but the general expression is included here for completeness. The experimental uncertainty of a given BF can be defined as

$$\begin{eqnarray}&&{\left(\displaystyle \frac{{\rm{\Delta }}{{\rm{BF}}}_{{ul}}}{{{\rm{BF}}}_{{ul}}}\right)}^{2}=(1-2{{\rm{BF}}}_{{ul}}){\left(\displaystyle \frac{{\rm{\Delta }}{I}_{{ul}}}{{I}_{{ul}}}\right)}^{2}+\displaystyle \sum _{j=1}^{n}{{\rm{BF}}}_{{uj}}^{2}{\left(\displaystyle \frac{{\rm{\Delta }}{I}_{{uj}}}{{I}_{{uj}}}\right)}^{2},\end{eqnarray} \tag{ 5 }$$

where I_ul is the calibrated relative intensity of the emission line associated with the electronic transition from level u to level l, and ${\rm{\Delta }}{I}_{{ul}}$ is the uncertainty in intensity of this line due to its measured S/N and the uncertainty in the intensity of the standard lamp. From Equation (4), it then follows that the uncertainty in A_ul is

$$\begin{eqnarray}&&{\left(\displaystyle \frac{{\rm{\Delta }}{A}_{{ul}}}{{A}_{{ul}}}\right)}^{2}={\left(\displaystyle \frac{{\rm{\Delta }}{{\rm{BF}}}_{{ul}}}{{{\rm{BF}}}_{{ul}}}\right)}^{2}+{\left(\displaystyle \frac{{\rm{\Delta }}{\tau }_{{ul}}}{{\tau }_{{ul}}}\right)}^{2}\,,\end{eqnarray} \tag{ 6 }$$

where ${\rm{\Delta }}{\tau }_{{ul}}$ is the uncertainty in our measured upper level lifetime. Finally, the uncertainty in $\mathrm{log}({gf})$ of a given line can be calculated as

$$\begin{eqnarray}&&{\rm{\Delta }}\mathrm{log}({gf})=\mathrm{log}\left(1+\displaystyle \frac{{\rm{\Delta }}{A}_{{ul}}}{{A}_{{ul}}}\right).\end{eqnarray} \tag{ 7 }$$

2.2. Radiative Lifetime Measurements

In Table 2, we report the results of lifetime measurements from this study as well as LIF results from the literature. Lifetimes measured using older, less reliable techniques are not listed. Lifetimes are given for 60 high-lying odd-parity levels of Fe i ranging in energy from 27 166.82 to 57 565.31 cm⁻¹. The fractional uncertainty in our measurements is 5%, except for those lifetimes less than 4 ns, for which the absolute uncertainty is 0.2 ns. Approximately two-thirds of these lifetimes are measured for the first time. The comparison with the earlier work is very favorable. The lifetimes in the O'Brian et al. (1991) work were measured in our (UW) lab with nearly the same apparatus as the current work (in the earlier work, a different digitizer was used). We re-measured some of the original O'Brian et al. (1991) lifetimes to ensure that, even after 25 years, the experiment is giving consistent results. Happily, we see very good agreement with this older work. For eight lifetimes in common, the mean and rms differences between the current study and O'Brian et al. (1991) are −1.5% and 3.1%, respectively, using the current study as reference (in the sense (theirs ours)/ours). The level of agreement with Engelke et al. (1993) is also very good with mean and rms differences of −1.1% and 5.4%, respectively. Our study overlaps with that of Marek et al. (1979) for only two lifetimes that agree within 0.5% for the longer lifetime around 64 ns and within 4.5% for a shorter lifetime around 9 ns. Our study overlaps with that of Langhans et al. (1995) for only two very short lifetimes less than 3 ns. We agree perfectly in one case and differ by only 0.1 ns for the other. The excellent level of agreement with these four earlier studies is typical of modern TRLIF measurements.

Measurements of branching fractions were attempted for all the transitions coming from the upper energy levels included in Table 2 and completed for 15 of them. These upper energy levels are listed in Table 3 together with their configuration, the lifetime of the level used for the determination of the $\mathrm{log}({gf}){\rm{s}}$ and the completeness of each set of transitions. The remaining energy levels were excluded from our study due to the impossibility of putting the different lines onto a common intensity scale or to the presence of blended or very low S/N lines. Table 4 lists the results for branching fractions, transition probabilities, and $\mathrm{log}({gf}){\rm{s}}$ with their uncertainties for 120 transitions of Fe i, 22 of which are new and 63 have improved uncertainties compared with existing data. The spectral lines are grouped by common upper energy level and each set is sorted in order of descending wavelength. The values of the air wavelengths, as well as the upper and lower energy levels and J were taken from Kramida et al. (2011) based on Nave et al. (1994). In addition, the log $({gf}){\rm{s}}$ measured in this experiment are compared when possible with the value recommended by Fuhr & Wiese (2006), included in the last column along with the reference from the work from which the oscillator strength was taken. The letters L and P are used to indicate the method used in the O'Brian work to obtain these values and stand for "lifetime" and "population method," respectively.

Table 4.  Experimental BFs, Transition Probabilities, and log $({gf})$ Values for 16 Odd-parity Energy Levels of Fe i

Wavelengtha	Upper Levela		Lower Levela		BFb	UBFb	Aulc	This Experimentd	Publishede
(nm)	E (cm−1)	J	E (cm−1)	J		(%)	(106 s−1)	$\mathrm{log}({gf})$	$\mathrm{log}({gf})$	References
358.1193	34843.957	6	6928.268	5	1.0000	0.00	108.70 (5)	0.43 ± 0.02	0.406 ± 0.005	BL79
463.0120	39969.853	3	18378.185	2	0.0003	11.9	0.12 (13)	−2.58 ± 0.05	−2.59 ± 0.12	OB91 L
449.4563	39969.853	3	17726.987	2	0.0090	3.4	3.44 (6)	−1.14 ± 0.03	−1.14 ± 0.01	BL82a
445.9117	39969.853	3	17550.180	3	0.0065	3.2	2.49 (6)	−1.29 ± 0.03	−1.28 ± 0.01	BL82a
312.5651	39969.853	3	7985.784	2	0.0049	7.5	1.90 (9)	−1.71 ± 0.04	−1.66 ± 0.08	OB91 L
310.0665	39969.853	3	7728.059	3	0.0362	5.9	13.94 (8)	−0.85 ± 0.03	−0.87 ± 0.08	OB91 L
306.7244	39969.853	3	7376.764	4	0.0999	5.6	38.42 (8)	−0.42 ± 0.03	−0.51 ± 0.07	OB91 L
254.5978	39969.853	3	704.007	2	0.1858	5.1	71.44 (7)	−0.31 ± 0.03	−0.31 ± 0.05	OB91 L
252.7435	39969.853	3	415.933	3	0.4774	3.1	183.63 (6)	0.090 ± 0.03	0.11 ± 0.04	OB91 L
250.1132	39969.853	3	0.000	4	0.1794	5.2	69.00 (7)	−0.34 ± 0.03	−0.35 ± 0.05	OB91 L
444.7717	40404.518	1	17927.381	1	0.0138	4.0	4.94 (6)	−1.36 ± 0.03	−1.34 ± 0.01	BL82a
440.8414	40404.518	1	17726.987	2	0.0058	5.5	2.08 (8)	−1.74 ± 0.03	−1.78 ± 0.12	OB91 L
309.9895	40404.518	1	8154.713	1	0.0417	6.0	14.91 (8)	−1.19 ± 0.03	−1.08 ± 0.05	OB91 L
308.3741	40404.518	1	7985.784	2	0.0655	5.9	23.41 (8)	−1.00 ± 0.03	−0.88 ± 0.05	OB91 L
253.5607	40404.518	1	978.074	0	0.2678	4.7	95.63 (7)	−0.56 ± 0.03	−0.56 ± 0.04	OB91 L
252.9835	40404.518	1	888.132	1	0.0881	6.9	31.48 (9)	−1.04 ± 0.04	−0.96 ± 0.04	OB91 L
251.8102	40404.518	1	704.007	2	0.5167	2.9	184.54 (6)	−0.28 ± 0.02	−0.26 ± 0.03	OB91 L
377.6455	44022.525	4	17550.180	3	0.1061	3.8	1.10 (6)	−1.68 ± 0.03	−1.49 ± 0.05	OB91 L
275.4427	44022.525	4	7728.059	3	0.1559	4.8	1.62 (7)	−1.78 ± 0.03	−1.78 ± 0.03	OB91 L
272.8021	44022.525	4	7376.764	4	0.3310	3.8	3.43 (6)	−1.46 ± 0.03	−1.46 ± 0.03	OB91 L
269.5036	44022.525	4	6928.268	5	0.0438	5.5	0.45 (8)	−2.35 ± 0.03	−2.33 ± 0.03	OB91 L
229.2525	44022.525	4	415.933	3	0.3122	4.0	3.24 (6)	−1.64 ± 0.03	−1.68 ± 0.03	OB91 L
227.0863	44022.525	4	0.000	4	0.0484	6.0	0.50 (8)	−2.46 ± 0.03	⋯	⋯
372.1272	44415.074	4	17550.180	3	0.0339	15.3	0.81 (16)	−1.82 ± 0.07	−1.79 ± 0.05	OB91 L
272.4953	44415.074	4	7728.059	3	0.1987	4.6	4.78 (7)	−1.32 ± 0.03	−1.32 ± 0.03	OB91 L
269.9107	44415.074	4	7376.764	4	0.2315	4.4	5.57 (7)	−1.26 ± 0.03	−1.26 ± 0.02	OB91 L
266.6812	44415.074	4	6928.268	5	0.3765	3.6	9.05 (6)	−1.061 ± 0.03	−1.07 ± 0.02	OB91 L
227.2070	44415.074	4	415.933	3	0.1170	5.1	2.81 (7)	−1.71 ± 0.03	−1.69 ± 0.02	OB91 L
225.0790	44415.074	4	0.000	4	0.0419	6.3	1.01 (8)	−2.16 ± 0.03	−2.08 ± 0.05	OB91 L
273.0982	44760.746	1	8154.713	1	0.1185	6.0	5.56 (8)	−1.73 ± 0.03	−1.68 ± 0.02	OB91 L
271.8436	44760.746	1	7985.784	2	0.7738	1.4	36.33 (5)	−0.92 ± 0.02	−0.90 ± 0.02	OB91 L
228.3304	44760.746	1	978.074	0	0.0510	8.3	2.39 (10)	−2.25 ± 0.04	−2.22 ± 0.02	OB91 L
226.9099	44760.746	1	704.007	2	0.0383	10.5	1.80 (12)	−2.38 ± 0.05	⋯	⋯
1033.3185	46720.842	4	37045.932	4	0.0010	12.8	0.09 (14)	−1.91 ± 0.06	⋯	⋯
721.9682	46720.842	4	32873.630	4	0.0065	6.9	0.53 (9)	−1.43 ± 0.04	⋯	⋯
451.4184	46720.842	4	24574.653	4	0.0049	11.2	0.40 (12)	−1.96 ± 0.05	−1.92 ± 0.18	MA74
435.8501	46720.842	4	23783.617	5	0.0129	5.4	1.06 (7)	−1.57 ± 0.03	−1.68 ± 0.05	OB91 P
399.8052	46720.842	4	21715.731	5	0.0875	4.7	7.17 (7)	−0.81 ± 0.03	−0.91 ± 0.04	OB91 P
383.3308	46720.842	4	20641.109	4	0.0647	5.1	5.30 (7)	−0.98 ± 0.03	−1.032 ± 0.004	BL82b
342.7120	46720.842	4	17550.180	3	0.6593	1.9	54.04 (5)	−0.067 ± 0.02	−0.10 ± 0.04	OB91 P
287.7301	46720.842	4	11976.238	4	0.0544	7.2	4.46 (9)	−1.30 ± 0.04	−1.29 ± 0.04	OB91 P
254.0916	46720.842	4	7376.764	4	0.0067	14.0	0.55 (15)	−2.32 ± 0.06	⋯	⋯
251.2275	46720.842	4	6928.268	5	0.0352	7.2	2.89 (9)	−1.61 ± 0.04	−1.73 ± 0.06	OB91 P
215.8920	46720.842	4	415.933	3	0.0128	13.4	1.05 (14)	−2.18 ± 0.06	⋯	⋯
213.9698	46720.842	4	0.000	4	0.0369	8.7	3.02 (10)	−1.73 ± 0.04	⋯	⋯
553.2747	46889.142	4	28819.952	5	0.0035	14.5	0.31 (15)	−1.89 ± 0.06	−2.10 ± 0.30	MA74
493.4084	46889.142	4	26627.607	4	0.0014	17.9	0.13 (19)	−2.39 ± 0.07	⋯	⋯
448.0137	46889.142	4	24574.653	4	0.0048	11.7	0.43 (13)	−1.93 ± 0.05	−1.93 ± 0.09	OB91 P
432.6753	46889.142	4	23783.617	5	0.0068	9.8	0.62 (11)	−1.81 ± 0.05	−1.93 ± 0.09	OB91 P
397.1322	46889.142	4	21715.731	5	0.0583	8.6	5.25 (10)	−0.95 ± 0.04	−0.98 ± 0.04	OB91 P
380.8729	46889.142	4	20641.109	4	0.0387	8.9	3.48 (10)	−1.17 ± 0.04	−1.159 ± 0.004	BL82b
340.7460	46889.142	4	17550.180	3	0.6629	2.8	59.72 (6)	−0.029 ± 0.02	−0.02 ± 0.04	OB91 P
286.3430	46889.142	4	11976.238	4	0.0462	7.3	4.16 (9)	−1.34 ± 0.04	−1.34 ± 0.04	OB91 P
250.1694	46889.142	4	6928.268	5	0.0524	7.4	4.72 (9)	−1.40 ± 0.04	−1.51 ± 0.05	OB91 P
213.2017	46889.142	4	0.000	4	0.0386	9.3	3.48 (11)	−1.67 ± 0.04	−1.33 ± 0.06	⋯
730.7931	47092.712	3	33412.715	3	0.0228	5.7	1.26 (8)	−1.15 ± 0.03	−1.53 ± 0.06	OB91 P
435.1544	47092.712	3	24118.817	4	0.0210	4.7	1.15 (7)	−1.64 ± 0.03	−1.73 ± 0.04	OB91 P
412.1802	47092.712	3	22838.321	2	0.0539	3.9	2.96 (6)	−1.28 ± 0.03	−1.45 ± 0.04	OB91 P
398.3956	47092.712	3	21999.129	4	0.1291	3.5	7.09 (6)	−0.93 ± 0.03	−1.02 ± 0.04	OB91 P
383.7135	47092.712	3	21038.986	2	0.0177	5.4	0.97 (7)	−1.82 ± 0.03	−1.78 ± 0.09	OB91 P
381.3058	47092.712	3	20874.481	3	0.1163	2.9	6.39 (6)	−1.01 ± 0.02	−1.07 ± 0.04	OB91 P
377.9416	47092.712	3	20641.109	4	0.0112	10.8	0.61 (12)	−2.036 ± 0.05	−1.99 ± 0.05	OB91 P
340.4354	47092.712	3	17726.987	2	0.2180	4.3	11.98 (7)	−0.84 ± 0.03	−0.88 ± 0.04	OB91 P
338.3979	47092.712	3	17550.180	3	0.1494	4.8	8.21 (7)	−1.006 ± 0.03	−1.11 ± 0.04	OB91 P
292.9618	47092.712	3	12968.553	2	0.0135	11.2	0.74 (12)	−2.18 ± 0.05	−2.22 ± 0.05	OB91 P
289.5035	47092.712	3	12560.933	3	0.1089	6.5	5.98 (8)	−1.28 ± 0.03	−1.43 ± 0.04	OB91 P
284.6830	47092.712	3	11976.238	4	0.0164	9.0	0.90 (10)	−2.12 ± 0.04	−2.13 ± 0.04	OB91 P
253.9587	47092.712	3	7728.059	3	0.0072	16.6	0.40 (17)	−2.57 ± 0.07	⋯	⋯
251.7123	47092.712	3	7376.764	4	0.0321	7.3	1.77 (9)	−1.93 ± 0.04	⋯	⋯
215.5020	47092.712	3	704.007	2	0.0157	25.2	0.86 (26)	−2.38 ± 0.10	⋯	⋯
214.1718	47092.712	3	415.933	3	0.0212	15.3	1.16 (16)	−2.25 ± 0.07	⋯	⋯
744.3022	47197.010	2	33765.304	2	0.0125	13.0	0.55 (14)	−1.64 ± 0.06	⋯	⋯
437.3561	47197.010	2	24338.765	3	0.0230	6.7	1.01 (8)	−1.84 ± 0.04	−1.83 ± 0.09	OB91 P
437.2987	47197.010	2	24335.764	2	0.0064	22.6	0.28 (23)	−2.40 ± 0.09	−2.58 ± 0.18	MA74
412.2516	47197.010	2	22946.814	1	0.0710	5.7	3.10 (8)	−1.40 ± 0.03	−1.39 ± 0.04	OB91 P
410.4154	47197.010	2	22838.321	2	0.0073	8.8	0.32 (10)	−2.40 ± 0.04	⋯	⋯
382.1835	47197.010	2	21038.986	2	0.1889	4.7	8.25 (7)	−1.044 ± 0.03	−1.10 ± 0.04	OB91 P
341.5531	47197.010	2	17927.381	1	0.0839	6.6	3.67 (8)	−1.49 ± 0.04	−1.39 ± 0.05	OB91 P
339.2305	47197.010	2	17726.987	2	0.1783	5.8	7.79 (8)	−1.17 ± 0.03	−1.07 ± 0.05	OB91 P
292.0691	47197.010	2	12968.553	2	0.1060	7.2	4.63 (9)	−1.53 ± 0.04	−1.39 ± 0.04	OB91 P
288.6317	47197.010	2	12560.933	3	0.0335	10.8	1.47 (12)	−2.039 ± 0.05	−2.09 ± 0.04	OB91 P
256.0557	47197.010	2	8154.713	1	0.0405	7.7	1.77 (9)	−2.061 ± 0.04	−2.11 ± 0.04	OB91 P
254.9525	47197.010	2	7985.784	2	0.0081	21.3	0.35 (22)	−2.77 ± 0.09	−2.49 ± 0.05	OB91 P
253.2876	47197.010	2	7728.059	3	0.0328	8.0	1.43 (10)	−2.16 ± 0.04	−2.16 ± 0.04	OB91 P
215.0185	47197.010	2	704.007	2	0.0311	18.2	1.36 (19)	−2.33 ± 0.08	⋯	⋯
393.5307	48350.606	1	22946.814	1	0.0102	16.0	0.91 (17)	−2.199 ± 0.07	−1.82 ± 0.18	MA74
328.6016	48350.606	1	17927.381	1	0.0106	20.6	0.94 (21)	−2.34 ± 0.08	⋯	⋯
326.4513	48350.606	1	17726.987	2	0.0261	15.2	2.33 (16)	−1.95 ± 0.06	−1.32 ± 0.05	OB91 P
248.7066	48350.606	1	8154.713	1	0.6014	2.6	53.70 (6)	−0.83 ± 0.02	−0.75 ± 0.05	OB91 P
247.6657	48350.606	1	7985.784	2	0.2956	4.9	26.39 (7)	−1.14 ± 0.03	−1.08 ± 0.04	OB91 P
537.9574	48382.603	5	29798.934	4	0.0128	3.9	0.79 (6)	−1.42 ± 0.03	−1.51 ± 0.04	OB91 P
524.2491	48382.603	5	29313.006	6	0.0526	2.7	3.25 (6)	−0.83 ± 0.02	−0.97 ± 0.04	OB91 P
511.0358	48382.603	5	28819.952	5	0.0148	4.0	0.91 (6)	−1.41 ± 0.03	−1.37 ± 0.04	OB91 P
459.5358	48382.603	5	26627.607	4	0.0087	5.0	0.54 (7)	−1.73 ± 0.03	−1.76 ± 0.04	OB91 P
419.9095	48382.603	5	24574.653	4	0.8193	0.6	50.57 (5)	0.17 ± 0.02	0.16 ± 0.04	OB91 P
412.0206	48382.603	5	24118.817	4	0.0345	3.1	2.13 (6)	−1.23 ± 0.03	−1.27 ± 0.04	OB91 P
378.9176	48382.603	5	21999.129	4	0.0317	4.1	1.96 (7)	−1.33 ± 0.03	−1.29 ± 0.04	OB91 P
360.3681	48382.603	5	20641.109	4	0.0060	11.7	0.37 (13)	−2.10 ± 0.05	−2.01 ± 0.08	OB91 P
347.5863	48382.603	5	19621.005	5	0.0115	18.4	0.71 (19)	−1.85 ± 0.08	⋯	⋯
470.8969	50586.878	3	29356.742	2	0.0068	28.4	0.37 (29)	−2.07 ± 0.11	−2.03 ± 0.09	OB91 P
454.7847	50586.878	3	28604.611	2	0.1279	2.1	6.91 (6)	−0.82 ± 0.02	−1.01 ± 0.12	OB91 P
417.1900	50586.878	3	26623.733	2	0.0221	6.1	1.20 (8)	−1.66 ± 0.03	−1.70 ± 0.05	OB91 P
410.3611	50586.878	3	26224.967	3	0.0022	18.8	0.12 (20)	−2.67 ± 0.08	⋯	⋯
384.3257	50586.878	3	24574.653	4	0.7374	0.8	39.86 (5)	−0.21 ± 0.02	−0.24 ± 0.04	OB91 P
380.8282	50586.878	3	24335.764	2	0.0177	16.3	0.95 (17)	−1.84 ± 0.07	−1.94 ± 0.06	OB91 P
352.7891	50586.878	3	22249.428	3	0.0148	21.3	0.80 (22)	−1.98 ± 0.09	⋯	⋯
302.6056	50586.878	3	17550.180	3	0.0161	26.2	0.87 (27)	−2.077 ± 0.10	⋯	⋯
697.7429	51373.910	5	37045.932	4	0.0068	10.7	0.47 (12)	−1.42 ± 0.05	⋯	⋯
540.3822	51373.910	5	32873.630	4	0.0319	3.1	2.20 (6)	−0.98 ± 0.03	−1.03 ± 0.05	OB91 P
453.1636	51373.910	5	29313.006	6	0.0048	12.1	0.33 (13)	−1.95 ± 0.05	⋯	⋯
443.2568	51373.910	5	28819.952	5	0.0117	12.0	0.80 (13)	−1.58 ± 0.05	−1.56 ± 0.18	MA74
395.6455	51373.910	5	26105.906	6	0.2287	2.5	15.77 (6)	−0.39 ± 0.02	−0.34 ± 0.04	OB91 P
373.0386	51373.910	5	24574.653	4	0.1296	4.9	8.94 (7)	−0.69 ± 0.03	−0.65 ± 0.04	OB91 P
337.0783	51373.910	5	21715.731	5	0.3413	3.9	23.54 (6)	−0.36 ± 0.03	−0.27 ± 0.04	OB91 P
325.2915	51373.910	5	20641.109	4	0.0267	9.8	1.84 (11)	−1.49 ± 0.05	−1.42 ± 0.04	OB91 P
312.5683	51373.910	5	19390.167	6	0.1049	5.7	7.23 (8)	−0.93 ± 0.03	−0.87 ± 0.04	OB91 P
253.7459	51373.910	5	11976.238	4	0.0604	9.6	4.17 (11)	−1.35 ± 0.05	−1.47 ± 0.06	OB91 P
420.3938	53093.528	6	29313.006	6	0.0342	7.2	3.23 (9)	−0.95 ± 0.04	−0.99 ± 0.04	OB91 P
411.8545	53093.528	6	28819.952	5	0.5906	3.2	55.72 (6)	0.27 ± 0.03	0.22 ± 0.04	OB91 P
373.8305	53093.528	6	26351.038	5	0.3624	5.2	34.18 (7)	−0.031 ± 0.03	−0.03 ± 0.04	OB91 P

Notes.

^aWavelengths, upper and lower energy levels and J quantum numbers are taken from Kramida et al. (2011). ^bThe measured branching fraction, BF, is expressed per unit and its relative uncertainty, δBF/BF, as a percentage. ^cThe measured transition probability, A_ul, in 10⁶ s⁻¹. In brackets, its uncertainty expressed in percentage. ^dThe log $({gf})$ values measured in this work together with their uncertainty index. ^eValues of log $({gf}){\rm{s}}$ from other authors used for comparison with their uncertainty index. The acronyms in the reference column correspond to BL79—Blackwell et al. (1979a, 1979b), OB91—O'Brian et al. (1991), BL82a—Blackwell et al. (1982a), MA74—May et al. (1974), BL82b—Blackwell et al. (1982b), and BA94—Bard & Kock (1994). The letter included after the reference OB91 indicates the method used by the authors, with "L" and "P" standing for "lifetime" and "population" method, respectively.

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Figures 2 and 3 show the comparison between the new log $({gf})$ values obtained in this experiment and those published previously, indicating if they agree within one or two σ, which represents the combined experimental uncertainty. Both plots include dashed horizontal lines indicating uncertainties of ±25%, which correspond to values classified as "C" by Fuhr & Wiese (2006), regarding their accuracy. In Figure 2, our log $({gf}){\rm{s}}$ are compared with those from O'Brian et al. (1991). We made a distinction between the log $({gf}){\rm{s}}$ that were obtained from measurements of lifetimes and branching fractions and those determined from extrapolated energy level populations and relative line intensities. For 13 of the compared transitions, marked in Figure 2 by filled symbols, O'Brian et al. (1991) log $({gf}){\rm{s}}$ do not agree with our new values within 2σ. It is noted that only one of these values from O'Brian et al. (1991) was obtained from lifetime measurements, with the remaining 12 being determined by using the population method. Figure 3 shows the comparison with log $({gf})$ values from Blackwell et al. (1979a, 1979b, 1982a, 1982b), May et al. (1974), Bard & Kock (1994), and Banfield & Huber (1973). It is possible to see how log $({gf}){\rm{s}}$ from Blackwell et al. agree within 1σ with our new values, which is reassuring as their experiments are considered to be the most precise by Fuhr & Wiese (2006), with uncertainties lower than 2%. Relative log $({gf}){\rm{s}}$ from Blackwell et al. are claimed to be better than 2%. The comparison with log $({gf}){\rm{s}}$ from May et al. (1974), obtained from emission measurements from a wall-stabilized arc, shows a wider scatter, which is not strange given the large uncertainties assigned by Fuhr & Wiese (2006). The only log $({gf})$ value from Bard & Kock (1994) available for comparison shows a good agreement within 1σ, whereas the $\mathrm{log}({gf})$ from Banfield & Huber (1973) differs significantly from our value, although the difference lies within 2σ.

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A subset of the new gf-values measured in this work were used to determine iron line abundances from the solar spectrum obtained with the Kitt Peak FTS by Kurucz et al. (1984). The high-quality observations and the well-known atmospheric parameters available for the Sun make it an ideal test case to evaluate the impact of new atomic data on stellar spectral synthesis. We selected 17 lines from Table 4 which show low contamination from blends at the spectral resolution of the solar flux atlas, and which are located in regions of good continuum placement. The observed spectrum has a minimum wavelength of 300 nm, and it is very crowded at wavelengths below ∼400 nm, which excludes about two-thirds of the lines published in this work. Among the remaining lines, about half were too blended to attempt any abundance derivation. The selected lines are listed in Table 5 together with the required input atomic data in columns 1–4 (central wavelength, lower level energy ${E}_{\mathrm{low}}$, gf-value, and van der Waals parameter). The latter is used to account for line broadening due to collisions with neutral hydrogen and was extracted from the VALD database (Kupka et al. 1999; Heiter et al. 2008). The meaning of the values for the van der Waals broadening parameter given in Table 5 (column 3) is as follows. Values greater than zero were obtained from Anstee, Barklem & O'Mara (ABO) theory (Anstee & O'Mara 1991, 1995; Barklem et al. 2000) and are expressed in a packed notation where the integer component is the broadening cross-section, σ, in atomic units, and the decimal component is the dimensionless velocity parameter, α. Values less than zero are the log of the broadening parameter, ${\gamma }_{6}$ (rad s⁻¹), per unit perturber number density, N (cm⁻³), at 10,000 K (i.e., log[${\gamma }_{6}/N]$ in units of rad s⁻¹ cm³) from Kurucz (2014). These were used only when ABO data were unavailable. See Gray (2005) for more details.

Table 5.  Lines from Table 4 Selected for Solar Synthesis

${\lambda }_{\mathrm{air}}$	${E}_{\mathrm{low}}$	VdWa	This Experiment		Previously Published			${v}_{\mathrm{macro}}$	New gf		Previous gf
(nm)	(eV)	Parameter	log(gf)	Unc.	log(gf)	Unc.b	Ref.c	(km s−1)	log(ε)	rmsd	log(ε)	rmsd
380.8729	2.559	265.262	−1.17	0.04	−1.16	0.00	BL82b	3.2	7.47	0.9	7.46	0.9
412.0206	2.990	338.253	−1.23	0.03	−1.27	0.04	OB91	3.6	7.56	1.9	7.60	2.0
443.2568	3.573	275.254	−1.58	0.05	−1.56	0.18	MA74	3.2	7.39	1.0	7.38	1.0
444.7717	2.223	429.302	−1.36	0.03	−1.34	0.01	BL82a	3.2	7.60	0.6	7.58	0.7
445.9117	2.176	417.302	−1.29	0.03	−1.28	0.01	BL82a	2.5	7.50	0.9	7.49	0.9
449.4563	2.198	416.302	−1.14	0.03	−1.14	0.01	BL82a	3.1	7.46	1.2	7.46	1.2
451.4184	3.047	296.271	−1.96	0.05	−1.92	0.18	MA74	3.2	7.40	1.1	7.36	1.2
454.7847	3.546	313.266	−0.82	0.02	−1.01	0.12	OB91	3.1	7.41	1.5	7.59	1.6
459.5358	3.301	286.270	−1.73	0.03	−1.76	0.04	OB91	3.4	7.60	1.2	7.62	1.2
463.0120	2.279	416.254	−2.58	0.05	−2.59	0.12	OB91	3.0	7.56	1.7	7.56	1.7
470.8969	3.640	−7.800	−2.07	0.11	−2.03	0.09	OB91	4.1	7.92	0.7	7.88	0.7
537.9574	3.695	363.249	−1.42	0.03	−1.51	0.04	OB91	3.2	7.43	0.9	7.53	0.9
540.3822	4.076	−7.810	−0.98	0.03	−1.03	0.05	OB91	3.7	7.62	1.1	7.66	1.1
553.2747	3.573	237.255	−1.89	0.06	−2.10	0.30	MA74	3.4	7.25	0.4	7.45	0.4
721.9682	4.076	−7.740	−1.43	0.04	−1.73	⋯	K14	3.1	7.40	0.5	7.70	0.5
730.7931	4.143	−7.810	−1.15	0.03	−1.53	0.06	OB91	3.4	7.33	0.4	7.69	0.5
744.3022	4.186	−7.810	−1.64	0.06	−1.40	⋯	K14	3.4	7.47	0.5	7.24	0.5

Notes.

^aVan der Waals broadening parameter (see the text for an explanation). ^bUncertainties are only available for experimentally measured log(gf) values. ^cReference acronyms are the same as for Table 4. In addition, K14 stands for Kurucz (2014). ^drms difference between observed and synthetic flux in percent, for the points included in the fit.

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The spectral synthesis was done with the one-dimensional, plane-parallel radiative transfer code SME (Valenti & Piskunov 1996; Piskunov & Valenti 2017, version 531), assuming LTE and using a model atmosphere interpolated in the MARCS grid included in the SME distribution (Gustafsson et al. 2008). We adopted an effective temperature of 5772 K and a logarithmic surface gravity (cm s⁻²) of 4.44 (Heiter et al. 2015a; Pršat et al. 2016), a microturbulence of 1.0 km s⁻¹, and a projected rotational velocity of ${v}_{\mathrm{rot}}$ sin(i) = 1.6 km s⁻¹ (Valenti & Piskunov 1996). The instrumental profile was assumed to be Gaussian, with a width corresponding to the spectral resolution of the observations (R = 200,000). Each line profile was fitted individually using ${\chi }^{2}$-minimization between observed and synthetic spectra while varying the iron abundance and the macroturbulence broadening, parameterized by a velocity ${v}_{\mathrm{macro}}$ in the radial-tangential model (Gray 2005). In addition, a small radial velocity correction was applied to each line, allowing for variations in the wavelength scale of the observations. For each line, we determined the region of the line profile which seemed to be free from blends in the observed spectrum, and only spectrum points within that region were used to calculate the ${\chi }^{2}$.

The results are given in Table 5, where we list the best-fit iron abundance log(ε) for each line (column 10) on the standard astronomical scale.⁴ We also list the ${v}_{\mathrm{macro}}$ values derived for each line (column 9), as well as a measure for the goodness of fit (rms deviation, column 11), ranging from 0.4% to 1.9%. The largest deviations are found for lines at wavelengths at or below 450 nm, and the smallest rms values for lines above 700 nm. Most of the abundances fall within the range from 7.3 to 7.6, with associated macroturbulence values between 2.5 and 3.7 km s⁻¹ and radial velocity corrections of 0.2 to 0.4 km s⁻¹. However, the line at 470.9 nm has ${v}_{\mathrm{macro}}\gtrsim 4$ and an abundance of 7.9, significantly higher than the above range. This indicates contamination by undetected blends that have not been taken into account in the fit. Excluding this line, the mean abundance and standard deviation are log ${(\varepsilon )}_{\mathrm{new}}$ = 7.47 ± 0.10 dex⁵ (16 lines), which is similar to the values found in the previous two papers in this series (7.44 ± 0.08 dex in Ruffoni et al. 2014 and 7.45 ± 0.06 dex in Den Hartog et al. 2014), and agrees with recent publications, such as 7.43 ± 0.05 from Bergemann et al. (2012) (MARCS LTE result), and 7.40 ± 0.04 from Scott et al. (2015) (mean of MARCS LTE abundances in their Table 1).

The line-to-line abundance scatter might be influenced by non-LTE effects, which are however expected to be small in solar-like atmospheres. Unfortunately non-LTE corrections have only been published for few of the lines analyzed here. Four of the lines were investigated by Gehren et al. (2001), who derived non-LTE−LTE abundance differences of 0.03 dex for the 449.5 and 538.0 nm lines, 0.05 dex for 444.8 nm, and −0.11 dex for 443.3 nm. Applying these corrections would lead to a slightly larger scatter. On the other hand, the more recent calculations by Bergemann et al. (2012) and Lind et al. (2012), made available through the INSPECT database,⁶ include two of the lines (449.5, 538.0 nm), both with non-LTE corrections of 0.01 dex. If similar corrections apply to the remaining lines then they do not have any impact on the abundance scatter derived here.

We repeated the abundance determination for the same set of lines using the best previously published experimental or theoretical log(gf) values (see Table 5 for values and references in columns 6–8, and for results in columns 12 and 13). The regions of the line profiles used for the fit were the same as above, and the macroturbulence values were those derived in the analysis with the new log(gf) values⁷ The results for both the previously published data and the new data are illustrated in Figure 4. The differences in derived abundances are consistent with the differences in log(gf), and are larger than 0.05 dex for six lines.⁸ The mean abundance and standard deviation for previous data including the same 16 lines as above are log ${(\varepsilon )}_{\mathrm{pub}}=7.52\pm 0.13$ dex, which is close to log ${(\varepsilon )}_{\mathrm{new}}$, although slightly offset toward higher abundances and with a somewhat larger scatter. In summary, the small scatter in the line abundances derived with the new data, and the satisfactory agreement with recently published values for the solar iron abundance validates the general accuracy of the new measurements.

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We report radiative lifetimes for 60 odd-parity energy levels ranging from 27,166 to 57,562 cm⁻¹, 39 of which have not been measured before. The uncertainties for these lifetimes are the larger of ±5% or 0.2 ns. When values are available in the literature, our results are in good agreement with them.

We provide 120 experimental log $({gf})$ values (transition probabilities) for Fe i transitions within the spectral range 213–1033 nm coming from 16 upper energy levels, 24 of which had no previous experimental data. The uncertainty of these oscillator strengths has been carefully calculated and it ranges between 0.02 dex for the strongest lines and 0.09 dex for the very weak ones. This accuracy is an improvement over previous log $({gf})$ measurements for around 72 of the transitions, making our new log $({gf})$ values good candidates for use in the analysis of stellar spectra and the determination of chemical abundances. Our log $({gf})$ results are in good agreement with those of Blackwell et al. (1979a, 1979b, 1982a, 1982b) and in general with O'Brian et al. (1991) data.

M.T.B., J.C.P., and M.P.R. thank the UK Science and Technology Facilities Council (STFC) for support under research grant ST/N000838/1. E.A.D.H., J.E.L., and A.G. acknowledge funding from the National Science Foundation through award AST-1211055 and through the NSF REU program award AST-0907732. U.H. acknowledges support from the Swedish National Space Board (SNSB/Rymdstyrelsen). This work has made use of the VALD database, operated at Uppsala University, the Institute of Astronomy RAS in Moscow, and the University of Vienna. This work has made use of the NSO/Kitt Peak FTS data, produced by NSF/NOAO.