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On the relative transition probabilities of rare gases in the 1si–2pj region
Optics Communications ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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On the relative transition probabilities of rare gases in the 1si–2pj region N.K. Piracha a,n, K.V. Duncan-Chamberlin a, John Kaminsky a, D. Delanis a, M.A. Baig b a b
Department of Physics, John Carroll University, University Heights, OH 44118, USA National Center for Physics, Quaid-i-Azam University Campus, 45320 Islamabad, Pakistan
art ic l e i nf o
a b s t r a c t
Article history: Received 23 March 2014 Received in revised form 23 April 2014 Accepted 26 April 2014
We have measured the relative transition probabilities of the 1si–2pj transitions in rare gases using hollow cathode lamps. The emission spectra of each rare gas were recorded as the function of discharge current. Two independent calibration modes for the spectrometer have been used to increase the reliability of our data. Uncertainty in the data have been measured and found to be within 5%. The relative transition probabilities are reported for 30 lines of Ne I, 25 lines of Ar I, fourteen lines of Kr I, and eighteen lines of Xe I. The present results are in good agreement with the published data. The data can also be used to calibrate the relative detection efficiency of a spectrometer over a range of 400–1000 nm. & 2014 Published by Elsevier B.V.
Keywords: Optogalvanic effect Transition probabilities Rare gases
1. Introduction The presence of buffer gases in the hollow cathode lamps provide accurately measured spectral lines that can be used for the wavelength calibration covering the UV to IR region. Since their relative line intensities are also well documented therefore it provides a reliable means of determining the relative detection efficiencies of different detectors. The knowledge of transition probabilities is helpful in understanding the atomic structure and plasma characteristics [1,2]. This data is also important in the field of astrophysics to model the upper atmosphere and to determine rare gas concentration in celestial bodies [3]. Of all the rare gases, the spectral characteristics of neon, in general, have been extensively studied. This is because of its emission spectrum that lies in the mid-visible region and is easily accessible compared to the other rare gases. Bridges and Wiese [4] studied the transition probabilities of the Ne I lines belonging to the 3s–3p transition array by using a wall-stabilized arc with an argon neon mixture at atmospheric pressure. Using a glow discharge containing a He–Ne–Ar mixture, Inatsugu and Holmes [5] measured the neon transition probabilities for the 3s–3p region. They compared the line intensities with the 632.8 nm neon line to determine the relative transition probabilities. These values were then converted to the absolute transition probabilities by using an accurate value of the Einstein coefficient for the 632.8 nm transition. Using a hollow cathode discharge, Chang and Setser [6] determined the neon absolute transition probabilities
n
Corresponding author. E-mail address: [email protected] (N.K. Piracha).
for the 3s–3p transition. The radiative lifetimes of the eight p states were measured and combined with the measured branching ratios to deduce the absolute transition probabilities. Recently, Bacławski [7] measured the neon line intensities belonging to the 3p–3d region. The relative transition probabilities obtained from line intensities were converted to the absolute scale by normalizing them to the radiative lifetime value of the 3d0 [3/2]2 state. The transition probabilities were used for evaluating the J-file sum rule for the transition array of 3p–3d. More recently, Asghar et al. [8] reported the transition probabilities of the 3p–3s transitions array in neon using the LIBS technique. In argon, the branching ratios of 329 emission lines ranging over wavelengths from 210 to 4591 nm were measured by Whaling et al. [1]. In the case of krypton, Ernst and Schultz-Gulde [9] reported the relative transition probabilities for the 5s–5p and 5s–6p transition arrays using a wall-stabilized arc at atmospheric pressure. Sabbagh and Sadeghi [10] used light absorption with Xe I plasma afterglow to measure the relative transition probabilities in the 6s–6p transition array. Two well known reference lines were chosen to determine the absolute transition probabilities. Using intermediate coupling and configuration mixing approach, Aymar and Coulombe [11] studied the transition probabilities and lifetimes of Kr I and Xe I. Cabrera et al. [12] used electron pulses and a monochromator to determine the relative and absolute transition probabilities in Xe for the lines belonging to the 6s–6p transition array. Nick and Helbig [13] used a low-pressure discharge to measure the relative transition probabilities in the 6s–6p0 and 6s–7p transition arrays in Xe and also computed the lifetime of several levels. Peraza et al. [14] determined the relative transition probabilities for the 6p–(7–13)s transition arrays of Xe I using the emission line-intensities from a Xe arc lamp. Coupled with the
http://dx.doi.org/10.1016/j.optcom.2014.04.063 0030-4018/& 2014 Published by Elsevier B.V.
Please cite this article as: N.K. Piracha, et al., Optics Communications (2014), http://dx.doi.org/10.1016/j.optcom.2014.04.063i
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line-strength sum rules, these relative values were converted into the absolute values. The National Institute of Standards and Technology (NIST) atomic spectra database enlists the transition probabilities for the excited levels in neutral rare gases [15]. The present contribution is in continuation of our studies on the optogalvanic spectroscopy of rare gases [2,16–19]. In this article, we report an extensive data on the measurement of transition probabilities of neon, argon, krypton and xenon in the 1si–2pj transition array using hollow cathode lamps filled with these gases. We have recorded the emission spectra of these gases at different discharge conditions. The intensity data (area under each spectral line) were plotted against the discharge current which resulted into linear plots. This new technique provided a very reliable data that have been used to calculate the relative branching ratios. The present experimental results are compared, where available, with the published data showing a good agreement.
2.2. Absolute irradiance Absolute irradiance uses a lamp of known output (in terms of microwatts per square centimeter per nanometer) to calibrate spectrometer's response at every pixel. This corrects the shape and magnitude of the spectrum and the resulting spectrum is in terms of microwatts per square centimeter per nanometer (mW/cm2/nm). The spectrometers were sent to Ocean Optics for this absolute calibration. The entire set of data collected with mode “a” calibration was repeated with these reconfigured (mode b) spectrometers. Each spectrum was recorded three times and the final data is the average of these sets. The reported measurement error of 5% is the maximum deviation that we observed in our data recorded in using both the calibration methods. We found that both the calibration techniques are acceptable and the extracted branching ratios are independent of the calibration modes used in the present work.
3. Results and discussion 2. Experimental details The experimental setup used in this work consisted of commercial hollow cathode lamps (Photron, Australia) and Ocean Optics spectrometers (HR4000). Each hollow cathode lamp is filled with a rare gas at low pressures between 5 and 8 Torr. We made use of two ocean optics spectrometers to cover the entire range from near UV through visible to near IR. One spectrometer works in the UV–vis (350–704 nm), whereas, the other is configured for the near infrared range (697–1100 nm). Every Ocean Optics spectrometer has what is called an “instrument response function”, or IRF. The IRF refers to how much the spectrometer responds to the light intensity across its wavelength range. The IRF for each spectrometer is unique but it is possible to compensate for the IRF. The two common corrections are relative irradiance and absolute irradiance modes. We used these two independent calibration modes of our spectrometers to record two full sets of emission spectra of the above mentioned gases that are discussed here.
2.1. Relative irradiance mode The two spectrometers have a detection efficiency response which is non-uniform across their spectral range. To compensate it, the relative irradiance mode of the ocean optics spectrasuite software was used. This method allowed for the direct comparison of any two peaks because it calibrates the individual detector's response. To accomplish this, a blackbody source of known color temperature was used. In this experiment, the source was an ocean optics LS-1 Tungsten halogen lamp with a color temperature of 2800 K. Once the lamp had warmed to a constant temperature a reference spectrum was recorded. A dark spectrum was also taken, and then the spectrometer was calibrated for relative irradiance measurements. The Spectrasuite software then used the following equation to determine the relative irradiance at any given wavelength λ; I L;T ¼ NBλ;T ðSλ Dλ Þ=ðRλ Dλ Þ where N is the normalizing term, Bλ,T is the energy of the blackbody source which is calculated from the temperature, Rλ is the intensity from the reference spectrum, Dλ is the dark spectrum intensity and Sλ is the intensity of the source spectrum. Once the system was calibrated, three sets of experimental data of the gas spectra were obtained and an average spectra were used for further analysis.
Excluding helium, the ground state electronic configuration of rare gases is mp6 1S0, where m¼ 2, 3, 4 and 5 for neon, argon, krypton and xenon respectively. The excited states of these gases are, in general, given by the jcK-coupling scheme [20]. According to this scheme, the first group of the excited levels has a mp5(mþ 1)s configuration. This results in four energy levels namely, mp5(mþ1) s[3/2]2, mp5 (mþ1)s [3/2]1, mp5 (mþ 1)s0 [1/2]0 and mp5 (mþ1)s0 [1/2]1. Two of these levels mp5 (mþ1)s [3/2]2 and mp5 (mþ1)s0 [1/2]0 possess long radiative lifetimes and are called the metastable levels. One, the mp5 (mþ1)s [3/2]1, is semi-metastable, while mp5 (mþ1)s0 [1/2]1 is short lived and is termed as resonance level. The second group of excited levels come from the mp5(mþ 1)p configuration. All of these levels are relatively short lived. A rather convenient and simplified way of naming the excited levels of rare gases is Paschen notation. According to this alternate notation, the first group of excited levels is termed as 1si and is subdivided into four levels namely, 1s5, 1s4, 1s3 and 1s2. Here 1s5 and 1s3 represent the two metastable levels, 1s4 is the semi-metastable and 1s3 is the resonance level. Similarly the second group, the mp5(mþ1)p configuration, is expressed by 2pj levels, subdivided to 2p1 to 2p10 levels. These 2pj levels are radiatively connected to at least one of the 1si levels and have typical radiative lifetimes in the range of nano seconds. We, in this article, have made use of both of these naming methods to maintain consistency with the published literature. To map the 1si–2pj transitions each rare gas spectrum was recorded both in the visible and in the infrared region using the two spectrometers. For every set of data, the current was increased at fixed increments. In both neon and xenon, the current range was 2–18 mA with increments of 2 mA; whereas, in argon and krypton, the spectra were recorded from 1 to 12 mA using 1 mA steps. These current ranges were selected to prevent detector saturation. The spectra in the visible region are rich in transitions as compared to that of the infrared region. To calculate the branching ratios, the area beneath the peaks in the spectra was determined. This was accomplished by using the integration utilities of Logger Pro and Origin. These areas were graphed against the discharge current and grouped based on transitions belonging to the same upper level in each gas. The slopes of these plots were determined. Fig. 1 shows plots of the transitions that belong to the upper level np0 [3/2]2, where n ¼3, 4, 5, and 6 for neon, argon, krypton, and xenon respectively. The neon plot shows the following transitions: 3p0 ½3=22 -3s0 ½1=21
ð667:82 nmÞ
-3s0 ½3=21
ð609:62 nmÞ
-3s0 ½3=22
ð594:48 nmÞ:
Please cite this article as: N.K. Piracha, et al., Optics Communications (2014), http://dx.doi.org/10.1016/j.optcom.2014.04.063i
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Ne 3p'[3/2]2 (2p4)
0.6
667.82nm 609.61nm 594.48nm
0.5
Intensity (uW/cm2)
0.7
0.4 0.3 0.2 0.1 0.0
3
1.2
Ar 4p'[3/2]2 (2p3)
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0.8 0.6 0.4 0.2 0.0
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14
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Kr 5p'[3/2]2 (2p2)
0.5
826.32nm 587.09nm 556.22nm
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12
Xe 6p'[3/2]2 (2p3)
0.10
Intensity (uW/cm2)
0.6
8
Current (mA)
Current (mA)
Intensity (uW/cm2)
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Intensity (uW/cm2)
N.K. Piracha et al. / Optics Communications ∎ (∎∎∎∎) ∎∎∎–∎∎∎
0.4 0.3 0.2
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8
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Fig. 1. Intensity vs. current plots for the transitions originating from the upper level np0 [3/2]2 where n¼ 3, 4, 5, and 6 for Ne, Ar, Kr and Xe respectively.
In argon plot, the transitions are 4p0 ½3=22 -4s0 ½1=21 ð840:82 nmÞ -4s½3=21 ð738:39 nmÞ -4s½3=22 ð706:72 nmÞ: In krypton plot, the transitions are 5p0 ½3=22 -5s0 ½1=21 ð826:32 nmÞ -5s½3=21 ð587:09 nmÞ -5s½3=22 ð556:22 nmÞ: Whereas, in xenon plot, the following transitions are shown: 0
6p ½3=22 -6s0 ½1=21 ð834:68 nmÞ -6s½3=21 ð473:41 nmÞ -6s½3=22 ð452:46 nmÞ: The branching ratios of the transitions were calculated from the slopes (M) of the plots for a set of transitions from the same upper level using Eq. (1): BR ¼
M1 M1 þ M2 þ M3 þ M4
data from this work is compared with Chang et al. [21] reported values (see Table 1) and both are in good agreement with each other. In our measurements over the entire current range, we did not observe the 3p[3/2]1–3s0 [1/2]1 transition at 702.41 nm. We, therefore, have assigned it a branching ratio value of zero. In Table 2, the branching ratios of argon for the 4s–4p region are presented. The data is compared with Whaling [1]. It may be noted that the two lines at 772.37 nm and 772.42 nm belonging to the 4p[3/2]1–4s[3/2]2 and 4p0 [1/2]1–4s0 [1/2]0 transitions, respectively, were not fully resolved. The branching ratios of krypton for the 5s–5p spectral region are given in Table 3. The data shows a good agreement with the literature values; Aymer [11] and Chang [21]. As seen in this table, there are many transitions for which the branching ratios cannot be determined. This is because one or more members of each of these radiative set lies beyond our detection capabilities. In Table 4, the relative transition probabilities in xenon in the 6s–6p region are presented and a comparison is made with that of Aymar [11], and Cabrera [12]. The agreement between the data is very good that reflects the validity and quality of the present experimental technique to determine the transition probabilities of the spectral lines.
ð1Þ
Because all these plots are linear (see Fig. 1), it is apparent that the branching ratios stay constant regardless of the current change in a certain range. Therefore, the slope method for determining the branching ratios is a good technique as it is based on the data averaging. Tables 1–4 show the branching ratios in the Ne, Ar, Kr and Xe spectra in the 1si–2pj transition array. The neon branching ratio
4. Conclusion This report provides a complete list on the relative transitions probabilities for multiplets in the spectra of neon, argon, krypton and xenon in the 1si–2pj region. As a result of the spectrometer's sensitivity, analysis in the wavelengths region from 400 nm to 1000 nm was conducted. Our experimental method yields a linear
Please cite this article as: N.K. Piracha, et al., Optics Communications (2014), http://dx.doi.org/10.1016/j.optcom.2014.04.063i
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Table 1 Relative transition probabilities in neon. Neon transitions (Racah)
Neon transitions (Paschen)
λ (nm)
This work
Chang et al. [6]
This work – Chang
3p0 [1/2]0–3s0 [1/2]1 3s[3/2]1 3p0 [1/2]1–3s0 [1/2]1 3s0 [1/2]0 3s[3/2]1 3s[3/2]2 3p[1/2]0–3s0 [1/2]1 3s[3/2]1 3p0 [3/2]2–3s0 [1/2]1 3s[3/2]1 3s[3/2]2 3p0 [3/2]1–3s0 [1/2]1 3s0 [1/2]0 3s[3/2]1 3s[3/2]2 3p[3/2]2–3s0 [1/2]1 3s[3/2]1 3s[3/2]2 3p[3/2]1–3s0 [1/2]1 3s0 [1/2]0 3s[3/2]1 3s[3/2]2 3p[5/2]2–3s0 [1/2]1 3s[3/2]1 3s[3/2]2 3p[5/2]3–3s[3/2]2 3p[1/2]1–3s0 [1/2]1 3s0 [1/2]0 3s[3/2]1 3s[3/2]2
2p1–1s2 1s4 2p2–1s2 1s3 1s4 1s5 2p3–1s2 1s4 2p4–1s2 1s4 1s5 2p5–1s2 1s3 1s4 1s5 2p6–1s2 1s4 1s5 2p7–1s2 1s3 1s4 1s5 2p8–1s2 1s4 1s5 2p9–1s5 2p1091s2 1s3 1s4 1s5
585.24 540.05 659.90 616.36 603.00 588.19 665.21 607.43 667.83 609.62 594.48 671.70 626.65 612.84 597.55 692.95 630.48 614.31 702.41 653.29 638.30 621.73 717.39 650.65 633.44 640.22 808.25 743.89 724.52 703.24
0.982 0.018 0.380 0.270 0.128 0.223 0.014 0.986 0.448 0.285 0.266 0.448 0.410 0.024 0.117 0.396 0.187 0.417 0.000 0.295 0.466 0.239 0.222 0.417 0.361 1.000 0.001 0.165 0.327 0.506
0.988 0.012 0.434 0.266 0.104 0.196 0.006 0.994 0.466 0.335 0.199 0.456 0.451 0.014 0.079 0.405 0.093 0.502 0.040 0.209 0.629 0.122 0.067 0.612 0.321 1.000 0.003 0.072 0.276 0.649
0.006 0.006 0.054 0.004 0.024 0.027 0.008 0.008 0.018 0.050 0.067 0.008 0.041 0.010 0.038 0.009 0.094 0.085 0.040 0.086 0.163 0.117 0.155 0.195 0.040 0.000 0.002 0.093 0.051 0.143
Table 2 Relative transition probabilities in argon. Argon transitions (Racah)
Argon transitions (Paschen)
λ (nm)
This work
Whaling et al. [1]
This work – Whaling
4p0 [1/2]0–s0 [1/2]1 4s[3/2]1 4p0 [1/2]1–s0 [1/2]1 4s0 [1/2]0 4s[3/2]1 4s[3/2]2 4p0 [3/2]2–s0 [1/2]1 4s[3/2]1 4s[3/2]2 4p0 [3/2]1–s0 [1/2]1 4s0 [1/2]0 4s[3/2]1 4s[3/2]2 4p[1/2]0-4s[3/2]1 4p[3/2]2–s0 [1/2]1 4s[3/2]1 4s[3/2]2 4p[3/2]1–s0 [1/2]1 4s0 [1/2]0 4s[3/2]1 4s[3/2]2 4p[5/2]2–s0 [1/2]1 4s[3/2]1 4s[3/2]2 4p[5/2]3–4s[3/2]2 4p[1/2]1–s0 [1/2]1 4s0 [1/2]0 4s[3/2]1 4s[3/2]2
2p1–1s2 1s4 2p2–1s2 1s3 1s4 1s5 2p3–1s2 1s4 1s5 2p4–1s2 1s3 1s4 1s5 2p5–1s4 2p6–1s2 1s4 1s5 2p7–1s2 1s3 1s4 1s5 2p8–1s2 1s4 1s5 2p9–1s5 2p10–1s2 1s3 1s4 1s5
750.38 667.72 826.45 772.42 727.93 696.54 840.82 738.39 706.72 852.14 794.81 747.11 714.7 751.46 922.44 800.61 763.51 935.42 866.79 810.36 772.37 978.45 842.46 801.47 811.53 1148.41 1047 965.77 912.29
0.99 0.01 0.27 0.40 0.04 0.29 0.56 0.32 0.13 0.46 0.54 0.00 0.00 1.00 0.26 0.25 0.49 0.04 0.10 0.42 0.43 0.07 0.51 0.43 1.00 – – – –
– – 0.43 0.33 0.05 0.18 0.65 0.25 0.11 – – – – – 0.15 0.14 0.71 0.03 0.07 0.74 0.15 – – – – 0.01 0.04 0.21 0.74
– – 0.17 0.07 0.01 0.11 0.09 0.07 0.02 – – – – – 0.12 0.11 0.22 0.01 0.03 0.32 0.28 – – – – – – – –
relationship between the signal intensity and discharge current. We found that the slope analysis is a good technique of finding the relative transition probabilities of the spectral lines within a multiplet. Some new branching ratios for argon are listed. The
uncertainty in the present work is about 5% that is attributed to the uncertainty attached to the measurement of the area under the line profile. A comparison between the reported data and the published work shows a good agreement.
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Table 3 Relative transition probabilities in krypton. Krypton transitions (Racah)
Krypton transitions (Paschen)
λ (nm)
This work
Aymar et al. [11]
Chang [21]
This work – Aymar
This work – Chang
5p0 [1/2]0–5s0 [1/2]1 5s[3/2]1 5p0 [3/2]2–5s0 [1/2]1 5s[3/2]1 5s[3/2]2 5p0 [1/2]1–5s0 [1/2]1 5s’[1/2]0 5s[3/2]1 5s[3/2]2 5p0 [3/2]1–5s0 [1/2]1 5s0 [1/2]0 5s[3/2]1 5s[3/2]2 5p[1/2]0–5s0 [1/2]1 5s[3/2]1 5p[3/2]2–5s0 [1/2]1 5s[3/2]1 5s[3/2]2 5p[3/2]1–5s0 [1/2]1 5s0 [1/2]0 5s[3/2]1 5s[3/2]2 5p[5/2]2–5s0 [1/2]1 5s[3/2]1 5s[3/2]2 5p[5/2]3–5s[3/2]2 5p[1/2]1–5s0 [1/2]1 5s0 [1/2]0 5s[3/2]1 5s[3/2]2
2p1–1s2 1s4 2p2–1s2 1s4 1s5 2p3–1s2 1s3 1s4 1s5 2p4–1s2 1s3 1s4 1s5 2p5–1s2 1s4 2p6–1s2 1s4 1s5 2p7–1s2 1s3 1s4 1s5 2p8–1s2 1s4 1s5 2p9–1s5 2p10–1s2 1s3 1s4 1s5
768.52 557.31 826.32 587.09 556.22 828.10 785.48 587.99 557.02 850.88 805.95 599.38 567.24 1212.35 758.74 1373.88 819.00 760.15 1404.60 1286.18 829.81 769.45 1547.40 877.67 810.43 811.29 1878.54 1672.65 975.17 892.86
1.00 0.00 0.93 0.06 0.01 0.42 0.51 0.02 0.05 0.50 0.47 0.01 0.02 – – – – – – – – – – – – 1.00 – – – –
0.93 0.07 0.93 0.05 0.01 0.42 0.57 0.00 0.01 0.49 0.51 0.00 0.00 – – – – – – – – – – – – 1.00 – – – –
1.00 – 0.95 0.04 0.01 0.41 0.54 0.00 0.05 0.56 0.43 0.00 0.00 0.02 0.98 0.07 0.22 0.71 0.01 0.01 0.84 0.13 0.01 0.69 0.30 1.00 0.05 0.02 0.19 0.75
0.07 0.07 0.00 0.01 0.00 0.00 0.06 0.02 0.04 0.01 0.04 0.01 0.02 – – – – – – – – – – – – 0.00 – – – –
0.00 – 0.02 0.02 0.00 0.01 0.02 0.01 0.00 0.07 0.04 0.01 0.02 – – – – – – – – – – – – 0.00 – – – –
Table 4 Relative transition probabilities in xenon. Xenon transitions (Racah)
Xenon transitions (Paschen)
λ (nm)
This work
Aymar et al. [11]
Cabrera et al. [12]
This work – Aymar
This work – Cabrera
6p0 [1/2]0–s0 [1/2]1 6s[3/2]1 6p0 [1/2]1–s0 [1/2]1 6s’[1/2]0 6s[3/2]1 6s[3/2]2 6p0 [3/2]2–s0 [1/2]1 6s[3/2]1 6s[3/2]2 6p0 [3/2]1–s0 [1/2]1 6s0 [1/2]0 6s[3/2]1 6s[3/2]2 6p[1/2]0–s0 [1/2]1 6s[3/2]1 6p[3/2]2–6s[3/2]1 6s[3/2]2 6p[3/2]1–s0 [1/2]0 6s[3/2]1 6s[3/2]2 6p[5/2]3–6s[3/2]2 6p[5/2]2–6s[3/2]1 6s[3/2]2 6p[1/2]1–6s[3/2]1 6s[3/2]2
2p1–1s2 1s4 2p2–1s2 1s3 1s4 1s5 2p3–1s2 1s4 1s5 2p4–1s2 1s3 1s4 1s5 2p5–1s2 1s4 2p6–1s4 1s5 2p7–1s3 1s4 1s5 2p8–1s5 2p9–1s4 1s5 2p10–1s4 1s5
788.73 458.27 826.65 764.2 470.82 450.09 834.68 473.41 452.46 893.08 820.63 491.65 469.09 3408.4 828.01 895.22 823.16 3624.15 916.26 840.91 881.94 992.31 904.54 1083.83 979.97
0.69 0.31 0.40 0.50 0.03 0.07 0.89 0.05 0.05 0.30 0.43 0.23 0.05 – – 0.33 0.67 – – – 1.00 0.65 0.35 – –
0.88 0.12 0.47 0.52 0.00 0.01 0.93 0.04 0.03 0.49 0.44 0.06 0.02 – 1.00 0.30 0.70 – 0.94 0.06 1.00 0.65 0.35 0.08 0.92
0.86 0.14 0.38 0.51 0.00 0.10 0.91 0.07 0.03 0.48 0.41 0.10 0.02 – 1.00 0.33 0.67 – 0.95 0.05 1.00 0.66 0.34 0.05 0.95
0.188 0.188 0.070 0.020 0.033 0.057 0.037 0.014 0.024 0.190 0.015 0.165 0.030 – – 0.027 0.027 – – – 0.000 0.000 0.000 – –
0.168 0.168 0.020 0.010 0.033 0.033 0.017 0.016 0.024 0.180 0.015 0.125 0.030 – – 0.003 0.003 – – – 0.000 0.010 0.010 – –
References [1] W. Whaling, M.T. Carle, M.L. Pitt, J. Quant. Spectrosc. Radiat.Transf. 50 (1993) 7. [2] N.K. Piracha, R. Feaver, T.H. Gilani, R. Ahmed, R. Ali, M.A. Baig, Opt. Commun.282 (13) (2009) 2532–2538.
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W.E. Ernst, E. Schulz-Gulde, Physica 93C (1978) 136. J. Sabbagh, N. Sadeghi, J. Quant. Spectrosc. Radiat. Transf. 17 (1977) 297. M. Aymar, M. Coulombe, At. Data Nucl. Data Tabl. 21 (1978) 537. J.A. Cabrera, M. Ortiz, J. Campos. Phys. C 104 (1980) 416. K.-P. Nick, V. Helbig, Phys. Scr. 32 (1985) 111. C. Peraza, P. MartinJ. Campos, J. Quant. Spectrosc. Radiat. Transf. 46 (1991) 455. The National Institute of Standards and Technology (NIST) 〈http://www.nist. gov/pml/data/asd.cfm〉.
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
On the relative transition probabilities of rare gases in the 1si–2pj region N.K. Piracha a,n, K.V. Duncan-Chamberlin a, John Kaminsky a, D. Delanis a, M.A. Baig b a b
Department of Physics, John Carroll University, University Heights, OH 44118, USA National Center for Physics, Quaid-i-Azam University Campus, 45320 Islamabad, Pakistan
art ic l e i nf o
a b s t r a c t
Article history: Received 23 March 2014 Received in revised form 23 April 2014 Accepted 26 April 2014
We have measured the relative transition probabilities of the 1si–2pj transitions in rare gases using hollow cathode lamps. The emission spectra of each rare gas were recorded as the function of discharge current. Two independent calibration modes for the spectrometer have been used to increase the reliability of our data. Uncertainty in the data have been measured and found to be within 5%. The relative transition probabilities are reported for 30 lines of Ne I, 25 lines of Ar I, fourteen lines of Kr I, and eighteen lines of Xe I. The present results are in good agreement with the published data. The data can also be used to calibrate the relative detection efficiency of a spectrometer over a range of 400–1000 nm. & 2014 Published by Elsevier B.V.
Keywords: Optogalvanic effect Transition probabilities Rare gases
1. Introduction The presence of buffer gases in the hollow cathode lamps provide accurately measured spectral lines that can be used for the wavelength calibration covering the UV to IR region. Since their relative line intensities are also well documented therefore it provides a reliable means of determining the relative detection efficiencies of different detectors. The knowledge of transition probabilities is helpful in understanding the atomic structure and plasma characteristics [1,2]. This data is also important in the field of astrophysics to model the upper atmosphere and to determine rare gas concentration in celestial bodies [3]. Of all the rare gases, the spectral characteristics of neon, in general, have been extensively studied. This is because of its emission spectrum that lies in the mid-visible region and is easily accessible compared to the other rare gases. Bridges and Wiese [4] studied the transition probabilities of the Ne I lines belonging to the 3s–3p transition array by using a wall-stabilized arc with an argon neon mixture at atmospheric pressure. Using a glow discharge containing a He–Ne–Ar mixture, Inatsugu and Holmes [5] measured the neon transition probabilities for the 3s–3p region. They compared the line intensities with the 632.8 nm neon line to determine the relative transition probabilities. These values were then converted to the absolute transition probabilities by using an accurate value of the Einstein coefficient for the 632.8 nm transition. Using a hollow cathode discharge, Chang and Setser [6] determined the neon absolute transition probabilities
n
Corresponding author. E-mail address: [email protected] (N.K. Piracha).
for the 3s–3p transition. The radiative lifetimes of the eight p states were measured and combined with the measured branching ratios to deduce the absolute transition probabilities. Recently, Bacławski [7] measured the neon line intensities belonging to the 3p–3d region. The relative transition probabilities obtained from line intensities were converted to the absolute scale by normalizing them to the radiative lifetime value of the 3d0 [3/2]2 state. The transition probabilities were used for evaluating the J-file sum rule for the transition array of 3p–3d. More recently, Asghar et al. [8] reported the transition probabilities of the 3p–3s transitions array in neon using the LIBS technique. In argon, the branching ratios of 329 emission lines ranging over wavelengths from 210 to 4591 nm were measured by Whaling et al. [1]. In the case of krypton, Ernst and Schultz-Gulde [9] reported the relative transition probabilities for the 5s–5p and 5s–6p transition arrays using a wall-stabilized arc at atmospheric pressure. Sabbagh and Sadeghi [10] used light absorption with Xe I plasma afterglow to measure the relative transition probabilities in the 6s–6p transition array. Two well known reference lines were chosen to determine the absolute transition probabilities. Using intermediate coupling and configuration mixing approach, Aymar and Coulombe [11] studied the transition probabilities and lifetimes of Kr I and Xe I. Cabrera et al. [12] used electron pulses and a monochromator to determine the relative and absolute transition probabilities in Xe for the lines belonging to the 6s–6p transition array. Nick and Helbig [13] used a low-pressure discharge to measure the relative transition probabilities in the 6s–6p0 and 6s–7p transition arrays in Xe and also computed the lifetime of several levels. Peraza et al. [14] determined the relative transition probabilities for the 6p–(7–13)s transition arrays of Xe I using the emission line-intensities from a Xe arc lamp. Coupled with the
http://dx.doi.org/10.1016/j.optcom.2014.04.063 0030-4018/& 2014 Published by Elsevier B.V.
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line-strength sum rules, these relative values were converted into the absolute values. The National Institute of Standards and Technology (NIST) atomic spectra database enlists the transition probabilities for the excited levels in neutral rare gases [15]. The present contribution is in continuation of our studies on the optogalvanic spectroscopy of rare gases [2,16–19]. In this article, we report an extensive data on the measurement of transition probabilities of neon, argon, krypton and xenon in the 1si–2pj transition array using hollow cathode lamps filled with these gases. We have recorded the emission spectra of these gases at different discharge conditions. The intensity data (area under each spectral line) were plotted against the discharge current which resulted into linear plots. This new technique provided a very reliable data that have been used to calculate the relative branching ratios. The present experimental results are compared, where available, with the published data showing a good agreement.
2.2. Absolute irradiance Absolute irradiance uses a lamp of known output (in terms of microwatts per square centimeter per nanometer) to calibrate spectrometer's response at every pixel. This corrects the shape and magnitude of the spectrum and the resulting spectrum is in terms of microwatts per square centimeter per nanometer (mW/cm2/nm). The spectrometers were sent to Ocean Optics for this absolute calibration. The entire set of data collected with mode “a” calibration was repeated with these reconfigured (mode b) spectrometers. Each spectrum was recorded three times and the final data is the average of these sets. The reported measurement error of 5% is the maximum deviation that we observed in our data recorded in using both the calibration methods. We found that both the calibration techniques are acceptable and the extracted branching ratios are independent of the calibration modes used in the present work.
3. Results and discussion 2. Experimental details The experimental setup used in this work consisted of commercial hollow cathode lamps (Photron, Australia) and Ocean Optics spectrometers (HR4000). Each hollow cathode lamp is filled with a rare gas at low pressures between 5 and 8 Torr. We made use of two ocean optics spectrometers to cover the entire range from near UV through visible to near IR. One spectrometer works in the UV–vis (350–704 nm), whereas, the other is configured for the near infrared range (697–1100 nm). Every Ocean Optics spectrometer has what is called an “instrument response function”, or IRF. The IRF refers to how much the spectrometer responds to the light intensity across its wavelength range. The IRF for each spectrometer is unique but it is possible to compensate for the IRF. The two common corrections are relative irradiance and absolute irradiance modes. We used these two independent calibration modes of our spectrometers to record two full sets of emission spectra of the above mentioned gases that are discussed here.
2.1. Relative irradiance mode The two spectrometers have a detection efficiency response which is non-uniform across their spectral range. To compensate it, the relative irradiance mode of the ocean optics spectrasuite software was used. This method allowed for the direct comparison of any two peaks because it calibrates the individual detector's response. To accomplish this, a blackbody source of known color temperature was used. In this experiment, the source was an ocean optics LS-1 Tungsten halogen lamp with a color temperature of 2800 K. Once the lamp had warmed to a constant temperature a reference spectrum was recorded. A dark spectrum was also taken, and then the spectrometer was calibrated for relative irradiance measurements. The Spectrasuite software then used the following equation to determine the relative irradiance at any given wavelength λ; I L;T ¼ NBλ;T ðSλ Dλ Þ=ðRλ Dλ Þ where N is the normalizing term, Bλ,T is the energy of the blackbody source which is calculated from the temperature, Rλ is the intensity from the reference spectrum, Dλ is the dark spectrum intensity and Sλ is the intensity of the source spectrum. Once the system was calibrated, three sets of experimental data of the gas spectra were obtained and an average spectra were used for further analysis.
Excluding helium, the ground state electronic configuration of rare gases is mp6 1S0, where m¼ 2, 3, 4 and 5 for neon, argon, krypton and xenon respectively. The excited states of these gases are, in general, given by the jcK-coupling scheme [20]. According to this scheme, the first group of the excited levels has a mp5(mþ 1)s configuration. This results in four energy levels namely, mp5(mþ1) s[3/2]2, mp5 (mþ1)s [3/2]1, mp5 (mþ 1)s0 [1/2]0 and mp5 (mþ1)s0 [1/2]1. Two of these levels mp5 (mþ1)s [3/2]2 and mp5 (mþ1)s0 [1/2]0 possess long radiative lifetimes and are called the metastable levels. One, the mp5 (mþ1)s [3/2]1, is semi-metastable, while mp5 (mþ1)s0 [1/2]1 is short lived and is termed as resonance level. The second group of excited levels come from the mp5(mþ 1)p configuration. All of these levels are relatively short lived. A rather convenient and simplified way of naming the excited levels of rare gases is Paschen notation. According to this alternate notation, the first group of excited levels is termed as 1si and is subdivided into four levels namely, 1s5, 1s4, 1s3 and 1s2. Here 1s5 and 1s3 represent the two metastable levels, 1s4 is the semi-metastable and 1s3 is the resonance level. Similarly the second group, the mp5(mþ1)p configuration, is expressed by 2pj levels, subdivided to 2p1 to 2p10 levels. These 2pj levels are radiatively connected to at least one of the 1si levels and have typical radiative lifetimes in the range of nano seconds. We, in this article, have made use of both of these naming methods to maintain consistency with the published literature. To map the 1si–2pj transitions each rare gas spectrum was recorded both in the visible and in the infrared region using the two spectrometers. For every set of data, the current was increased at fixed increments. In both neon and xenon, the current range was 2–18 mA with increments of 2 mA; whereas, in argon and krypton, the spectra were recorded from 1 to 12 mA using 1 mA steps. These current ranges were selected to prevent detector saturation. The spectra in the visible region are rich in transitions as compared to that of the infrared region. To calculate the branching ratios, the area beneath the peaks in the spectra was determined. This was accomplished by using the integration utilities of Logger Pro and Origin. These areas were graphed against the discharge current and grouped based on transitions belonging to the same upper level in each gas. The slopes of these plots were determined. Fig. 1 shows plots of the transitions that belong to the upper level np0 [3/2]2, where n ¼3, 4, 5, and 6 for neon, argon, krypton, and xenon respectively. The neon plot shows the following transitions: 3p0 ½3=22 -3s0 ½1=21
ð667:82 nmÞ
-3s0 ½3=21
ð609:62 nmÞ
-3s0 ½3=22
ð594:48 nmÞ:
Please cite this article as: N.K. Piracha, et al., Optics Communications (2014), http://dx.doi.org/10.1016/j.optcom.2014.04.063i
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Ne 3p'[3/2]2 (2p4)
0.6
667.82nm 609.61nm 594.48nm
0.5
Intensity (uW/cm2)
0.7
0.4 0.3 0.2 0.1 0.0
3
1.2
Ar 4p'[3/2]2 (2p3)
1.0
840.82nm 738.39nm 706.72nm
0.8 0.6 0.4 0.2 0.0
4
2
6
8
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14
2
4
6
Kr 5p'[3/2]2 (2p2)
0.5
826.32nm 587.09nm 556.22nm
10
12
Xe 6p'[3/2]2 (2p3)
0.10
Intensity (uW/cm2)
0.6
8
Current (mA)
Current (mA)
Intensity (uW/cm2)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
Intensity (uW/cm2)
N.K. Piracha et al. / Optics Communications ∎ (∎∎∎∎) ∎∎∎–∎∎∎
0.4 0.3 0.2
834.68nm 473.41nm 452.46nm
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Current (mA)
Fig. 1. Intensity vs. current plots for the transitions originating from the upper level np0 [3/2]2 where n¼ 3, 4, 5, and 6 for Ne, Ar, Kr and Xe respectively.
In argon plot, the transitions are 4p0 ½3=22 -4s0 ½1=21 ð840:82 nmÞ -4s½3=21 ð738:39 nmÞ -4s½3=22 ð706:72 nmÞ: In krypton plot, the transitions are 5p0 ½3=22 -5s0 ½1=21 ð826:32 nmÞ -5s½3=21 ð587:09 nmÞ -5s½3=22 ð556:22 nmÞ: Whereas, in xenon plot, the following transitions are shown: 0
6p ½3=22 -6s0 ½1=21 ð834:68 nmÞ -6s½3=21 ð473:41 nmÞ -6s½3=22 ð452:46 nmÞ: The branching ratios of the transitions were calculated from the slopes (M) of the plots for a set of transitions from the same upper level using Eq. (1): BR ¼
M1 M1 þ M2 þ M3 þ M4
data from this work is compared with Chang et al. [21] reported values (see Table 1) and both are in good agreement with each other. In our measurements over the entire current range, we did not observe the 3p[3/2]1–3s0 [1/2]1 transition at 702.41 nm. We, therefore, have assigned it a branching ratio value of zero. In Table 2, the branching ratios of argon for the 4s–4p region are presented. The data is compared with Whaling [1]. It may be noted that the two lines at 772.37 nm and 772.42 nm belonging to the 4p[3/2]1–4s[3/2]2 and 4p0 [1/2]1–4s0 [1/2]0 transitions, respectively, were not fully resolved. The branching ratios of krypton for the 5s–5p spectral region are given in Table 3. The data shows a good agreement with the literature values; Aymer [11] and Chang [21]. As seen in this table, there are many transitions for which the branching ratios cannot be determined. This is because one or more members of each of these radiative set lies beyond our detection capabilities. In Table 4, the relative transition probabilities in xenon in the 6s–6p region are presented and a comparison is made with that of Aymar [11], and Cabrera [12]. The agreement between the data is very good that reflects the validity and quality of the present experimental technique to determine the transition probabilities of the spectral lines.
ð1Þ
Because all these plots are linear (see Fig. 1), it is apparent that the branching ratios stay constant regardless of the current change in a certain range. Therefore, the slope method for determining the branching ratios is a good technique as it is based on the data averaging. Tables 1–4 show the branching ratios in the Ne, Ar, Kr and Xe spectra in the 1si–2pj transition array. The neon branching ratio
4. Conclusion This report provides a complete list on the relative transitions probabilities for multiplets in the spectra of neon, argon, krypton and xenon in the 1si–2pj region. As a result of the spectrometer's sensitivity, analysis in the wavelengths region from 400 nm to 1000 nm was conducted. Our experimental method yields a linear
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Table 1 Relative transition probabilities in neon. Neon transitions (Racah)
Neon transitions (Paschen)
λ (nm)
This work
Chang et al. [6]
This work – Chang
3p0 [1/2]0–3s0 [1/2]1 3s[3/2]1 3p0 [1/2]1–3s0 [1/2]1 3s0 [1/2]0 3s[3/2]1 3s[3/2]2 3p[1/2]0–3s0 [1/2]1 3s[3/2]1 3p0 [3/2]2–3s0 [1/2]1 3s[3/2]1 3s[3/2]2 3p0 [3/2]1–3s0 [1/2]1 3s0 [1/2]0 3s[3/2]1 3s[3/2]2 3p[3/2]2–3s0 [1/2]1 3s[3/2]1 3s[3/2]2 3p[3/2]1–3s0 [1/2]1 3s0 [1/2]0 3s[3/2]1 3s[3/2]2 3p[5/2]2–3s0 [1/2]1 3s[3/2]1 3s[3/2]2 3p[5/2]3–3s[3/2]2 3p[1/2]1–3s0 [1/2]1 3s0 [1/2]0 3s[3/2]1 3s[3/2]2
2p1–1s2 1s4 2p2–1s2 1s3 1s4 1s5 2p3–1s2 1s4 2p4–1s2 1s4 1s5 2p5–1s2 1s3 1s4 1s5 2p6–1s2 1s4 1s5 2p7–1s2 1s3 1s4 1s5 2p8–1s2 1s4 1s5 2p9–1s5 2p1091s2 1s3 1s4 1s5
585.24 540.05 659.90 616.36 603.00 588.19 665.21 607.43 667.83 609.62 594.48 671.70 626.65 612.84 597.55 692.95 630.48 614.31 702.41 653.29 638.30 621.73 717.39 650.65 633.44 640.22 808.25 743.89 724.52 703.24
0.982 0.018 0.380 0.270 0.128 0.223 0.014 0.986 0.448 0.285 0.266 0.448 0.410 0.024 0.117 0.396 0.187 0.417 0.000 0.295 0.466 0.239 0.222 0.417 0.361 1.000 0.001 0.165 0.327 0.506
0.988 0.012 0.434 0.266 0.104 0.196 0.006 0.994 0.466 0.335 0.199 0.456 0.451 0.014 0.079 0.405 0.093 0.502 0.040 0.209 0.629 0.122 0.067 0.612 0.321 1.000 0.003 0.072 0.276 0.649
0.006 0.006 0.054 0.004 0.024 0.027 0.008 0.008 0.018 0.050 0.067 0.008 0.041 0.010 0.038 0.009 0.094 0.085 0.040 0.086 0.163 0.117 0.155 0.195 0.040 0.000 0.002 0.093 0.051 0.143
Table 2 Relative transition probabilities in argon. Argon transitions (Racah)
Argon transitions (Paschen)
λ (nm)
This work
Whaling et al. [1]
This work – Whaling
4p0 [1/2]0–s0 [1/2]1 4s[3/2]1 4p0 [1/2]1–s0 [1/2]1 4s0 [1/2]0 4s[3/2]1 4s[3/2]2 4p0 [3/2]2–s0 [1/2]1 4s[3/2]1 4s[3/2]2 4p0 [3/2]1–s0 [1/2]1 4s0 [1/2]0 4s[3/2]1 4s[3/2]2 4p[1/2]0-4s[3/2]1 4p[3/2]2–s0 [1/2]1 4s[3/2]1 4s[3/2]2 4p[3/2]1–s0 [1/2]1 4s0 [1/2]0 4s[3/2]1 4s[3/2]2 4p[5/2]2–s0 [1/2]1 4s[3/2]1 4s[3/2]2 4p[5/2]3–4s[3/2]2 4p[1/2]1–s0 [1/2]1 4s0 [1/2]0 4s[3/2]1 4s[3/2]2
2p1–1s2 1s4 2p2–1s2 1s3 1s4 1s5 2p3–1s2 1s4 1s5 2p4–1s2 1s3 1s4 1s5 2p5–1s4 2p6–1s2 1s4 1s5 2p7–1s2 1s3 1s4 1s5 2p8–1s2 1s4 1s5 2p9–1s5 2p10–1s2 1s3 1s4 1s5
750.38 667.72 826.45 772.42 727.93 696.54 840.82 738.39 706.72 852.14 794.81 747.11 714.7 751.46 922.44 800.61 763.51 935.42 866.79 810.36 772.37 978.45 842.46 801.47 811.53 1148.41 1047 965.77 912.29
0.99 0.01 0.27 0.40 0.04 0.29 0.56 0.32 0.13 0.46 0.54 0.00 0.00 1.00 0.26 0.25 0.49 0.04 0.10 0.42 0.43 0.07 0.51 0.43 1.00 – – – –
– – 0.43 0.33 0.05 0.18 0.65 0.25 0.11 – – – – – 0.15 0.14 0.71 0.03 0.07 0.74 0.15 – – – – 0.01 0.04 0.21 0.74
– – 0.17 0.07 0.01 0.11 0.09 0.07 0.02 – – – – – 0.12 0.11 0.22 0.01 0.03 0.32 0.28 – – – – – – – –
relationship between the signal intensity and discharge current. We found that the slope analysis is a good technique of finding the relative transition probabilities of the spectral lines within a multiplet. Some new branching ratios for argon are listed. The
uncertainty in the present work is about 5% that is attributed to the uncertainty attached to the measurement of the area under the line profile. A comparison between the reported data and the published work shows a good agreement.
Please cite this article as: N.K. Piracha, et al., Optics Communications (2014), http://dx.doi.org/10.1016/j.optcom.2014.04.063i
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Table 3 Relative transition probabilities in krypton. Krypton transitions (Racah)
Krypton transitions (Paschen)
λ (nm)
This work
Aymar et al. [11]
Chang [21]
This work – Aymar
This work – Chang
5p0 [1/2]0–5s0 [1/2]1 5s[3/2]1 5p0 [3/2]2–5s0 [1/2]1 5s[3/2]1 5s[3/2]2 5p0 [1/2]1–5s0 [1/2]1 5s’[1/2]0 5s[3/2]1 5s[3/2]2 5p0 [3/2]1–5s0 [1/2]1 5s0 [1/2]0 5s[3/2]1 5s[3/2]2 5p[1/2]0–5s0 [1/2]1 5s[3/2]1 5p[3/2]2–5s0 [1/2]1 5s[3/2]1 5s[3/2]2 5p[3/2]1–5s0 [1/2]1 5s0 [1/2]0 5s[3/2]1 5s[3/2]2 5p[5/2]2–5s0 [1/2]1 5s[3/2]1 5s[3/2]2 5p[5/2]3–5s[3/2]2 5p[1/2]1–5s0 [1/2]1 5s0 [1/2]0 5s[3/2]1 5s[3/2]2
2p1–1s2 1s4 2p2–1s2 1s4 1s5 2p3–1s2 1s3 1s4 1s5 2p4–1s2 1s3 1s4 1s5 2p5–1s2 1s4 2p6–1s2 1s4 1s5 2p7–1s2 1s3 1s4 1s5 2p8–1s2 1s4 1s5 2p9–1s5 2p10–1s2 1s3 1s4 1s5
768.52 557.31 826.32 587.09 556.22 828.10 785.48 587.99 557.02 850.88 805.95 599.38 567.24 1212.35 758.74 1373.88 819.00 760.15 1404.60 1286.18 829.81 769.45 1547.40 877.67 810.43 811.29 1878.54 1672.65 975.17 892.86
1.00 0.00 0.93 0.06 0.01 0.42 0.51 0.02 0.05 0.50 0.47 0.01 0.02 – – – – – – – – – – – – 1.00 – – – –
0.93 0.07 0.93 0.05 0.01 0.42 0.57 0.00 0.01 0.49 0.51 0.00 0.00 – – – – – – – – – – – – 1.00 – – – –
1.00 – 0.95 0.04 0.01 0.41 0.54 0.00 0.05 0.56 0.43 0.00 0.00 0.02 0.98 0.07 0.22 0.71 0.01 0.01 0.84 0.13 0.01 0.69 0.30 1.00 0.05 0.02 0.19 0.75
0.07 0.07 0.00 0.01 0.00 0.00 0.06 0.02 0.04 0.01 0.04 0.01 0.02 – – – – – – – – – – – – 0.00 – – – –
0.00 – 0.02 0.02 0.00 0.01 0.02 0.01 0.00 0.07 0.04 0.01 0.02 – – – – – – – – – – – – 0.00 – – – –
Table 4 Relative transition probabilities in xenon. Xenon transitions (Racah)
Xenon transitions (Paschen)
λ (nm)
This work
Aymar et al. [11]
Cabrera et al. [12]
This work – Aymar
This work – Cabrera
6p0 [1/2]0–s0 [1/2]1 6s[3/2]1 6p0 [1/2]1–s0 [1/2]1 6s’[1/2]0 6s[3/2]1 6s[3/2]2 6p0 [3/2]2–s0 [1/2]1 6s[3/2]1 6s[3/2]2 6p0 [3/2]1–s0 [1/2]1 6s0 [1/2]0 6s[3/2]1 6s[3/2]2 6p[1/2]0–s0 [1/2]1 6s[3/2]1 6p[3/2]2–6s[3/2]1 6s[3/2]2 6p[3/2]1–s0 [1/2]0 6s[3/2]1 6s[3/2]2 6p[5/2]3–6s[3/2]2 6p[5/2]2–6s[3/2]1 6s[3/2]2 6p[1/2]1–6s[3/2]1 6s[3/2]2
2p1–1s2 1s4 2p2–1s2 1s3 1s4 1s5 2p3–1s2 1s4 1s5 2p4–1s2 1s3 1s4 1s5 2p5–1s2 1s4 2p6–1s4 1s5 2p7–1s3 1s4 1s5 2p8–1s5 2p9–1s4 1s5 2p10–1s4 1s5
788.73 458.27 826.65 764.2 470.82 450.09 834.68 473.41 452.46 893.08 820.63 491.65 469.09 3408.4 828.01 895.22 823.16 3624.15 916.26 840.91 881.94 992.31 904.54 1083.83 979.97
0.69 0.31 0.40 0.50 0.03 0.07 0.89 0.05 0.05 0.30 0.43 0.23 0.05 – – 0.33 0.67 – – – 1.00 0.65 0.35 – –
0.88 0.12 0.47 0.52 0.00 0.01 0.93 0.04 0.03 0.49 0.44 0.06 0.02 – 1.00 0.30 0.70 – 0.94 0.06 1.00 0.65 0.35 0.08 0.92
0.86 0.14 0.38 0.51 0.00 0.10 0.91 0.07 0.03 0.48 0.41 0.10 0.02 – 1.00 0.33 0.67 – 0.95 0.05 1.00 0.66 0.34 0.05 0.95
0.188 0.188 0.070 0.020 0.033 0.057 0.037 0.014 0.024 0.190 0.015 0.165 0.030 – – 0.027 0.027 – – – 0.000 0.000 0.000 – –
0.168 0.168 0.020 0.010 0.033 0.033 0.017 0.016 0.024 0.180 0.015 0.125 0.030 – – 0.003 0.003 – – – 0.000 0.010 0.010 – –
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