Observation of the Cs233Σg+ state by infrared–infrared double resonance

Chemical Physics Letters 458 (2008) 267–271

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Observation of the Cs2 33 Rþ g state by infrared–infrared double resonance Dan Li, Feng Xie, Li Li * Department of Physics and Key Laboratory of Atomic and Molecular Nanosciences, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 17 January 2008 In final form 28 April 2008 Available online 4 May 2008

a b s t r a c t The Cs2 33 Rþ g state, which was observed previously by two-photon excitation [D. Li, F. Xie, Li Li, S. Magnier, V.B. Sovkov, V.S. Ivanov, Chem. Phys. Lett. 441 (2007) 39], has been observed by infrared–infrared (IR–IR) double resonance spectroscopy. One hundred and seventy IR–IR double resonance lines have been assigned to transitions into the 33 Rþ g v = 2–12 levels. Hyperfine structure of this state has been resolved in the excitation spectra. Molecular constants and the potential energy curve of this state are reported in this Letter. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction In an earlier paper, we reported theoretical calculation and experimental observation by two-photon spectroscopy of the 3 þ Cs2 33 Rþ g and a Ru states [1]. Fifty two-photon transitions into the 33 Rþ v = 2–9 levels have been observed. The vibrational quang tum numbers of the 33 Rþ g levels observed by two-photon transitions were determined by resolving fluorescence to the a3 Rþ u state. Because no accurate molecular constants of the intermediate 3 A1 Rþ u and b Pu states are available and the resolution of the 3 þ 33 Rþ ! a R g u fluorescence spectra was low, the rotational quantum numbers of the two-photon excited 33 Rþ g levels could not be determined in the previous work. Thus molecular constants of the 33 Rþ g and a3 Rþ u states could not be obtained. Accurate molecular constants of the Cs2 ground state are avail3 able [2]. The spin–orbit interaction of the Cs2 A1 Rþ u and b P0u 1 þ states is quite strong and most levels of the A Ru state are perturbed by the b3P0u state [3,4]. Although no accurate molecular 3 constants are available for the A1 Rþ u and b Pu states, Verges and 1 þ 1 þ Amiot reported A Ru $ X Rg transition frequencies observed by Fourier transform spectroscopy (FTS) [4]. Recently, we carried out infrared–infrared (IR–IR) double resonance excitation spectros3 þ copy via the A1 Rþ u levels determined by FTS and observed the 3 Rg state with sub-Doppler resolution. This paper reports our new experimental results. 2. Experimental The experimental setup is similar to the setup in our previous K2 IR–IR double resonance experiment [5]. Cesium vapor was generated in a heatpipe oven. Argon was used as the buffer gas at a pressure of about 1 Torr and the vapor temperature was about

* Corresponding author. Fax: +86 10 6278 1598. E-mail address: [email protected] (L. Li). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.04.115

300 °C. A single mode tunable Toptica DL100 diode laser (9620– 9830 cm1 scanning range, 25 mW power at the entrance window of the oven, 5 MHz linewidth) was used as the pump laser, and another DL100 diode laser (9560–9750 cm1 scanning range, 30 mW power at the entrance window of the oven, 5 MHz linewidth) was used as the probe laser. The two laser beams counter-propagated and crossed at the center of the heatpipe. While 0 the pump laser frequency was held fixed to excite an A1 Rþ u v, 00 00 00 0 J0 X1 Rþ v , J (J = J ± 1) transition, the probe laser frequency g 0 0 was scanned to further excite the 33 Rþ A1 Rþ g u v , J transition, and double resonance signals were detected by monitoring the 3 þ 33 Rþ g ! a Ru fluorescence with interference filters and a photomultiplier tube. When the pump and probe lasers were held fixed 3 þ 3 þ to excite an upper 33 Rþ g level, 3 Rg ! a Ru fluorescence was dispersed by a 0.85 m double grating Spex 1404 monochromator. 3. Results 3 The Cs2 A1 Rþ u state is strongly perturbed by the b P0u state [3,4]. Recently, we observed the b3P0u v0 = 0–47 levels by resolved fluorescence from the 23D1g state [6]. In our fluorescence spectra all b3P0u e-symmetry levels (J0 = 12–100) below the A1 Rþ u state are shifted down by 15–40 cm1 from their unperturbed f-symmetry K-components due to the perturbation of the A1 Rþ u state. Although the ground state is a singlet state and transitions from singlet states to triplet states are forbidden, two-photon and double resonance excitation from the singlet ground state into triplet states via the perturbed intermediate A1 Rþ u state is possible.

3.1. Observation Sixty-eight 33 Rþ g levels of v = 2–12 have been observed by IR–IR double resonance excitation spectroscopy. The number of the vibrational and rotational levels observed is mainly limited by the wavelength range of the diode, the number of the confirmed intermediate A1 Rþ u levels, and Franck–Condon factors in our obser-

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D. Li et al. / Chemical Physics Letters 458 (2008) 267–271

0 0 vation region. The 33 Rþ A1 Rþ g v u v , J probe transition consists of 0 0 a ‘P’ (N = J -1 J ) line and an ‘R’ (N = J0 + 1 J0 ) rotational line, as predicted for the 3R+ (case b) 3P0 (case a) J0 , e-symmetry transitions. Because the rotational constants of Cs2 are small, the pump laser could have excited several A X transitions simultaneously, and the double resonance signals might not be all via the selected 0 0 intermediate A1 Rþ u v , J level. We have used two different methods 0 0 to confirm the 33 Rþ A1 Rþ g v, N u v , J transitions: (1) probing the 3 þ 0 0 3 Rg v, N level by pumping the intermediate A1 Rþ u v , J level from 1 þ 00 00 00 00 0 0 the X1 Rþ v , J = J + 1 and the X R v , J = J 1 levels. The two difg g ferent pump frequencies would not excite the same intermediate 1 þ 0 0 A1 Rþ u levels except the selected A Ru v , J level. Thus only the signals which appeared at the same probe frequencies with the same line shape and intensity are considered to be double resonance sig3 þ 0 0 nals via the selected A1 Rþ u v , J level, (2) probing the 3 Rg v, N level 1 þ 0 0 0 0 from both A1 Rþ v , J = N + 1 and A R v , J = N1 intermediate levu u els. This J0 = N+1 vs. J0 = N1 scheme could also confirm the N assignment of the upper 33 Rþ g levels. Hyperfine structure of the rotational lines has been resolved. Fig. 1 shows the excitation spectra of the 33 Rþ g v ¼ 4, N ¼ 3 þ 0 0 0 159 A1 Rþ A1 Rþ u v ¼ 9, J = 160 and 3 Rg v ¼ 5, N ¼ 102 u v ¼ 0 10, J = 101 lines. The fine–hyperfine components of a N J0 rotational line spread about 10 GHz. Line shapes of other excitation

a

10

Relative Intensity

19811.860 cm-1 8

3.2. Molecular constants and potential energy curve

6

4

-6

-4

-2

0

2

4

6

GHz

b

12

10

Relative Intensity

transitions are similar and we take the positions of the center of gravity of the excitation lines as the probe frequencies to calculate the term values of the rotational levels. The excitation data are given in Table A1 of Appendix A. 3 þ 3 þ The 33 Rþ g ! a Ru fluorescence pattern from a given 3 Rg v level excited by IR–IR double resonance excitation is the same as the pattern from the same vibrational level excited by two-photon excitation [1]. The vibrational quantum numbers are thus determined by resolved fluorescence to the a3 Rþ u state as described in the two-photon spectroscopy. In our previous Li2, Na2, and K2 experiments, double resonance signals were normally much stronger than two-photon excitation signals, and resolved fluorescence spectra from double resonance excited levels have much better signal/noise ratio. In this Cs2 33 Rþ g state case, however, the resolved fluorescence spectra recorded from two-photon excited 33 Rþ g levels have better S/N. Our previous Cs2 two-photon excitation was Doppler-limited. The Cs2 molecules absorbed two photons with same propagating direction and no fine–hyperfine structure was resolved. The current double resonance excitation, however, has sub-Doppler resolution and hyperfine structure has been resolved. The hyperfine components of a rotational line spread 10 GHz. Although the total intensity (the sum of all components) is stronger than the two-photon signal, the fluorescence spectra could be recorded only when the probe laser was held fixed to one component, and thus the S/N is not as good as in Ref. [1]. The rotational constant of the a3 Rþ state is very small u 3 þ (0.006 cm1) [1]. Our S/N ratio of the 33 Rþ g ! a Ru fluorescence spectra could not provide more information for the a3 Rþ u state. High-resolution fluorescence spectroscopy, FTS for example, will be more powerful to solve this problem.

Table 1 gives the molecular constants by a standard Dunham fit. Using these molecular constants, the Rydberg–Klein–Rees (RKR) potential curve has been constructed (Table 2). We also performed a direct-potential-fit (DPF) [7] from the observed term values and obtained the expanded Morse oscillator (EMO) potential curve (Table 3, the vibrational energies and rotational constants calculated from this potential curve are also listed in Table 2). The RKR and EMO potential curves can reproduce the observed energy levels as well as the Dunham constants. Fig. 2 (from Table A2 of Appendix A) shows the deviations between the observed term values and the calculated values from the Dunham constants, the RKR potential curve, and the EMO curve. The EMO potential curve reproduces the energy levels better than the RKR curve. The 33 Rþ g v = 2, N = 41 and v = 11, N = 173 levels have bigger deviations (Fig. 2 and Table A2 of Appendix A), which could be due to perturbations.

19710.995 cm-1 Table 1 Molecular constants of the Cs2 33 Rþ g state

8

6

4 -6

-4

-2

0

2

4

6

GHz Fig. 1. Hyperfine splitting of the excitation lines: (a) 33 Rþ A 1 Rþ g v ¼ 4, N ¼ 159 u 0 0 v0 = 9, J0 = 160 transition and (b) 33 Rþ A 1 Rþ g v ¼ 5, N ¼ 102 u v = 10, J = 101 transition.

Te Y10 Y20 Y30 Y01 Y11 Y02 Re (Å) y00

This worka

Magnier et al. [1]

Spies [3]

19463.1259(400) 28.8918(190) 0.07518(280) 5.4(1.3)  104 8.86687(160)  103 2.8103(140)  105 3.340 (23)  109 5.34880 (48) 0.0024 (7)

19 449 29.16 – – 0.00916 – – 5.26 –

19 500 28.8 – – 0.008877 – – 5.344 –

All constants are in cm1 except Re, which is in Å. Parameters are quoted with two standard deviation uncertainties (given in parenthesis) in units of the last digit shown. a y00 has been included in the Te, and Y 02 ¼ 4Y 301 =Y 210 ¼ 3:34058  109 agrees well with the value from our dunham fit.

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D. Li et al. / Chemical Physics Letters 458 (2008) 267–271 Table 2 RKR potential curve and the Ev and Bv values of the 33 Rþ g state calculated by RKR and DPF–EMO potential curves RKR potential curvea

v

0 1 2 3 4 5 6 7 8 9 10 11 12 a

DPF–EMO potential curve

Rmin (Å)

Rmax (Å)

Ev (cm1)

Bv (cm1)

Ev (cm1)

Bv (cm1)

5.22063 5.13199 5.07337 5.02711 4.98808 4.95396 4.92344 4.89571 4.87022 4.84660 4.82455 4.80386 4.78435

5.48592 5.59251 5.66915 5.73351 5.79071 5.84308 5.89193 5.93805 5.98199 6.02415 6.06479 6.10415 6.14239

19477.5507 19506.2939 19534.8916 19563.3470 19591.6634 19619.8441 19647.8922 19675.8110 19703.6037 19731.2736 19758.8239 19786.2579 19813.5788

0.00885282 0.00882472 0.00879661 0.00876851 0.00874041 0.00871230 0.00868420 0.00865610 0.00862799 0.00859989 0.00857179 0.00854369 0.00851558

19477.5463 19506.2745 19534.8643 19563.3172 19591.6347 19619.8183 19647.8695 19675.7896 19703.5800 19731.2418 19758.7765 19786.1850 19813.4686

0.00885678 0.00882753 0.00879849 0.00876967 0.00874106 0.00871267 0.00868448 0.00865649 0.00862871 0.00860112 0.00857372 0.00854652 0.00851950

Re = 5.34880 Å, y00 =  0.0024 cm1, Te = 19463.1259 cm1, vmin =  0.49992.

Table 3 Parameters defining the recommended EMO (NS = 3, NL = 3) potential energy function [16] for direct-potential-fit of the Cs2 33 Rþ g state; numbers in parentheses are 95% confidence limit uncertainties in the last digits shown

DPF-EMO + RKR ⎯ Theoretical curve by Magnier (Ref.1) • Theoretical curve by Spies (Ref.3)

22000

3 3 Rþ g state

1

Vlim/cm De/cm1 Re/Å p /0 /1 /2 /3

22185.41 2722.28 5.3474208 (4200) 2 0.5492646 (2800) 0.03716 (650) 0.0405 (260) 1.5137 (2900)

Vlim is the fixed absolute energy (in cm1) at the potential asymptote. This sets the absolute energy scale.

20000

21500

19900

E υ / cm-1

EMO parameter

21000 19800

19700

20500

19600

20000 19500

19500

0.1

Dunham RKR DPF-EMO

4.6 4.8

4

6

8

10

5.0

12

5.2

5.4 5.6

14

5.8 6.0

16

6.2

6.4

18

R /Å

Cal.− Obs. / cm-1

Fig. 3. Potential curves of the 33 Rþ g state.

0.0

Fig. 3 gives the RKR and EMO potential curves and the theoretical curves. The RKR and EMO potential curves have better agreement with the theoretical curve by Spies [3].

contact interaction with the nuclei, hyperfine splitting is expected in our sub-Doppler excitation spectra. Hyperfine structure of triplet Rydberg states in Li2, 6Li7Li, Na2, NaK and K2 molecules has been observed and analyzed [8,9]. Fermi contact interaction is the dominant source of the hyperfine splitting in the alkali diatomic molecules. For alkali dimers, the Fermi contact constants of the triplet Rydberg states are all approximately equal to 1/4 of the Fermi contact constants of their atomic ground states. The Fermi contact constant of the 133Cs 6s ground state is much bigger than that of other alkali atoms [10]: 7Li, 401.80 MHz; 23Na, 885.7 MHz; 39K, 231.54 MHz; 85Rb, 1011.90 MHz and 133Cs, 2298.20 MHz. Thus a large hyperfine splitting is expected for Cs2 triplet Rydberg states. 3 þ The hyperfine splitting of the a3 Rþ u [11–13] and 2 Ru [14,15] states has been observed. The nuclear spin of the 133Cs is 7/2, so the total nuclear spin of the 133Cs2 molecule, I is 7, 6, 5, 4, 3, 2, 1, or 0. Fig. 1 shows complicated structure, which is not typical case bbS or case bbJ coupling scheme. Detailed analysis and simulations of the hyperfine structure will be performed and reported separately.

3.3. Hyperfine structures

Acknowledgements

Since the Cs2 triplet Rydberg states excited by double resonance spectroscopy have a rg valence electron, which has a strong Fermi

Support from the NSFC (20473042 and 20773072), NKBRSF, and KGPCME (No. 306020) of China is gratefully acknowledged.

-0.1

2

4

6

υ

8

10

12

Fig. 2. The deviations between the observed term values and the calculated values from the Dunham constants, the RKR potential curve, and the EMO curve.

270

D. Li et al. / Chemical Physics Letters 458 (2008) 267–271 Table A1 (continued)

Appendix A

Intermediate A level

See Tables A1 and A2.

Table A1 Supplemental IR–IR excitation data: intermediate levels, probe laser frequencies, the v, N assignment and term values of the 33 Rþ g state Intermediate A level

Probe laser frequency cm1

v0

J0

6 6 6 6 6 6 6 6 6 6 6 6 4 4 4 4 7 7 7 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 6 6 6 6 6 6 6 6 6 6 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 8

42 42 42 42 44 44 44 44 46 46 46 46 70 70 70 70 24 24 24 42 42 42 42 44 44 44 44 46 46 46 24 24 24 24 42 42 42 42 44 44 44 46 46 46 78 78 78 78 160 160 160 160 222 222 222 222 224 224 226 226 226 226 78 78

9659.130 9659.130 9660.595 9660.595 9658.998 9658.998 9660.562 9660.562 9658.890 9658.890 9660.524 9660.524 9735.803 9735.803 9738.274 9738.274 9648.684 9649.542 9649.543 9687.510 9687.510 9688.999 9688.998 9687.402 9687.402 9688.960 9688.960 9687.289 9688.917 9688.917 9676.989 9676.990 9677.845 9677.845 9715.782 9715.781 9717.266 9717.265 9715.668 9717.222 9717.222 9715.550 9717.173 9717.174 9633.377 9633.378 9636.108 9636.109 9581.050 9581.051 9586.550 9586.550 9565.440 9565.440 9572.925 9572.925 9564.818 9572.329 9564.192 9564.192 9571.789 9571.789 9661.391 9661.393

33 Rþ g state

Term value (cm1)

v

N

19550.054 19550.054 19551.519 19551.519 19551.519 19551.519 19553.083 19553.083 19553.082 19553.082 19554.716 19554.716 19577.302 19577.302 19579.773 19579.773 19568.182 19569.040 19569.041 19578.434 19578.434 19579.923 19579.922 19579.923 19579.923 19581.481 19581.481 19581.481 19583.109 19583.109 19596.487 19596.488 19597.343 19597.343 19606.706 19606.705 19608.190 19608.189 19608.189 19609.743 19609.743 19609.742 19611.365 19611.366 19644.039 19644.040 19646.770 19646.771 19811.860 19811.861 19817.360 19817.360 20012.448 20012.448 20019.933 20019.933 20019.933 20027.444 20027.480 20027.480 20035.077 20035.077 19672.053 19672.055

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5

41 41 43 43 43 43 45 45 45 45 47 47 69 69 71 71 23 25 25 41 41 43 43 43 43 45 45 45 47 47 23 23 25 25 41 41 43 43 43 45 45 45 47 47 77 77 79 79 159 159 161 161 221 221 223 223 223 225 225 225 227 227 77 77

Probe laser frequency cm1

v0

J0

8 8 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 9 9 9 9 11 11 11 11 11 11 10 10 10 10 10 10 10 10

78 78 99 99 100 100 99 99 101 101 100 100 102 102 101 101 102 102 160 160 160 160 99 99 100 100 99 99 101 101 100 100 102 102 101 101 102 102 78 78 78 78 80 80 80 80 100 100 100 100 102 102 102 102 160 160 160 160 170 170 172 172 172 172 100 100 100 100 102 102 102 102

9664.114 9664.114 9578.687 9578.687 9578.486 9578.486 9582.127 9582.127 9578.270 9578.271 9581.961 9581.961 9578.104 9578.104 9581.781 9581.780 9581.648 9581.647 9608.512 9608.512 9613.996 9613.996 9606.463 9606.464 9606.258 9606.258 9609.895 9609.895 9606.036 9606.036 9609.722 9609.721 9605.863 9605.865 9609.533 9609.534 9609.395 9609.395 9717.023 9717.024 9719.730 9719.730 9716.803 9716.804 9719.577 9719.576 9661.411 9661.411 9664.854 9664.854 9660.997 9660.997 9664.506 9664.506 9690.128 9690.130 9695.581 9695.581 9606.192 9606.192 9605.649 9605.649 9611.463 9611.463 9688.801 9688.801 9692.230 9692.229 9688.374 9688.374 9691.870 9691.870

33 Rþ g state

Term value (cm1)

v

N

19674.776 19674.776 19704.043 19704.043 19705.773 19705.773 19707.483 19707.483 19707.484 19707.485 19709.248 19709.248 19709.247 19709.247 19710.995 19710.994 19712.791 19712.790 19839.322 19839.322 19844.806 19844.806 19731.819 19731.820 19733.545 19733.545 19735.251 19735.251 19735.250 19735.250 19737.009 19737.008 19737.006 19737.008 19738.747 19738.748 19740.538 19740.538 19727.685 19727.686 19730.392 19730.392 19730.391 19730.392 19733.165 19733.164 19788.698 19788.698 19792.141 19792.141 19792.140 19792.140 19795.649 19795.649 19920.938 19920.940 19926.391 19926.391 19948.730 19948.730 19954.483 19954.483 19960.297 19960.297 19816.088 19816.088 19819.517 19819.516 19819.517 19819.517 19823.013 19823.013

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9

79 79 98 98 99 99 100 100 100 100 101 101 101 101 102 102 103 103 159 159 161 161 98 98 99 99 100 100 100 100 101 101 101 101 102 102 103 103 77 77 79 79 79 79 81 81 99 99 101 101 101 101 103 103 159 159 161 161 169 169 171 171 173 173 99 99 101 101 101 101 103 103

271

D. Li et al. / Chemical Physics Letters 458 (2008) 267–271 Table A1 (continued) Intermediate A level v0

J0

11 11 11 11 11 11 11 11 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 13 13 13 13 13 13 13

170 170 170 170 172 172 172 172 100 100 100 100 102 102 102 102 170 170 170 170 172 172 172 172 176 176 176 176 178 178 180

Table A2 (continued) Probe laser frequency cm1

9633.058 9633.058 9638.790 9638.790 9632.494 9632.494 9638.279 9638.279 9716.064 9716.064 9719.485 9719.485 9715.629 9715.627 9719.113 9719.113 9686.431 9686.431 9692.127 9692.127 9685.831 9685.831 9691.509 9691.509 9629.491 9629.490 9635.343 9635.344 9628.833 9634.781 9628.199

33 Rþ g state

Term value (cm1)

v

N

19975.596 19975.596 19981.328 19981.328 19981.328 19981.328 19987.113 19987.113 19843.351 19843.351 19846.772 19846.772 19846.772 19846.770 19850.256 19850.256 20028.969 20028.969 20034.665 20034.665 20034.665 20034.665 20040.343 20040.343 20072.705 20072.704 20078.557 20078.558 20078.553 20084.501 20084.502

9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12

169 169 171 171 171 171 173 173 99 99 101 101 101 101 103 103 169 169 171 171 171 171 173 173 175 175 177 177 177 179 179

v

N

Term value (cm1)

Cal.Dun-Obs. (cm1)

Cal.RKR-Obs. (cm1)

Cal.DPF-Obs. (cm1)

5 5 5 5 5 6 6 6 6 6 6 7 7 7 8 8 8 8 8 8 8 8 9 9 9 9 9 9 10 10 10 11 11 11 12 12 12

101 102 103 159 161 98 99 100 101 102 103 77 79 81 99 101 103 159 161 169 171 173 99 101 103 169 171 173 99 101 103 169 171 173 175 177 179

19709.248 19710.995 19712.792 19839.322 19844.806 19731.820 19733.545 19735.251 19737.006 19738.747 19740.538 19727.685 19730.392 19733.165 19788.698 19792.141 19795.649 19920.938 19926.391 19948.730 19954.483 19960.297 19816.088 19819.516 19823.012 19975.596 19981.328 19987.113 19843.351 19846.772 19850.256 20028.969 20034.665 20040.343 20072.705 20078.557 20084.502

0.004 0.012 0.005 0.001 0.000 0.012 0.007 0.011 0.004 0.013 0.004 0.006 0.008 0.008 0.005 0.006 0.006 0.000 0.024 0.001 0.002 0.000 0.003 0.001 0.000 0.004 0.004 0.008 0.006 0.004 0.006 0.008 0.010 0.070 0.015 0.002 0.018

0.004 0.012 0.005 0.013 0.015 0.013 0.006 0.012 0.003 0.013 0.004 0.002 0.004 0.004 0.002 0.004 0.003 0.008 0.032 0.011 0.013 0.012 0.001 0.003 0.004 0.010 0.010 0.002 0.011 0.009 0.011 0.028 0.031 0.047 0.123 0.116 0.140

0.004 0.012 0.005 0.005 0.007 0.014 0.005 0.013 0.002 0.015 0.002 0.001 0.003 0.003 0.000 0.002 0.001 0.001 0.026 0.004 0.006 0.004 0.001 0.001 0.002 0.003 0.002 0.009 0.001 0.003 0.001 0.006 0.007 0.074 0.017 0.002 0.018

Table A2 A comparison between observed term values and calculated term values (from the Dunham coefficients, RKR potential, and DPF-EMO potential) v

N

Term value (cm1)

Cal.Dun-Obs. (cm1)

Cal.RKR-Obs. (cm1)

Cal.DPF-Obs. (cm1)

2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5

41 43 45 47 69 71 23 25 41 43 45 47 23 25 41 43 45 47 77 79 159 161 221 223 225 227 77 79 98 99 100

19550.054 19551.519 19553.083 19554.716 19577.302 19579.773 19568.182 19569.040 19578.434 19579.923 19581.481 19583.109 19596.487 19597.343 19606.706 19608.190 19609.743 19611.365 19644.039 19646.770 19811.860 19817.360 20012.448 20019.933 20027.480 20035.077 19672.053 19674.776 19704.043 19705.773 19707.483

0.025 0.004 0.003 0.004 0.001 0.000 0.004 0.005 0.002 0.002 0.003 0.003 0.000 0.000 0.002 0.002 0.001 0.000 0.001 0.001 0.002 0.001 0.002 0.003 0.003 0.008 0.003 0.004 0.013 0.005 0.015

0.023 0.005 0.005 0.005 0.000 0.001 0.006 0.007 0.005 0.004 0.005 0.005 0.003 0.003 0.001 0.001 0.001 0.002 0.000 0.001 0.016 0.016 0.040 0.041 0.042 0.031 0.001 0.001 0.014 0.004 0.015

0.024 0.005 0.005 0.006 0.006 0.007 0.000 0.001 0.000 0.000 0.000 0.001 0.003 0.003 0.004 0.004 0.004 0.002 0.002 0.001 0.002 0.002 0.002 0.002 0.002 0.010 0.003 0.003 0.014 0.004 0.015

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