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Rotational analysis of the (7,1) band of the A2Πi–X2Σ+ system of CS+ studied by velocity modulation laser spectroscopy
Journal of Molecular Spectroscopy 217 (2003) 146–148 www.elsevier.com/locate/jms
Note
Rotational analysis of the (7,1) band of the A2Pi–X 2Rþ system of CSþ studied by velocity modulation laser spectroscopy Chuanxi Duan,a Ling Wu,a Yangqin Chen,b and Yuyan Liub,* a
State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, PR China b Department of Physics, Key Laboratory of Optical and Magnetic Resonance Spectroscopy, East China Normal University, Shanghai 200062, PR China Received 20 May 2002; in revised form 16 September 2002
The CSþ cation has received considerable attention in recent years [1–5]. One of the reasons is that it might play an important role in the formation of CS in the interstellar medium [2]. In addition, the rotational analysis of observed electronic spectra of CSþ has revealed that some vibrational levels of the A2 Pi state, especially the t0 ¼ 1, 5, and 6 levels, are strongly perturbed by high vibrational levels of the X 2 Rþ state [1,3–5]. In this note, we present the first rotational deperturbation analysis of the (7,1) band of the A2 Pi –X 2 Rþ system of CSþ by using optical-heterodyne magnetic-rotation enhanced velocity modulation laser spectroscopy (OH-MR-VMLS). The experimental setup for OH-MR-VMLS used in this work has been described in detail elsewhere [5]. Briefly, a Coherent 899-29 R6G dye laser pumped by a 10 W Coherent Verdi diode laser was used as the tunable laser source and the absorption spectrum of I2 [6] was used as the wavelength reference. The CSþ cation was produced by an AC discharge in the flowing mixture of He and CS2 . The optimal pressures for He and CS2 were about 4 Torr and 30 mTorr, respectively. The typical discharge current was about 200 mA at 38 kHz. Two hundred and eleven lines in the recorded spectra in the region 16 880–17 300 cm1 were assigned to the (7,1) band of the A2 Pi –X 2 Rþ system of CSþ . Some lines of the A2 P3=2 –X 2 Rþ sub-band of the (6,0) band with high J values in the region mentioned above had already been assigned and analyzed elsewhere [5]. The calculated Franck–Condon factor of the (7,1) band (0.0979) is larger than that of the (6,0) band (0.0913) [5], but the observed absorption signals of the (7,1) band are about * Corresponding author. Fax: +86-27-87641741. E-mail address: [email protected] (Y. Liu).
three times weaker than those of the (6,0) band. It may be because that the relative population of CSþ in the X 2 Rþ ðt00 ¼ 1Þ state is much less than that in the X 2 Rþ ðt00 ¼ 0Þ state. A part of the observed spectra around 17 001 cm1 is shown in Fig. 1. The wavenumbers of observed lines of the (7,1) band and their assignments are listed in Table 1. In our initial analysis of the (7,1) band, the standard effective Hamiltonians for 2 P and 2 Rþ states [7] were used. In the effective Hamiltonian for the 2 P state, the strong local perturbation was not considered. The wavenumbers of observed lines of the A2 P3=2 –X 2 Rþ subband could be well fitted. But the RMS error of the fit increased dramatically when the A2 P1=2 –X 2 Rþ sub-band was included, indicating the A2 P1=2 sub-level was perturbed. The observed wavenumber of the band-head for the A2 P3=2 –X 2 Rþ sub-band (the head of R11 branch) is in good agreement with that reported by Coxon et al. [8], namely about 17 019 cm1 . The spin–orbit constant A of the A2 Pi ðt0 ¼ 7Þ state extrapolated from the values of A2 Pi ðt0 ¼ 1–6Þ [1,4,5] is about 291 cm1 . If the A2 P1=2 sub-level were not strongly perturbed, we estimated that the band-head for the A2 P1=2 –X 2 Rþ subband (the head of R21 branch) should be located at about 17 310 cm1 . However, the band-head was actually observed at about 17 291 cm1 , shifted about 19 cm1 to the red in comparison with the estimated value, indicating the A2 P1=2 ðt0 ¼ 7Þ sub-level was probably perturbed by a high-lying state. The most likely perturbing level is the X 2 Rþ ðt00 ¼ 15Þ state, lying at about 18 774 cm1 with respect to the t00 ¼ 0 level [5]. The standard 2 P–2 Rþ Hamiltonian was then employed to describe the interactions between the rovibrational levels of A2 Pi ðt0 ¼ 7Þ and X 2 Rþ ðt00 ¼ 15Þ states [5,9]. Molecular constants of the X 2 Rþ ðt00 ¼ 15Þ
0022-2852/02/$ - see front matter Ó 2002 Elsevier Science (USA). All rights reserved. PII: S 0 0 2 2 - 2 8 5 2 ( 0 2 ) 0 0 0 2 4 - 3
C. Duan et al. / Journal of Molecular Spectroscopy 217 (2003) 146–148
147
Table 1 Wavenumbers (in cm1 ) of the observed lines of the CSþ A2 Pi –X 2 Rþ (7,1) banda N
P22
0 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 N
a
Q22
Q21
R22
R21
17285.046()5) 17285.489(1)
17261.578(10) 17256.849(6) 17251.764(8) 17246.321(9) 17240.521(9) 17234.360(10) 17227.838()8) 17220.953(11) 17213.704()6) 17206.090()5)
P12
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
P21
16996.502(5) 16992.234(0) 16987.588()5) 16982.564()13) 16977.160(0) 16971.379(1) 16965.219()4) 16958.681(0) 16951.764(3) 16944.469()6) 16936.796()1) 16928.744()5) 16920.315(10) 16911.507(2) 16902.321(0) 16892.758(7)
17274.962(7) 17272.063()9) 17268.816()2) 17265.222(9) 17261.279(7) 17256.987(3) 17252.345(5) 17247.352(1) 17242.007()4) 17236.309(9) 17230.257(4) 17223.849(4) 17217.085()4) 17209.962()11) 17202.479()4)
P11
17002.407()8) 16999.455()13) 16996.125(8) 16992.416()4) 16988.329()7) 16983.862()10) 16979.017()6) 16973.793()7) 16968.190()2) 16962.208()4) 16955.848(3) 16949.109()4) 16941.991(3) 16934.494(13) 16926.619()9) 16918.365(6) 16909.732()2) 16900.720(11) 16891.330()9)
Numbers in parentheses are ðobs: cal:Þ 103 cm1 .
17281.623()2) 17279.786(3) 17277.602(5) 17275.070(3) 17272.191()5) 17268.964(1) 17265.389(0) 17261.466(2) 17257.194()11) 17252.572()8) 17247.598(11) 17242.273(2)
Q12
17005.068(1) 17002.515()13) 16999.584(9) 16996.273(13) 16992.584()6) 16988.516(2) 16984.069(14) 16979.244()13) 16968.456(9) 16962.494(7) 16956.154()13) 16949.434()8) 16942.336()8) 16927.003(0) 16918.769()3) 16910.156()15) 16901.164()9)
17285.322(15) 17284.711()7) 17283.746(12)
17278.715(6) 17276.322()14) 17273.568()7) 17270.453(5) 17266.973()12) 17263.129()11) 17258.918(0)
17285.391()7) 17284.800()10) 17283.854()14) 17282.554()4) 17280.898()14) 17278.883()2) 17276.510(8) 17273.776()2) 17270.679()9) 17267.220()2) 17263.395(4) 17259.204(4) 17254.645(10) 17249.717(10) 17244.419()8) 17238.749()4) 17232.706(11) 17226.290(3) 17219.499(10) 17212.333()3) 17204.790()10)
17291.132(0) 17290.966()6) 17290.452()8) 17289.588()6) 17288.373(0) 17286.807()1) 17284.888(0) 17282.615()4) 17279.987(4) 17277.003()5) 17273.660(10) 17269.958(2) 17265.895(1) 17261.470()1) 17256.681()1) 17251.526()12) 17246.004()1) 17240.114(9) 17233.854()1) 17227.223()1) 17220.219(5) 17212.843(2) 17205.091()2)
Q11
R12
R11
17012.328()3) 17011.850(4) 17010.992()7) 17009.756(7) 17008.141(1) 17006.146(7) 17003.773()8) 17001.021()3) 16997.889()9)
17012.378(10) 17011.919(8) 17011.081(2) 17009.865()13) 17008.269(0) 17006.294(8) 17003.941(7) 17001.208(7) 16998.096(11) 16994.606(7) 16990.736(4) 16986.487(6) 16981.858(6) 16976.851(2) 16971.464(2) 16965.699()11) 16959.554(9) 16953.029(10) 16946.126(2) 16938.843()13) 16931.180()11) 16923.139(11) 16914.718(4) 16905.917()4) 16896.737()6)
17017.005()4) 17017.863(8) 17018.342()7) 17018.441()2) 17018.161()3) 17017.502(13) 17016.463(4)
16990.489(1) 16986.220()3) 16981.572()13) 16976.545()8) 16971.139(11)
17013.248()2) 17011.071(7) 17008.514(0) 17005.578(1) 17002.262(4) 16998.566()7) 16994.491(2) 16990.035(4) 16985.200(2) 16979.984(11) 16974.389(2) 16968.413(8) 16962.057(2) 16955.320()6) 16948.204()9) 16940.706()1) 16932.829(10) 16924.570(1) 16915.932(0) 16906.912(2)
148
C. Duan et al. / Journal of Molecular Spectroscopy 217 (2003) 146–148
Fig. 1. A part of observed spectra around 17 001 cm1 . The labeled lines were assigned to the (7,1) band of the A2 Pi –X 2 Rþ system of CSþ . The strong S atom line Sð5 P1 –5 S20 Þ at 17003.4 cm1 was also observed.
Table 2 Deperturbed molecular constants of the tA ¼ 7 tX ¼ 15 complex of CSþ (in cm1 )a
T70 A07 A0D7 104 B07 D07 105 p70 q07 103 n 2g 00 T15 B0015 D0015 106 c0015
This work
Calculated values
18520.073(65) )290.91(13) )0.51(30) 0.669942(38) 0.1438(14) 0.0328(15) )0.141(46) 49.96(17) )0.0059(14) 18 774d 0.7632d 1.0e 0e
18520.45b )291.467b 0.6696b 0.14b
54.4c )0.017c
a
Values in the parentheses are 1r uncertainties in units of the last digit. b Values are extrapolated from the data of A2 Pi ðt0 ¼ 2; 3; 4Þ states in [1, Table 10]. c See text. d Values are extrapolated from the equilibrium constants of X 2 Rþ given in [5] and fixed in the fit. e Values are fixed in the fit.
state and the two interaction parameters n, 2g could not be simultaneously determined due to our limited experimental data and the negative J-values of the crossing points between the A2 P1=2 ðt0 ¼ 7Þ and X 2 Rþ ðt00 ¼ 15Þ rovibrational levels. In our final fit, molecular constants
of the lower state X 2 Rþ ðt00 ¼ 1Þ were fixed at their welldetermined values given in [2], and two molecular 00 constants of the X 2 Rþ ðt00 ¼ 15Þ state, T15 , B0015 , were extrapolated from the equilibrium constants of X 2 Rþ given in [5], with D0015 fixed at 1:0 106 cm1 and c0015 fixed at zero, respectively. Only seven molecular constants of A2 Pi ðt0 ¼ 7Þ (T70 , A07 , A0D7 , B07 , D07 , p70 , and q07 ) and the two interaction parameters (n; 2g) were allowed to float. Molecular constants derived from the fit are given in Table 2, where they are compared with the theoretical calculations. The RMS error of the fit is 0.008 cm1 , which is within the experimental uncertainty of 0:005–0:01 cm1 . Our values for T70 , A07 , B07 , and D07 derived with the single perturber model are in good agreement with their extrapolations from the A2 Pi ðt0 ¼ 2; 3; 4Þ states in which the two perturber model was employed [1], considering the expected small changes for T70 and A07 . For the perturbation parameters, n ¼ 49:96 0:17 cm1 is very close to the calculated value ncal ¼ 12aS7;15 ¼ 54:4 cm1 , but 2g ¼ 0:0059 0:0014 cm1 differs significantly from the calculated value ð2gÞcal ¼ bB7;5 ¼ 0:027 cm1 , assuming a ¼ 290:4 0:5 cm1 , b ¼ 0:08 0:01 [1] and S7;15 ¼ 0:3746, B7;15 ¼ 0:2164 cm1 [5]. It may be because that a shows better radial invariance than b, as discussed in [5]. The remaining constants, A0D7 , p70 , and q07 , are not comparable because the values of the lower states have not shown clear t-dependence. In conclusion, the single perturber model for describing the perturbation between A2 Pi ðt0 ¼ 7Þ and X 2 Rþ ðt00 ¼ 15Þ states has produced reliable molecular constants for the A2 Pi ðt0 ¼ 7Þ state and the perturbation parameters.
References [1] D. Gauyacq, M. Horani, Can. J. Phys. 56 (1978) 587. [2] M. Horani, M. Vervloet, Astron. Astrophys. 256 (1992) 683. [3] D. Cossart, M. Horani, M. Verloet, Am. Inst. Phys. Conf. Proc. 312 (September) (1993) 367–372. [4] Y. Liu, H. Liu, H. Gao, C. Duan, P.A. Hamilton, P.B. Davies, Chem. Phys. Lett. 317 (2000) 181. [5] Y. Liu, C. Duan, J. Liu, L. Wu, C. Xu, Y. Chen, P.A. Hamilton, P.B. Davies, J. Chem. Phys. 116 (2002) 9768. [6] S. Gerstenkorn, P. Luc, Atlas du Spectra dÕAbsorption de la Molecule dÕIodine, Ed. du CNRS, Paris, 1978. [7] R.N. Zare, A.L. Schmeltekopf, W.J. Harrop, D.L. Albritton, J. Mol. Spectrosc. 46 (1973) 37. [8] J.A. Coxon, P.J. Marcoux, D.W. Setser, Chem. Phys. 17 (1976) 403. [9] A.J. Kotlar, R.W. Field, J.I. Steinfeld, J.A. Coxon, J. Mol. Spectrosc. 80 (1980) 86.
Note
Rotational analysis of the (7,1) band of the A2Pi–X 2Rþ system of CSþ studied by velocity modulation laser spectroscopy Chuanxi Duan,a Ling Wu,a Yangqin Chen,b and Yuyan Liub,* a
State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, PR China b Department of Physics, Key Laboratory of Optical and Magnetic Resonance Spectroscopy, East China Normal University, Shanghai 200062, PR China Received 20 May 2002; in revised form 16 September 2002
The CSþ cation has received considerable attention in recent years [1–5]. One of the reasons is that it might play an important role in the formation of CS in the interstellar medium [2]. In addition, the rotational analysis of observed electronic spectra of CSþ has revealed that some vibrational levels of the A2 Pi state, especially the t0 ¼ 1, 5, and 6 levels, are strongly perturbed by high vibrational levels of the X 2 Rþ state [1,3–5]. In this note, we present the first rotational deperturbation analysis of the (7,1) band of the A2 Pi –X 2 Rþ system of CSþ by using optical-heterodyne magnetic-rotation enhanced velocity modulation laser spectroscopy (OH-MR-VMLS). The experimental setup for OH-MR-VMLS used in this work has been described in detail elsewhere [5]. Briefly, a Coherent 899-29 R6G dye laser pumped by a 10 W Coherent Verdi diode laser was used as the tunable laser source and the absorption spectrum of I2 [6] was used as the wavelength reference. The CSþ cation was produced by an AC discharge in the flowing mixture of He and CS2 . The optimal pressures for He and CS2 were about 4 Torr and 30 mTorr, respectively. The typical discharge current was about 200 mA at 38 kHz. Two hundred and eleven lines in the recorded spectra in the region 16 880–17 300 cm1 were assigned to the (7,1) band of the A2 Pi –X 2 Rþ system of CSþ . Some lines of the A2 P3=2 –X 2 Rþ sub-band of the (6,0) band with high J values in the region mentioned above had already been assigned and analyzed elsewhere [5]. The calculated Franck–Condon factor of the (7,1) band (0.0979) is larger than that of the (6,0) band (0.0913) [5], but the observed absorption signals of the (7,1) band are about * Corresponding author. Fax: +86-27-87641741. E-mail address: [email protected] (Y. Liu).
three times weaker than those of the (6,0) band. It may be because that the relative population of CSþ in the X 2 Rþ ðt00 ¼ 1Þ state is much less than that in the X 2 Rþ ðt00 ¼ 0Þ state. A part of the observed spectra around 17 001 cm1 is shown in Fig. 1. The wavenumbers of observed lines of the (7,1) band and their assignments are listed in Table 1. In our initial analysis of the (7,1) band, the standard effective Hamiltonians for 2 P and 2 Rþ states [7] were used. In the effective Hamiltonian for the 2 P state, the strong local perturbation was not considered. The wavenumbers of observed lines of the A2 P3=2 –X 2 Rþ subband could be well fitted. But the RMS error of the fit increased dramatically when the A2 P1=2 –X 2 Rþ sub-band was included, indicating the A2 P1=2 sub-level was perturbed. The observed wavenumber of the band-head for the A2 P3=2 –X 2 Rþ sub-band (the head of R11 branch) is in good agreement with that reported by Coxon et al. [8], namely about 17 019 cm1 . The spin–orbit constant A of the A2 Pi ðt0 ¼ 7Þ state extrapolated from the values of A2 Pi ðt0 ¼ 1–6Þ [1,4,5] is about 291 cm1 . If the A2 P1=2 sub-level were not strongly perturbed, we estimated that the band-head for the A2 P1=2 –X 2 Rþ subband (the head of R21 branch) should be located at about 17 310 cm1 . However, the band-head was actually observed at about 17 291 cm1 , shifted about 19 cm1 to the red in comparison with the estimated value, indicating the A2 P1=2 ðt0 ¼ 7Þ sub-level was probably perturbed by a high-lying state. The most likely perturbing level is the X 2 Rþ ðt00 ¼ 15Þ state, lying at about 18 774 cm1 with respect to the t00 ¼ 0 level [5]. The standard 2 P–2 Rþ Hamiltonian was then employed to describe the interactions between the rovibrational levels of A2 Pi ðt0 ¼ 7Þ and X 2 Rþ ðt00 ¼ 15Þ states [5,9]. Molecular constants of the X 2 Rþ ðt00 ¼ 15Þ
0022-2852/02/$ - see front matter Ó 2002 Elsevier Science (USA). All rights reserved. PII: S 0 0 2 2 - 2 8 5 2 ( 0 2 ) 0 0 0 2 4 - 3
C. Duan et al. / Journal of Molecular Spectroscopy 217 (2003) 146–148
147
Table 1 Wavenumbers (in cm1 ) of the observed lines of the CSþ A2 Pi –X 2 Rþ (7,1) banda N
P22
0 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 N
a
Q22
Q21
R22
R21
17285.046()5) 17285.489(1)
17261.578(10) 17256.849(6) 17251.764(8) 17246.321(9) 17240.521(9) 17234.360(10) 17227.838()8) 17220.953(11) 17213.704()6) 17206.090()5)
P12
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
P21
16996.502(5) 16992.234(0) 16987.588()5) 16982.564()13) 16977.160(0) 16971.379(1) 16965.219()4) 16958.681(0) 16951.764(3) 16944.469()6) 16936.796()1) 16928.744()5) 16920.315(10) 16911.507(2) 16902.321(0) 16892.758(7)
17274.962(7) 17272.063()9) 17268.816()2) 17265.222(9) 17261.279(7) 17256.987(3) 17252.345(5) 17247.352(1) 17242.007()4) 17236.309(9) 17230.257(4) 17223.849(4) 17217.085()4) 17209.962()11) 17202.479()4)
P11
17002.407()8) 16999.455()13) 16996.125(8) 16992.416()4) 16988.329()7) 16983.862()10) 16979.017()6) 16973.793()7) 16968.190()2) 16962.208()4) 16955.848(3) 16949.109()4) 16941.991(3) 16934.494(13) 16926.619()9) 16918.365(6) 16909.732()2) 16900.720(11) 16891.330()9)
Numbers in parentheses are ðobs: cal:Þ 103 cm1 .
17281.623()2) 17279.786(3) 17277.602(5) 17275.070(3) 17272.191()5) 17268.964(1) 17265.389(0) 17261.466(2) 17257.194()11) 17252.572()8) 17247.598(11) 17242.273(2)
Q12
17005.068(1) 17002.515()13) 16999.584(9) 16996.273(13) 16992.584()6) 16988.516(2) 16984.069(14) 16979.244()13) 16968.456(9) 16962.494(7) 16956.154()13) 16949.434()8) 16942.336()8) 16927.003(0) 16918.769()3) 16910.156()15) 16901.164()9)
17285.322(15) 17284.711()7) 17283.746(12)
17278.715(6) 17276.322()14) 17273.568()7) 17270.453(5) 17266.973()12) 17263.129()11) 17258.918(0)
17285.391()7) 17284.800()10) 17283.854()14) 17282.554()4) 17280.898()14) 17278.883()2) 17276.510(8) 17273.776()2) 17270.679()9) 17267.220()2) 17263.395(4) 17259.204(4) 17254.645(10) 17249.717(10) 17244.419()8) 17238.749()4) 17232.706(11) 17226.290(3) 17219.499(10) 17212.333()3) 17204.790()10)
17291.132(0) 17290.966()6) 17290.452()8) 17289.588()6) 17288.373(0) 17286.807()1) 17284.888(0) 17282.615()4) 17279.987(4) 17277.003()5) 17273.660(10) 17269.958(2) 17265.895(1) 17261.470()1) 17256.681()1) 17251.526()12) 17246.004()1) 17240.114(9) 17233.854()1) 17227.223()1) 17220.219(5) 17212.843(2) 17205.091()2)
Q11
R12
R11
17012.328()3) 17011.850(4) 17010.992()7) 17009.756(7) 17008.141(1) 17006.146(7) 17003.773()8) 17001.021()3) 16997.889()9)
17012.378(10) 17011.919(8) 17011.081(2) 17009.865()13) 17008.269(0) 17006.294(8) 17003.941(7) 17001.208(7) 16998.096(11) 16994.606(7) 16990.736(4) 16986.487(6) 16981.858(6) 16976.851(2) 16971.464(2) 16965.699()11) 16959.554(9) 16953.029(10) 16946.126(2) 16938.843()13) 16931.180()11) 16923.139(11) 16914.718(4) 16905.917()4) 16896.737()6)
17017.005()4) 17017.863(8) 17018.342()7) 17018.441()2) 17018.161()3) 17017.502(13) 17016.463(4)
16990.489(1) 16986.220()3) 16981.572()13) 16976.545()8) 16971.139(11)
17013.248()2) 17011.071(7) 17008.514(0) 17005.578(1) 17002.262(4) 16998.566()7) 16994.491(2) 16990.035(4) 16985.200(2) 16979.984(11) 16974.389(2) 16968.413(8) 16962.057(2) 16955.320()6) 16948.204()9) 16940.706()1) 16932.829(10) 16924.570(1) 16915.932(0) 16906.912(2)
148
C. Duan et al. / Journal of Molecular Spectroscopy 217 (2003) 146–148
Fig. 1. A part of observed spectra around 17 001 cm1 . The labeled lines were assigned to the (7,1) band of the A2 Pi –X 2 Rþ system of CSþ . The strong S atom line Sð5 P1 –5 S20 Þ at 17003.4 cm1 was also observed.
Table 2 Deperturbed molecular constants of the tA ¼ 7 tX ¼ 15 complex of CSþ (in cm1 )a
T70 A07 A0D7 104 B07 D07 105 p70 q07 103 n 2g 00 T15 B0015 D0015 106 c0015
This work
Calculated values
18520.073(65) )290.91(13) )0.51(30) 0.669942(38) 0.1438(14) 0.0328(15) )0.141(46) 49.96(17) )0.0059(14) 18 774d 0.7632d 1.0e 0e
18520.45b )291.467b 0.6696b 0.14b
54.4c )0.017c
a
Values in the parentheses are 1r uncertainties in units of the last digit. b Values are extrapolated from the data of A2 Pi ðt0 ¼ 2; 3; 4Þ states in [1, Table 10]. c See text. d Values are extrapolated from the equilibrium constants of X 2 Rþ given in [5] and fixed in the fit. e Values are fixed in the fit.
state and the two interaction parameters n, 2g could not be simultaneously determined due to our limited experimental data and the negative J-values of the crossing points between the A2 P1=2 ðt0 ¼ 7Þ and X 2 Rþ ðt00 ¼ 15Þ rovibrational levels. In our final fit, molecular constants
of the lower state X 2 Rþ ðt00 ¼ 1Þ were fixed at their welldetermined values given in [2], and two molecular 00 constants of the X 2 Rþ ðt00 ¼ 15Þ state, T15 , B0015 , were extrapolated from the equilibrium constants of X 2 Rþ given in [5], with D0015 fixed at 1:0 106 cm1 and c0015 fixed at zero, respectively. Only seven molecular constants of A2 Pi ðt0 ¼ 7Þ (T70 , A07 , A0D7 , B07 , D07 , p70 , and q07 ) and the two interaction parameters (n; 2g) were allowed to float. Molecular constants derived from the fit are given in Table 2, where they are compared with the theoretical calculations. The RMS error of the fit is 0.008 cm1 , which is within the experimental uncertainty of 0:005–0:01 cm1 . Our values for T70 , A07 , B07 , and D07 derived with the single perturber model are in good agreement with their extrapolations from the A2 Pi ðt0 ¼ 2; 3; 4Þ states in which the two perturber model was employed [1], considering the expected small changes for T70 and A07 . For the perturbation parameters, n ¼ 49:96 0:17 cm1 is very close to the calculated value ncal ¼ 12aS7;15 ¼ 54:4 cm1 , but 2g ¼ 0:0059 0:0014 cm1 differs significantly from the calculated value ð2gÞcal ¼ bB7;5 ¼ 0:027 cm1 , assuming a ¼ 290:4 0:5 cm1 , b ¼ 0:08 0:01 [1] and S7;15 ¼ 0:3746, B7;15 ¼ 0:2164 cm1 [5]. It may be because that a shows better radial invariance than b, as discussed in [5]. The remaining constants, A0D7 , p70 , and q07 , are not comparable because the values of the lower states have not shown clear t-dependence. In conclusion, the single perturber model for describing the perturbation between A2 Pi ðt0 ¼ 7Þ and X 2 Rþ ðt00 ¼ 15Þ states has produced reliable molecular constants for the A2 Pi ðt0 ¼ 7Þ state and the perturbation parameters.
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