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Potential curve of the 41Σ+ state of NaK by polarisation labelling spectroscopy
Chemical Physics Letters 374 (2003) 297–301 www.elsevier.com/locate/cplett
Potential curve of the 41Rþ state of NaK by polarisation labelling spectroscopy W. Jastrzebski a
a,*
, R. Nadyak a, P. Kowalczyk
b
Institute of Physics, Polish Academy of Sciences, Al. Lotnik ow 32/46, 02-668 Warsaw, Poland Institute of Experimental Physics, Warsaw University, ul. Ho_za 69, 00-681 Warsaw, Poland
b
Received 17 March 2003; in final form 30 April 2003
Abstract The 41 Rþ state of NaK molecule has been observed for the first time and studied by polarisation labelling spectroscopy technique. A total of 1567 rovibronic levels in this state were measured with an accuracy better than 0.1 cm1 . The inverted perturbation approach method was used to construct the potential energy curve of the 41 Rþ state. The irregular shape of the potential confirms earlier theoretical predictions. Ó 2003 Elsevier Science B.V. All rights reserved.
The sodium–potassium dimer, NaK, has received a great deal of attention from both spectroscopists and theoreticians over the past years [1–9]. Yet a relatively low lying electronic state, 41 Rþ , has not been observed experimentally up to now. This is particularly surprising when we take into account that this state is available for transitions from the ground X1 Rþ state of NaK and the corresponding band system is placed in the 415– 455 nm spectral range, easily accessible for laser excitation. The only reason of the long neglect of the 41 Rþ state can be in unusual properties of this state, predicted by calculations [7–9]. Due to multiple avoided crossings between a diabatic covalent state and two ion pair states (correlated with Naþ K and Na Kþ configurations) the
*
Corresponding author. Fax: +48-22-8430926. E-mail address: [email protected] (W. Jastrzebski).
potential well of the resulting 41 Rþ state is expected to be unusually broad with peculiarly shaped bottom. The calculated transition dipole moment for the 41 Rþ X1 Rþ system [9] is low and nearly constant around the equilibrium distance of the electronic ground state, although for larger R values it changes significantly, following changes in nature of the 41 Rþ state. All this implies relatively weak spectra and irregular spacing of vibrational levels, escaping traditional analysis. It is worth noting that exotic shapes of potential curves have been predicted for corresponding 41 Rþ states also in other heteronuclear alkali dimers: NaLi [10], KLi [11], LiRb, NaRb [12] and KRb [13,14]. The present experiment was undertaken to obtain an accurate spectroscopic characterisation of the 41 Rþ state and thus to fill the last gap in the experimental knowledge of singlet states in NaK giving rise to absorption spectra in the visible. The experiment was performed by the polarisation
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00729-2
298
W. Jastrzebski et al. / Chemical Physics Letters 374 (2003) 297–301
labelling spectroscopy on the 41 Rþ X1 Rþ band system. Since the experimental arrangement is the same as described in our recent Letter [6] it will not be presented here. Owing to high sensitivity of the polarisation method we were able to detect the required molecular spectra. The spectra consisted of several long vibronic progressions belonging to the 41 Rþ X1 Rþ system (Fig. 1). Spacing of the recorded P, R doublets, unusually close for NaK (typically 25–30 cm1 ), is characteristic for transitions to a state with a broad potential energy curve. The observed transitions originated from altogether 28 rovibrational levels labelled in the ground state by light of the argon ion laser and terminated on all levels of the 41 Rþ state accessible due to the selection rules and non-negligible Franck–Condon factors. Thus our measurements in the main isotopomer 23 Na39 K spanned 86 vibrational levels with quantum numbers J ranging between 7 and 123. In addition, about 40 weak transitions forming a single vibrational progression could be assigned to the 23 Na41 K isotopomer; these were crucial in further analysis (the wave numbers of all transitions observed in the experiment can be obtained on request from the
authors). The energies of 41 Rþ state levels were obtained from wave numbers of the identified lines by adding highly accurate term values of the ground X1 Rþ state [5]. Our analysis encountered two serious problems. First, as the lowest vibrational levels of the 41 Rþ state were inaccessible from the levels labelled in the ground state (because of insufficient Franck– Condon overlap), we could not establish vibrational numbering in 41 Rþ directly. Second, the expected peculiar shape of the 41 Rþ potential curve, indeed confirmed by irregularities of the observed spectra, did not allow for conventional description of the state in terms of a Rydberg– Klein–Rees potential. The solution to the second problem is to construct the potential curve of the 41 Rþ state by a quantum-mechanical variational procedure, known as the inverted perturbation approach (IPA) [15]. The IPA method is based on iterative optimisation of the initial ÔguessedÕ potential energy curve in such a way that the calculated energy eigenvalues agree in a least-squares sense with the measured level energies. In the version of the procedure developed by us [16], the correction to
Fig. 1. Part of the polarisation spectrum of NaK obtained with the 501.7 nm line of the Arþ laser as the probe and circularly polarised pump light. The assigned v0 progressions correspond to transitions 41 Rþ ðv0 ; J 0 ¼ J 00 1Þ X1 Rþ ðv00 ; J 00 Þ from the ground state levels: (a) ðv00 ¼ 2; J 00 ¼ 104Þ and (b) ðv00 ¼ 3; J 00 ¼ 24Þ.
W. Jastrzebski et al. / Chemical Physics Letters 374 (2003) 297–301
the potential and the potential itself are defined as sets of points interpolated with cubic spline functions and the experimental energies are furnished directly to the program. It is always a crucial point to choose a reasonable initial potential energy curve for the IPA procedure, as it affects stability and rate of convergence of the routine. The recently published pseudopotential calculations for NaK [9], which proved accurate for several other medium excited states of this molecule [3,6], offered a good starting curve. It is known, however, that the theoretical potential curves usually depict better the actual shape of the potential than its absolute position in the energy scale and a vertical adjustment of the whole curve is often necessary. For the investigated 41 Rþ state of NaK such vertical shift was even more justified, as the numbering of vibrational levels in this state remained unknown at this stage of the analysis. Therefore our procedure was as follows. Using the experimental level energies of 23 Na39 K only, we repeated
299
the IPA procedure assuming several initial potentials, each of them of the same shape but shifted in energy and consequently imposing different vibrational numbering on the observed levels. As a result of many runs of the IPA routine, several improved potential curves have been generated, every curve reproducing well the experimental level energies. However, only one of this potentials allowed to predict correctly positions of the levels observed in the 23 Na41 K isotopomer (identified as v0 ¼ 41–61, J 0 ¼ 59 and 61). As an additional test of the vibrational numbering established in the 41 Rþ state in this way, we compared the intensity patterns in several observed vibrational progressions with Franck– Condon intensities calculated for the 41 Rþ X1 Rþ system. Even though our experiment is not well suited to precise intensity measurements, at least the positions of minima in the observed and calculated spectra should coincide. An exemplary comparison is shown in Fig. 2. The results taken
Fig. 2. Average relative intensities (experimental: solid lines; calculated: hollow bars) of the P and R lines in the 41 Rþ ðv0 ; J 0 ¼ 33; 35Þ X1 Rþ ðv00 ¼ 5; J 00 ¼ 34Þ for five vibrational numberings in the 41 Rþ state, differing by one vibrational quantum (a)–(e). The numbering inferred from the isotopic data corresponds to the trace (c).
300
W. Jastrzebski et al. / Chemical Physics Letters 374 (2003) 297–301
alone are probably not conclusive enough but they support nicely the vibrational assignment inferred from the isotopic data. In Table 1 and Fig. 3 we present the potential energy curve of the 41 Rþ state given in a grid of 55 points. For interpolation of the potential to an arbitrary middle point the natural cubic spline [17] should be used (i.e., the second derivative at the first and the last point should be set to zero). With the vibrational numbering imposed by the potential curve from Table 1, the energy levels used in the analysis correspond to v0 ¼ 30–115. Such input Þ and data actually allow only the inner (3.05–4.8 A ) parts of the potential to be outer (8.4–11.8 A determined reliably. We found that the shape of the bottom of the potential curve between 4.8 and does not influence significantly positions of 8.4 A levels studied in the present work. Therefore we used in this region a raw (uncorrected) theoretical curve [9], which after an upward shift of 50.5 cm1 smoothly matches the walls of the potential. Points range are given in Table 1 beyond the 3.05–11.8 A mostly to ensure proper boundary conditions for solving the Schr€ odinger equation. It must be noted, however, that these points have also some influence on the values of the potential for 3.05 < R < 11.8 A because of the properties of the A cubic spline interpolation. When solving the Schr€ odinger equation with the potential from Table 1 by the Numerov–Cooley method [18] with grid space, the energies of 1567 rovib0.0017 A rational levels observed in the present experiment are reproduced with a standard deviation of 0.07 cm1 , matching the experimental accuracy of 0.1 cm1 . It is worth noting that the eigenenergies of levels of the 41 Rþ state investigated here can be reproduced by a set of Dunham-like coefficients, listed in Table 2. Although the coefficients have no direct physical meaning and are applicable only to the range of v0 and J 0 quantum numbers used for their definition, they provide an easy way to predict rovibrational energies in the 41 Rþ state. In conclusion, we have derived a potential energy curve of the 41 Rþ state of the NaK molecule, which reproduces energies of vibrational levels v0 ¼ 30–115 with an accuracy of 0.07 cm1 . Closer examination of the bottom of the 41 Rþ state is still necessary as the lowest vibrational levels were
Table 1 The IPA potential energy curve of the 41 Rþ state in NaK R A
U cm1
2.4 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.2 13.6 14.0
32415.0310 27385.1883 25649.9188 24384.4860 23542.5866 23042.1872 22797.7874 22722.1089 22715.5665 22677.9096 22586.4526 22501.7587 22438.1802 22392.8477 22349.2489 22301.6368 22247.3795 22187.8679 22124.2092 22063.9579 22021.9219 21993.6464 21971.8137 21957.4781 21958.0486 21979.7892 22023.3006 22087.7511 22173.0163 22279.6876 22408.3498 22557.4797 22723.4119 22901.5861 23088.2248 23280.1910 23474.9597 23670.5898 23865.2757 24057.9567 24247.8239 24433.9395 24615.5641 24791.8085 24961.9040 25125.7753 25283.8324 25437.3303 25584.4204 25710.7036 25805.2728 25883.8131 26034.9491 26123.9457 26178.3128
W. Jastrzebski et al. / Chemical Physics Letters 374 (2003) 297–301
301
as the initial state for fluorescence may allow then a direct observation of the lowest vibrational levels in the 41 Rþ . Acknowledgements This work has been funded in part by Grant No. 2 P03B 063 23 from the Polish Committee for Scientific Research. We thank Dr. L. Lis for preparation of hollow-cathode lamps employed in frequency calibration of our spectra. Fig. 3. The IPA potential energy curve of the 41 Rþ state in NaK (solid line) compared with the most recent theoretical calculation [9] (pluses). The arrows indicate boundaries of the regions discussed in the text. The position of the atomic asymptote of the 41 Rþ state, Na(32 S) + K(52 S), is also shown.
Table 2 Dunham-type coefficients representing energies of rovibrational levels of the 41 Rþ state in 23 Na39 K with a standard deviation 0.09 cm1 Constant
Value
Y 00 Y 10 Y 20 10 Y 30 103 Y 40 106 Y 50 108 Y 60 10 Y 01 103 Y 11 104 Y 21 106 Y 31 109 Y 41 107 Y 02 109 Y 12
22583.35 )19.7541 1.222536 )0.1711181 0.1428097 )0.6546037 0.124408 0.561077 )0.803714 0.127521 )0.101124 0.29769 )0.29042 )0.4774
All values are given in cm1 . The coefficients are meaningful only for v ¼ 30–115, J ¼ 7–123.
lacking in our analysis. This task requires however another experimental technique. As an example, high resolution Fourier transform spectroscopy of the laser induced fluorescence to the 41 Rþ state may be a good choice. Selecting a highly excited singlet state with sufficiently broad potential curve
References [1] A. Pashov, I. Jackowska, W. Jastrzebski, P. Kowalczyk, Phys. Rev. A 58 (1998) 1048. [2] A. Krou-Adohi, S. Giraud-Cotton, J. Mol. Spectrosc. 190 (1998) 171. [3] P. Kowalczyk, W. Jastrzebski, A. Pashov, S. Magnier, M. Aubert-Frecon, Chem. Phys. Lett. 314 (1999) 47. [4] J. Huennekens, I. Prodan, A. Marks, L. Sibbach, E. Galle, T. Morgus, J. Chem. Phys. 113 (2000) 7384. [5] I. Russier-Antoine, A.J. Ross, M. Aubert-Frecon, F. Martin, P. Crozet, J. Phys. B 33 (2000) 2753. [6] R. Nadyak, W. Jastrzebski, P. Kowalczyk, Chem. Phys. Lett. 353 (2002) 414. [7] W.J. Stevens, D.D. Konowalow, L.B. Ratcliff, J. Chem. Phys. 80 (1984) 1215. [8] S. Magnier, Ph. Millie, Phys. Rev. A 54 (1996) 204. [9] S. Magnier, M. Aubert-Frecon, Ph. Millie, J. Mol. Spectrosc. 200 (2000) 96. [10] I. Schmidt-Mink, W. M€ uller, W. Meyer, Chem. Phys. Lett. 112 (1984) 120. [11] S. Rousseau, A.R. Allouche, M. Aubert-Frecon, S. Magnier, P. Kowalczyk, W. Jastrzebski, Chem. Phys. 247 (1999) 193. [12] M. Korek, A.R. Allouche, M. Kobeissi, A. Chaalan, M. Dagher, K. Fakherddin, M. Aubert-Frecon, Chem. Phys. 256 (2000) 1. [13] S. Rousseau, A.R. Allouche, M. Aubert-Frecon, J. Mol. Spectrosc. 203 (2000) 235. [14] S.J. Park, Y.J. Choi, Y.S. Lee, G.H. Jeung, Chem. Phys. 257 (2000) 135. [15] C. Vidal, Commun. At. Mol. Phys. 17 (1986) 173. [16] A. Pashov, W. Jastrzebski, P. Kowalczyk, Comput. Phys. Commun. 128 (2000) 622. [17] C. de Boor, A Practical Guide to Splines, Springer, Berlin, 1978. [18] J.W. Cooley, Math. Comput. 15 (1961) 363.
Potential curve of the 41Rþ state of NaK by polarisation labelling spectroscopy W. Jastrzebski a
a,*
, R. Nadyak a, P. Kowalczyk
b
Institute of Physics, Polish Academy of Sciences, Al. Lotnik ow 32/46, 02-668 Warsaw, Poland Institute of Experimental Physics, Warsaw University, ul. Ho_za 69, 00-681 Warsaw, Poland
b
Received 17 March 2003; in final form 30 April 2003
Abstract The 41 Rþ state of NaK molecule has been observed for the first time and studied by polarisation labelling spectroscopy technique. A total of 1567 rovibronic levels in this state were measured with an accuracy better than 0.1 cm1 . The inverted perturbation approach method was used to construct the potential energy curve of the 41 Rþ state. The irregular shape of the potential confirms earlier theoretical predictions. Ó 2003 Elsevier Science B.V. All rights reserved.
The sodium–potassium dimer, NaK, has received a great deal of attention from both spectroscopists and theoreticians over the past years [1–9]. Yet a relatively low lying electronic state, 41 Rþ , has not been observed experimentally up to now. This is particularly surprising when we take into account that this state is available for transitions from the ground X1 Rþ state of NaK and the corresponding band system is placed in the 415– 455 nm spectral range, easily accessible for laser excitation. The only reason of the long neglect of the 41 Rþ state can be in unusual properties of this state, predicted by calculations [7–9]. Due to multiple avoided crossings between a diabatic covalent state and two ion pair states (correlated with Naþ K and Na Kþ configurations) the
*
Corresponding author. Fax: +48-22-8430926. E-mail address: [email protected] (W. Jastrzebski).
potential well of the resulting 41 Rþ state is expected to be unusually broad with peculiarly shaped bottom. The calculated transition dipole moment for the 41 Rþ X1 Rþ system [9] is low and nearly constant around the equilibrium distance of the electronic ground state, although for larger R values it changes significantly, following changes in nature of the 41 Rþ state. All this implies relatively weak spectra and irregular spacing of vibrational levels, escaping traditional analysis. It is worth noting that exotic shapes of potential curves have been predicted for corresponding 41 Rþ states also in other heteronuclear alkali dimers: NaLi [10], KLi [11], LiRb, NaRb [12] and KRb [13,14]. The present experiment was undertaken to obtain an accurate spectroscopic characterisation of the 41 Rþ state and thus to fill the last gap in the experimental knowledge of singlet states in NaK giving rise to absorption spectra in the visible. The experiment was performed by the polarisation
0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00729-2
298
W. Jastrzebski et al. / Chemical Physics Letters 374 (2003) 297–301
labelling spectroscopy on the 41 Rþ X1 Rþ band system. Since the experimental arrangement is the same as described in our recent Letter [6] it will not be presented here. Owing to high sensitivity of the polarisation method we were able to detect the required molecular spectra. The spectra consisted of several long vibronic progressions belonging to the 41 Rþ X1 Rþ system (Fig. 1). Spacing of the recorded P, R doublets, unusually close for NaK (typically 25–30 cm1 ), is characteristic for transitions to a state with a broad potential energy curve. The observed transitions originated from altogether 28 rovibrational levels labelled in the ground state by light of the argon ion laser and terminated on all levels of the 41 Rþ state accessible due to the selection rules and non-negligible Franck–Condon factors. Thus our measurements in the main isotopomer 23 Na39 K spanned 86 vibrational levels with quantum numbers J ranging between 7 and 123. In addition, about 40 weak transitions forming a single vibrational progression could be assigned to the 23 Na41 K isotopomer; these were crucial in further analysis (the wave numbers of all transitions observed in the experiment can be obtained on request from the
authors). The energies of 41 Rþ state levels were obtained from wave numbers of the identified lines by adding highly accurate term values of the ground X1 Rþ state [5]. Our analysis encountered two serious problems. First, as the lowest vibrational levels of the 41 Rþ state were inaccessible from the levels labelled in the ground state (because of insufficient Franck– Condon overlap), we could not establish vibrational numbering in 41 Rþ directly. Second, the expected peculiar shape of the 41 Rþ potential curve, indeed confirmed by irregularities of the observed spectra, did not allow for conventional description of the state in terms of a Rydberg– Klein–Rees potential. The solution to the second problem is to construct the potential curve of the 41 Rþ state by a quantum-mechanical variational procedure, known as the inverted perturbation approach (IPA) [15]. The IPA method is based on iterative optimisation of the initial ÔguessedÕ potential energy curve in such a way that the calculated energy eigenvalues agree in a least-squares sense with the measured level energies. In the version of the procedure developed by us [16], the correction to
Fig. 1. Part of the polarisation spectrum of NaK obtained with the 501.7 nm line of the Arþ laser as the probe and circularly polarised pump light. The assigned v0 progressions correspond to transitions 41 Rþ ðv0 ; J 0 ¼ J 00 1Þ X1 Rþ ðv00 ; J 00 Þ from the ground state levels: (a) ðv00 ¼ 2; J 00 ¼ 104Þ and (b) ðv00 ¼ 3; J 00 ¼ 24Þ.
W. Jastrzebski et al. / Chemical Physics Letters 374 (2003) 297–301
the potential and the potential itself are defined as sets of points interpolated with cubic spline functions and the experimental energies are furnished directly to the program. It is always a crucial point to choose a reasonable initial potential energy curve for the IPA procedure, as it affects stability and rate of convergence of the routine. The recently published pseudopotential calculations for NaK [9], which proved accurate for several other medium excited states of this molecule [3,6], offered a good starting curve. It is known, however, that the theoretical potential curves usually depict better the actual shape of the potential than its absolute position in the energy scale and a vertical adjustment of the whole curve is often necessary. For the investigated 41 Rþ state of NaK such vertical shift was even more justified, as the numbering of vibrational levels in this state remained unknown at this stage of the analysis. Therefore our procedure was as follows. Using the experimental level energies of 23 Na39 K only, we repeated
299
the IPA procedure assuming several initial potentials, each of them of the same shape but shifted in energy and consequently imposing different vibrational numbering on the observed levels. As a result of many runs of the IPA routine, several improved potential curves have been generated, every curve reproducing well the experimental level energies. However, only one of this potentials allowed to predict correctly positions of the levels observed in the 23 Na41 K isotopomer (identified as v0 ¼ 41–61, J 0 ¼ 59 and 61). As an additional test of the vibrational numbering established in the 41 Rþ state in this way, we compared the intensity patterns in several observed vibrational progressions with Franck– Condon intensities calculated for the 41 Rþ X1 Rþ system. Even though our experiment is not well suited to precise intensity measurements, at least the positions of minima in the observed and calculated spectra should coincide. An exemplary comparison is shown in Fig. 2. The results taken
Fig. 2. Average relative intensities (experimental: solid lines; calculated: hollow bars) of the P and R lines in the 41 Rþ ðv0 ; J 0 ¼ 33; 35Þ X1 Rþ ðv00 ¼ 5; J 00 ¼ 34Þ for five vibrational numberings in the 41 Rþ state, differing by one vibrational quantum (a)–(e). The numbering inferred from the isotopic data corresponds to the trace (c).
300
W. Jastrzebski et al. / Chemical Physics Letters 374 (2003) 297–301
alone are probably not conclusive enough but they support nicely the vibrational assignment inferred from the isotopic data. In Table 1 and Fig. 3 we present the potential energy curve of the 41 Rþ state given in a grid of 55 points. For interpolation of the potential to an arbitrary middle point the natural cubic spline [17] should be used (i.e., the second derivative at the first and the last point should be set to zero). With the vibrational numbering imposed by the potential curve from Table 1, the energy levels used in the analysis correspond to v0 ¼ 30–115. Such input Þ and data actually allow only the inner (3.05–4.8 A ) parts of the potential to be outer (8.4–11.8 A determined reliably. We found that the shape of the bottom of the potential curve between 4.8 and does not influence significantly positions of 8.4 A levels studied in the present work. Therefore we used in this region a raw (uncorrected) theoretical curve [9], which after an upward shift of 50.5 cm1 smoothly matches the walls of the potential. Points range are given in Table 1 beyond the 3.05–11.8 A mostly to ensure proper boundary conditions for solving the Schr€ odinger equation. It must be noted, however, that these points have also some influence on the values of the potential for 3.05 < R < 11.8 A because of the properties of the A cubic spline interpolation. When solving the Schr€ odinger equation with the potential from Table 1 by the Numerov–Cooley method [18] with grid space, the energies of 1567 rovib0.0017 A rational levels observed in the present experiment are reproduced with a standard deviation of 0.07 cm1 , matching the experimental accuracy of 0.1 cm1 . It is worth noting that the eigenenergies of levels of the 41 Rþ state investigated here can be reproduced by a set of Dunham-like coefficients, listed in Table 2. Although the coefficients have no direct physical meaning and are applicable only to the range of v0 and J 0 quantum numbers used for their definition, they provide an easy way to predict rovibrational energies in the 41 Rþ state. In conclusion, we have derived a potential energy curve of the 41 Rþ state of the NaK molecule, which reproduces energies of vibrational levels v0 ¼ 30–115 with an accuracy of 0.07 cm1 . Closer examination of the bottom of the 41 Rþ state is still necessary as the lowest vibrational levels were
Table 1 The IPA potential energy curve of the 41 Rþ state in NaK R A
U cm1
2.4 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4 12.6 12.8 13.2 13.6 14.0
32415.0310 27385.1883 25649.9188 24384.4860 23542.5866 23042.1872 22797.7874 22722.1089 22715.5665 22677.9096 22586.4526 22501.7587 22438.1802 22392.8477 22349.2489 22301.6368 22247.3795 22187.8679 22124.2092 22063.9579 22021.9219 21993.6464 21971.8137 21957.4781 21958.0486 21979.7892 22023.3006 22087.7511 22173.0163 22279.6876 22408.3498 22557.4797 22723.4119 22901.5861 23088.2248 23280.1910 23474.9597 23670.5898 23865.2757 24057.9567 24247.8239 24433.9395 24615.5641 24791.8085 24961.9040 25125.7753 25283.8324 25437.3303 25584.4204 25710.7036 25805.2728 25883.8131 26034.9491 26123.9457 26178.3128
W. Jastrzebski et al. / Chemical Physics Letters 374 (2003) 297–301
301
as the initial state for fluorescence may allow then a direct observation of the lowest vibrational levels in the 41 Rþ . Acknowledgements This work has been funded in part by Grant No. 2 P03B 063 23 from the Polish Committee for Scientific Research. We thank Dr. L. Lis for preparation of hollow-cathode lamps employed in frequency calibration of our spectra. Fig. 3. The IPA potential energy curve of the 41 Rþ state in NaK (solid line) compared with the most recent theoretical calculation [9] (pluses). The arrows indicate boundaries of the regions discussed in the text. The position of the atomic asymptote of the 41 Rþ state, Na(32 S) + K(52 S), is also shown.
Table 2 Dunham-type coefficients representing energies of rovibrational levels of the 41 Rþ state in 23 Na39 K with a standard deviation 0.09 cm1 Constant
Value
Y 00 Y 10 Y 20 10 Y 30 103 Y 40 106 Y 50 108 Y 60 10 Y 01 103 Y 11 104 Y 21 106 Y 31 109 Y 41 107 Y 02 109 Y 12
22583.35 )19.7541 1.222536 )0.1711181 0.1428097 )0.6546037 0.124408 0.561077 )0.803714 0.127521 )0.101124 0.29769 )0.29042 )0.4774
All values are given in cm1 . The coefficients are meaningful only for v ¼ 30–115, J ¼ 7–123.
lacking in our analysis. This task requires however another experimental technique. As an example, high resolution Fourier transform spectroscopy of the laser induced fluorescence to the 41 Rþ state may be a good choice. Selecting a highly excited singlet state with sufficiently broad potential curve
References [1] A. Pashov, I. Jackowska, W. Jastrzebski, P. Kowalczyk, Phys. Rev. A 58 (1998) 1048. [2] A. Krou-Adohi, S. Giraud-Cotton, J. Mol. Spectrosc. 190 (1998) 171. [3] P. Kowalczyk, W. Jastrzebski, A. Pashov, S. Magnier, M. Aubert-Frecon, Chem. Phys. Lett. 314 (1999) 47. [4] J. Huennekens, I. Prodan, A. Marks, L. Sibbach, E. Galle, T. Morgus, J. Chem. Phys. 113 (2000) 7384. [5] I. Russier-Antoine, A.J. Ross, M. Aubert-Frecon, F. Martin, P. Crozet, J. Phys. B 33 (2000) 2753. [6] R. Nadyak, W. Jastrzebski, P. Kowalczyk, Chem. Phys. Lett. 353 (2002) 414. [7] W.J. Stevens, D.D. Konowalow, L.B. Ratcliff, J. Chem. Phys. 80 (1984) 1215. [8] S. Magnier, Ph. Millie, Phys. Rev. A 54 (1996) 204. [9] S. Magnier, M. Aubert-Frecon, Ph. Millie, J. Mol. Spectrosc. 200 (2000) 96. [10] I. Schmidt-Mink, W. M€ uller, W. Meyer, Chem. Phys. Lett. 112 (1984) 120. [11] S. Rousseau, A.R. Allouche, M. Aubert-Frecon, S. Magnier, P. Kowalczyk, W. Jastrzebski, Chem. Phys. 247 (1999) 193. [12] M. Korek, A.R. Allouche, M. Kobeissi, A. Chaalan, M. Dagher, K. Fakherddin, M. Aubert-Frecon, Chem. Phys. 256 (2000) 1. [13] S. Rousseau, A.R. Allouche, M. Aubert-Frecon, J. Mol. Spectrosc. 203 (2000) 235. [14] S.J. Park, Y.J. Choi, Y.S. Lee, G.H. Jeung, Chem. Phys. 257 (2000) 135. [15] C. Vidal, Commun. At. Mol. Phys. 17 (1986) 173. [16] A. Pashov, W. Jastrzebski, P. Kowalczyk, Comput. Phys. Commun. 128 (2000) 622. [17] C. de Boor, A Practical Guide to Splines, Springer, Berlin, 1978. [18] J.W. Cooley, Math. Comput. 15 (1961) 363.