- Email: [email protected]
On the 51Σ+ state of NaK
26 February 2002
Chemical Physics Letters 353 (2002) 414–417 www.elsevier.com/locate/cplett
On the 51Rþ state of NaK R. Nadyak a, W. Jastrzebski a, P. Kowalczyk a
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 6 December 2001
Abstract Polarization labelling spectroscopy is applied to study the previously unobserved 51 Rþ state of the NaK molecule. Molecular constants and a Rydberg–Klein–Rees (RKR) potential energy curve based on these constants are deter, respectively. Ó 2002 Published mined. The values of Te , xe and Re are 23530.62(6) cm1 , 115.60(6) cm1 and 4.307 A by Elsevier Science B.V.
Polarization labelling spectroscopy has already proved to be a useful technique in studies of both homonuclear and heteronuclear alkali dimers [1–4]. Using this method for investigation of the NaK molecule, in previous experiments [5–7] we observed and characterized the 31 P, 41 P, 51 P and 61 Rþ states located between 25 500 and 27 700 cm1 above the bottom of the ground state potential well. The aim of the present work was to extend this study to the previously unobserved lower electronic state of NaK, the 51 Rþ state. This state, with Te predicted by theoretical calculations at about 23 530 cm1 [8,9], has escaped experimental observation for a surprisingly long time. The reason has been revealed by a recent theoretical study by Magnier et al. [9]. The calculated transition dipole moment for excitation of the 51 Rþ state from the ground X1 Rþ state shows a complicated dependence on internuclear distance R (see Fig. 1) which
*
Corresponding author. Fax: +48-22-6256406. E-mail address: [email protected] (P. Kowalczyk).
results in small probabilities of transitions originating from low vibrational levels in the ground state. Owing to high sensitivity of polarization spectroscopy we were able to record the X1 Rþ band system and to characterize the 51 R þ 1 þ 5 R state to nearly 45% of its potential well depth. Our experimental apparatus and procedure have been described in detail in the previous paper [5]. In short, we used the polarization labelling spectroscopy technique with a V-type optical–optical double resonance excitation scheme. Vapour containing NaK molecules was produced by heating a mixture of metallic sodium and potassium in a stainless steel heat pipe. The temperature was maintained at about 450 °C and a total pressure of 4 Torr was established using helium as a buffer gas. The copropagating pump and probe laser beams were crossed at the centre of the heat pipe. The probe laser was of fixed wavelength (Arþ laser at 514.5, 501.7, 496.5, 488.0 or 476.5 nm) and excited a few known molecular transitions in the D1 P X1 Rþ system of NaK, thus labelling the rotational levels involved in the ground state.
0009-2614/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 0 5 4 - 4
R. Nadyak et al. / Chemical Physics Letters 353 (2002) 414–417
Fig. 1. The RKR potential curve for the 51 Rþ state of NaK (from this work), bottom part of the X1 Rþ state potential [10], showing limiting vibrational levels from which absorption was observed in the present experiment, and theoretical transition dipole moment dðRÞ for the 51 Rþ X 1 Rþ system [9].
The pumped laser (pulsed dye laser and XeCl excimer laser system, 2 mJ pulse energy, 0:1 cm1 linewidth), tuned in the spectral range 22 650– 24 550 cm1 , induced transitions in the investigated 51 Rþ X1 Rþ band system. The dye laser wavelengths were calibrated by means of optogalvanic spectrum of argon and transmission spectrum by a Fabry–Perot interferometer (1 cm1 FSR) recorded simultaneously. The accuracy in determination of transition energies was 0:1 cm1 . The interpretation of the observed polarization spectra was based on previous knowledge of rovibrational levels in the ground state labelled by individual lines of the argon ion laser [5]. The principal progressions of P and R doublets could be identified immediately and the remaining, weaker ones were fitted accordingly. A total of 257 transitions in 23 Na39 K were assigned, spanning the
415
range v0 ¼ 0–15, J 0 ¼ 18–121 in the 51 Rþ state. Originally all observed lines were subjected to a global least-squares fit with a Dunham expansion. Constants of the ground state were fixed at the values given by Russier-Antoine et al. [10]. As could be expected, the initial fit revealed that part of the lines displayed shifts from the expected positions exceeding 0:2 cm1 (twice the experimental uncertainty) due to perturbations of the 51 Rþ state by the neighbouring electronic states, the 43 Rþ state [9] being the most plausible candidate. All such lines were excluded from the final fit, which provided the Dunham coefficients for the 51 Rþ state listed in Table 1 (235 lines used, rms error of the fit 0:09 cm1 ). For each coefficient a total of at least five figures are given (more than are statistically significant), as this number is required to reproduce the measured transitions. Since the data field is somewhat limited, we display it explicitly in Fig. 2. Once the coefficients in the Dunham expansion have been determined, we applied the Rydberg–Klein–Rees (RKR) method to obtain the rotationless potential curve for the 51 Rþ state (Table 2 and Fig. 1). The absolute vibrational numbering in the 51 Rþ state was based on observation that a few vibrational progressions displayed sharp limits of the signal to the red, each of them terminating on the same vibrational level of the excited state. This lowest observed level was assumed to correspond to v0 ¼ 0. The numbering was subsequently verified by comparison of the Table 1 The Dunham coefficients for the 51 Rþ state of NaK Constant
Value ðcm1 Þ
Uncertainty (%)
Te Y10 Y20 Y30 Y40 Y50 Y01 Y11 Y21 Y02 Y12
23530.62 0:115604 103 0:27484 101 0.14892 0:64596 102 0:11411 103 0:628504 101 0:17411 103 0:87091 105 0:83994 107 0:67297 108
0.0003 0.051 0.75 2.1 3.2 4.5 0.022 1.3 1.9 1.3 2.2
The quoted uncertainty of a constant is one standard deviation.
416
R. Nadyak et al. / Chemical Physics Letters 353 (2002) 414–417
Fig. 2. Distribution of the data used to fit the Dunham coefficients in the field of vibrational and rotational quantum numbers of the 51 Rþ state in NaK.
observed line intensities with the calculated Franck–Condon factors for the 51 Rþ X1 Rþ transition. Unfortunately, low intensity of the Table 2 Rotationless RKR potential for the 51 Rþ state of NaK v
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Gv (cm1 )
Rmin ) (A
Rmax ) (A
0.0 56.500 167.059 273.284 375.787 475.060 571.487 665.360 756.890 846.222 933.450 1018.629 1101.787 1182.943 1262.118 1339.349 1414.703
4.3070 4.1688 4.0684 3.9994 3.9433 3.8951 3.8523 3.8135 3.7780 3.7451 3.7143 3.6853 3.6579 3.6317 3.6067 3.5828 3.5600
4.3070 4.4541 4.5732 4.6622 4.7394 4.8100 4.8764 4.9397 5.0010 5.0608 5.1196 5.1777 5.2357 5.2935 5.3516 5.4099 5.4684
The first line refers to the bottom of the potential curve: R is the equilibrium distance.
spectrum did not allow us to record lines belonging to the 23 Na39 K isotopomer and to reconfirm the vibrational assignment by isotope effect. The dissociation energy of the 51 Rþ state can be obtained in a standard way, from separation of the atomic asymptotes [11] and dissociation energy of the ground state [10]. Taking into account a correlation diagram of molecular states in NaK we find the atomic asymptote corresponding to the 51 Rþ state as Nað3S1=2 Þ þ Kð3D5=2 Þ, which provides De ð51 Rþ Þ ¼ 3277:9 cm1 . We also note high quality of the recent pseudopotential calculations for NaK [8,9] which predict the main spectroscopic
Table 3 Comparison of the experimental and theoretical molecular constants of the 51 Rþ state in NaK (values in cm1 , except for ) Re in A Constant
This work
Calculations [8]
[9]
Te xe De Re
23530.62 115.60 3277.9 4.307
23 527 112 3193 4.292
23535 110.73 3195 4.286
R. Nadyak et al. / Chemical Physics Letters 353 (2002) 414–417
constants of the 51 Rþ state with high accuracy (Table 3). Acknowledgements This work was partially supported by the Polish Committee for Scientific Research, in particular under grant No. 2 P03B 067 16. The authors wish to thank Dr. L. Lis for preparing hollow-cathode lamps used to record the optogalvanic spectra. References [1] N.W. Carlson, A.J. Taylor, K.M. Jones, A.L. Schawlow, Phys. Rev. A 24 (1981) 822.
417
[2] P. Bernage, P. Niay, H. Bocquet, J. Mol. Spectrosc. 98 (1983) 304. [3] W. Jastrzebski, P. Kowalczyk, Phys. Rev. A 51 (1995) 1046. [4] A. Pashov, W. Jastrzebski, P. Kowalczyk, Chem. Phys. Lett. 292 (1998) 615. [5] A. Pashov, I. Jackowska, W. Jastrzebski, P. Kowalczyk, Phys. Rev. A 58 (1998) 1048. [6] P. Kowalczyk, W. Jastrzebski, A. Pashov, S. Magnier, M. Aubert-Frecon, Chem. Phys. Lett. 314 (1999) 47. [7] A. Pashov, W. Jastrzebski, P. Kowalczyk, J. Phys. B 33 (2000) L611. [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. Russier-Antoine, A.J. Ross, M. Aubert-Frecon, F. Martin, P. Crozet, J. Phys. B 33 (2000) 2753. [11] A.A. Radzig, P.M. Smirnov, Reference Data on Atoms, Molecules and Ions, Springer, Berlin, 1985.
Chemical Physics Letters 353 (2002) 414–417 www.elsevier.com/locate/cplett
On the 51Rþ state of NaK R. Nadyak a, W. Jastrzebski a, P. Kowalczyk a
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 6 December 2001
Abstract Polarization labelling spectroscopy is applied to study the previously unobserved 51 Rþ state of the NaK molecule. Molecular constants and a Rydberg–Klein–Rees (RKR) potential energy curve based on these constants are deter, respectively. Ó 2002 Published mined. The values of Te , xe and Re are 23530.62(6) cm1 , 115.60(6) cm1 and 4.307 A by Elsevier Science B.V.
Polarization labelling spectroscopy has already proved to be a useful technique in studies of both homonuclear and heteronuclear alkali dimers [1–4]. Using this method for investigation of the NaK molecule, in previous experiments [5–7] we observed and characterized the 31 P, 41 P, 51 P and 61 Rþ states located between 25 500 and 27 700 cm1 above the bottom of the ground state potential well. The aim of the present work was to extend this study to the previously unobserved lower electronic state of NaK, the 51 Rþ state. This state, with Te predicted by theoretical calculations at about 23 530 cm1 [8,9], has escaped experimental observation for a surprisingly long time. The reason has been revealed by a recent theoretical study by Magnier et al. [9]. The calculated transition dipole moment for excitation of the 51 Rþ state from the ground X1 Rþ state shows a complicated dependence on internuclear distance R (see Fig. 1) which
*
Corresponding author. Fax: +48-22-6256406. E-mail address: [email protected] (P. Kowalczyk).
results in small probabilities of transitions originating from low vibrational levels in the ground state. Owing to high sensitivity of polarization spectroscopy we were able to record the X1 Rþ band system and to characterize the 51 R þ 1 þ 5 R state to nearly 45% of its potential well depth. Our experimental apparatus and procedure have been described in detail in the previous paper [5]. In short, we used the polarization labelling spectroscopy technique with a V-type optical–optical double resonance excitation scheme. Vapour containing NaK molecules was produced by heating a mixture of metallic sodium and potassium in a stainless steel heat pipe. The temperature was maintained at about 450 °C and a total pressure of 4 Torr was established using helium as a buffer gas. The copropagating pump and probe laser beams were crossed at the centre of the heat pipe. The probe laser was of fixed wavelength (Arþ laser at 514.5, 501.7, 496.5, 488.0 or 476.5 nm) and excited a few known molecular transitions in the D1 P X1 Rþ system of NaK, thus labelling the rotational levels involved in the ground state.
0009-2614/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 0 5 4 - 4
R. Nadyak et al. / Chemical Physics Letters 353 (2002) 414–417
Fig. 1. The RKR potential curve for the 51 Rþ state of NaK (from this work), bottom part of the X1 Rþ state potential [10], showing limiting vibrational levels from which absorption was observed in the present experiment, and theoretical transition dipole moment dðRÞ for the 51 Rþ X 1 Rþ system [9].
The pumped laser (pulsed dye laser and XeCl excimer laser system, 2 mJ pulse energy, 0:1 cm1 linewidth), tuned in the spectral range 22 650– 24 550 cm1 , induced transitions in the investigated 51 Rþ X1 Rþ band system. The dye laser wavelengths were calibrated by means of optogalvanic spectrum of argon and transmission spectrum by a Fabry–Perot interferometer (1 cm1 FSR) recorded simultaneously. The accuracy in determination of transition energies was 0:1 cm1 . The interpretation of the observed polarization spectra was based on previous knowledge of rovibrational levels in the ground state labelled by individual lines of the argon ion laser [5]. The principal progressions of P and R doublets could be identified immediately and the remaining, weaker ones were fitted accordingly. A total of 257 transitions in 23 Na39 K were assigned, spanning the
415
range v0 ¼ 0–15, J 0 ¼ 18–121 in the 51 Rþ state. Originally all observed lines were subjected to a global least-squares fit with a Dunham expansion. Constants of the ground state were fixed at the values given by Russier-Antoine et al. [10]. As could be expected, the initial fit revealed that part of the lines displayed shifts from the expected positions exceeding 0:2 cm1 (twice the experimental uncertainty) due to perturbations of the 51 Rþ state by the neighbouring electronic states, the 43 Rþ state [9] being the most plausible candidate. All such lines were excluded from the final fit, which provided the Dunham coefficients for the 51 Rþ state listed in Table 1 (235 lines used, rms error of the fit 0:09 cm1 ). For each coefficient a total of at least five figures are given (more than are statistically significant), as this number is required to reproduce the measured transitions. Since the data field is somewhat limited, we display it explicitly in Fig. 2. Once the coefficients in the Dunham expansion have been determined, we applied the Rydberg–Klein–Rees (RKR) method to obtain the rotationless potential curve for the 51 Rþ state (Table 2 and Fig. 1). The absolute vibrational numbering in the 51 Rþ state was based on observation that a few vibrational progressions displayed sharp limits of the signal to the red, each of them terminating on the same vibrational level of the excited state. This lowest observed level was assumed to correspond to v0 ¼ 0. The numbering was subsequently verified by comparison of the Table 1 The Dunham coefficients for the 51 Rþ state of NaK Constant
Value ðcm1 Þ
Uncertainty (%)
Te Y10 Y20 Y30 Y40 Y50 Y01 Y11 Y21 Y02 Y12
23530.62 0:115604 103 0:27484 101 0.14892 0:64596 102 0:11411 103 0:628504 101 0:17411 103 0:87091 105 0:83994 107 0:67297 108
0.0003 0.051 0.75 2.1 3.2 4.5 0.022 1.3 1.9 1.3 2.2
The quoted uncertainty of a constant is one standard deviation.
416
R. Nadyak et al. / Chemical Physics Letters 353 (2002) 414–417
Fig. 2. Distribution of the data used to fit the Dunham coefficients in the field of vibrational and rotational quantum numbers of the 51 Rþ state in NaK.
observed line intensities with the calculated Franck–Condon factors for the 51 Rþ X1 Rþ transition. Unfortunately, low intensity of the Table 2 Rotationless RKR potential for the 51 Rþ state of NaK v
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Gv (cm1 )
Rmin ) (A
Rmax ) (A
0.0 56.500 167.059 273.284 375.787 475.060 571.487 665.360 756.890 846.222 933.450 1018.629 1101.787 1182.943 1262.118 1339.349 1414.703
4.3070 4.1688 4.0684 3.9994 3.9433 3.8951 3.8523 3.8135 3.7780 3.7451 3.7143 3.6853 3.6579 3.6317 3.6067 3.5828 3.5600
4.3070 4.4541 4.5732 4.6622 4.7394 4.8100 4.8764 4.9397 5.0010 5.0608 5.1196 5.1777 5.2357 5.2935 5.3516 5.4099 5.4684
The first line refers to the bottom of the potential curve: R is the equilibrium distance.
spectrum did not allow us to record lines belonging to the 23 Na39 K isotopomer and to reconfirm the vibrational assignment by isotope effect. The dissociation energy of the 51 Rþ state can be obtained in a standard way, from separation of the atomic asymptotes [11] and dissociation energy of the ground state [10]. Taking into account a correlation diagram of molecular states in NaK we find the atomic asymptote corresponding to the 51 Rþ state as Nað3S1=2 Þ þ Kð3D5=2 Þ, which provides De ð51 Rþ Þ ¼ 3277:9 cm1 . We also note high quality of the recent pseudopotential calculations for NaK [8,9] which predict the main spectroscopic
Table 3 Comparison of the experimental and theoretical molecular constants of the 51 Rþ state in NaK (values in cm1 , except for ) Re in A Constant
This work
Calculations [8]
[9]
Te xe De Re
23530.62 115.60 3277.9 4.307
23 527 112 3193 4.292
23535 110.73 3195 4.286
R. Nadyak et al. / Chemical Physics Letters 353 (2002) 414–417
constants of the 51 Rþ state with high accuracy (Table 3). Acknowledgements This work was partially supported by the Polish Committee for Scientific Research, in particular under grant No. 2 P03B 067 16. The authors wish to thank Dr. L. Lis for preparing hollow-cathode lamps used to record the optogalvanic spectra. References [1] N.W. Carlson, A.J. Taylor, K.M. Jones, A.L. Schawlow, Phys. Rev. A 24 (1981) 822.
417
[2] P. Bernage, P. Niay, H. Bocquet, J. Mol. Spectrosc. 98 (1983) 304. [3] W. Jastrzebski, P. Kowalczyk, Phys. Rev. A 51 (1995) 1046. [4] A. Pashov, W. Jastrzebski, P. Kowalczyk, Chem. Phys. Lett. 292 (1998) 615. [5] A. Pashov, I. Jackowska, W. Jastrzebski, P. Kowalczyk, Phys. Rev. A 58 (1998) 1048. [6] P. Kowalczyk, W. Jastrzebski, A. Pashov, S. Magnier, M. Aubert-Frecon, Chem. Phys. Lett. 314 (1999) 47. [7] A. Pashov, W. Jastrzebski, P. Kowalczyk, J. Phys. B 33 (2000) L611. [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. Russier-Antoine, A.J. Ross, M. Aubert-Frecon, F. Martin, P. Crozet, J. Phys. B 33 (2000) 2753. [11] A.A. Radzig, P.M. Smirnov, Reference Data on Atoms, Molecules and Ions, Springer, Berlin, 1985.