Precise Molecular Constants for the6Li2A1Σ+u–X1Σ+gSystem by Sub-Doppler Polarization Spectroscopy

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

191, 295–305 (1998)

MS987645

1 1 Precise Molecular Constants for the 6Li2 A1 S1 u –X Sg System by Sub-Doppler Polarization Spectroscopy

Xuejun Wang, Jie Yang, Jianbing Qi, and A. Marjatta Lyyra Physics Department, Temple University, Philadelphia, Pennsylvania 19122 Received February 12, 1998; in revised form May 13, 1998

We report here new and more accurate molecular constants from sub-Doppler polarization spectroscopy of the A 1 S 1 u – 6 X S1 g system of Li2 using single mode cw dye lasers. These new constants cover the range of vibrational levels from v 0 5 0 – 8 in the ground state and v9 5 0 –24 in the excited state. New molecular constants and RKR potential energy curves for 1 1 1 1 21 the A 1 S 1 . The analysis indicates that u and X S g states are given. The Te value for the A S u state is 14068.043(34) cm there is a noticeable breakdown of the Born–Oppenheimer approximation for the 6Li2 and 7Li2 isotopomers. © 1998 Academic Press 1

INTRODUCTION

Since lithium dimer is the lightest neutral homonuclear molecule with core electrons, it has been of interest both theoretically (1) and experimentally (2–9) for quite some time. Accurate determination of molecular constants is especially important for the 1 1 1 1 A1 S1 u and X Sg states for the following reasons. The A Su – 1 1 X Sg transition is the most convenient system through which one can observe (1) higher lying electronic states including Rydberg states through OODR spectroscopy (2–6), and (2) the long range regions of electronic states by using multiple resonance spectroscopy (7–9). Since the lithium spin–orbit interaction is weak, the 1 1 A1 S1 u –X Sg system is less perturbed than the corresponding states in heavier alkali dimers. In fact, very few singlet–triplet perturbed gateway levels have been found to access the higher lying triplet states by OODR spectroscopy (10–12). Therefore, 1 1 the A1 S1 u –X Sg system is also a good prospect for observation of the breakdown of the Born–Oppenheimer approximation (B–O approximation thereafter) (13). 1 1 7 The A 1 S 1 u and X S g states of Li2 had already been studied quite extensively by Kusch and Hessel (14), who analyzed the 1 1 7 A1 S1 u –X S g band system of Li2 up to v9 5 25 and v 0 5 14 in 1977. Urbanski et al. (9) observed levels up to v9 5 62 in the 7 A1 S1 u state of Li2 by using all-optical triple resonance. Recently, Linton et al. (15) observed the 6Li2 A 1 S 1 u state from v9 5 0 to the dissociation limit using OODR excitation 1 1 1 1 1 1 ~F 1 S 1 g , E Sg ! 4 A Su 4 X Sg .

They observed fluorescence to the A 1 S 1 u state subsequently by using Fourier transform spectroscopy 1 1 1 1 ~F 1 S 1 g , E Sg ! 3 A Su .

We calculated the 6Li2 transition frequencies for the A 1 S 1 u – X S1 g band system either using the molecular constants from 1

Kusch and Hessel (14) and the reduced mass relationship or by using the RKR curve given by Linton. We found that neither approach was accurate enough. Generally, the discrepancy between the calculated and observed transitions was between 0.02 and 0.2 cm21 and it varied from band to band. In addition to needing accurate pump frequencies for double resonance excitation of 6Li2, the breakdown of the B–O approximation (13) should be investigated for such a light molecule. We have discovered recently that the isotope shift in the value of the ground state dissociation energy between 7Li2 and 6 Li2 (16) has to be corrected since the Te value of the 1Pg of 6 Li2 (4) did not include Y00 correction (17). Because the 2p–2s atomic transition of lithium has a shift of about 0.35 cm21 for the two isotopes, we expect that the electronic isotope shift between two isotopomers would be small but noticeable. To determine B–O approximation breakdown for the lithium isotopomers, more accurate molecular constants are needed. 1 1 6 Therefore a reanalysis of the A 1 S 1 u –X S g system of Li2 seemed timely. In the experiment we chose polarization spectroscopy technique because it provides high resolutions and high signal–noise ratios; therefore, we can obtain accurate transition frequencies, detect weak bands, and get access to all thermally populated rotational levels with one scan. All of these features are crucial to the experiment. In the present paper we report the results from our polarization spectroscopy experiment and subsequent analysis of the 6 1 1 Li2, A 1 S 1 u –X S g system, which allows us to determine accurately the molecular constants and new RKR curves. The analysis of the anomalous isotope shift and its dependence on internuclear distance will be reported later. EXPERIMENTAL

In our experiment we use a typical polarization spectroscopy setup (18). A single mode (Coherent 699-29 Autoscan, linewidth 0.5 MHZ) cw dye laser was used with either R6G (16 650–17 200 cm21, 250 mW) or pyridine 2 (13 800–14 350 cm21, 180 mW)

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TABLE 1 6 21 Dunham Constants of X1S1 ) g State of Li2 (in cm

dyes. The output of the laser was split into a strong (95%) pump and a weak (5%) probe beam. The circularly polarized pump and the linearly polarized probe beams were crossed in the center of the heat pipe at a small angle, about 2 mrad. Both beams were modulated with a mechanical chopper. A Glan–Thompson-type linear polarizer crystal was placed on each side of the 6Li2 (95% purity) heat pipe. The extinction ratio of the two crossed polarizers was ,1026. The heat pipe was operated at about 1000 K with 1 Torr of argon buffer gas. The polarization signal from the photomultiplier tube was monitored by a lock-in amplifier at the sum frequency of the pump and probe modulation frequencies. The

polarization signal and the LIF spectrum of I2 were simultaneously recorded for calibration. ANALYSIS AND RESULTS

A portion of the observed polarization spectrum near 14 000 cm21 is given in Fig. 1. There is noticeable saturation broadening and power broadening of linewidth of polarization signals. However, due to the sparcity of the spectral lines, there is rare overlapping in the bands studied. The power dependence of the line-

TABLE 2 6 21 Dunham Constants of A1S1 ) u State of Li2 (in cm

FIG. 1. Portion of the spectrum near 14 142 cm21. The assignment is A (v9, J9 ) 4 X (v 0, J0 ) . The transition labeled with * is due to 6Li 7Li. Copyright © 1998 by Academic Press

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TABLE 4 RKR Potential Curve for the A1S1 g State of 6Li2

6 1 1 FIG. 2. (a) Data field of X 1 S 1 g state of Li2. (b) Data field of A S u state of 6Li2.

width was not studied. The residual Doppler linewidth due to the choice of the laser beam crossing angle is estimated to be small (,15 MHz). Although there are many overlapping bands in the TABLE 3 RKR Potential Curve for the X1S1 g State of 6Li2

same region due to appreciable population of many vibrational levels at about 1000 K, the assignment is quite straightforward. By using the reduced mass relation (19), the 7Li2 constants by Urbanski et al. (9) predict the transition frequencies with an error of less than 0.2 cm21. Rough intensity estimates were made according to the thermal population, Franck–Condon factors (assuming the same as for 7Li2), nuclear statistical weights (2:1 for 6Li2), and rotational line intensity factors (20). Almost all the lines scanned in the R6G region were assigned. The 0–0, 0–1, 0–2, 1–1, 1–2 bands in the pyridine region are strong due to large thermal populations and Franck–Condon factors. Overall, we could assign 38 bands and about 976 lines in the 6Li2 spectrum unambiguously. 1 1 The analysis of the 6Li7Li A1 S1 u –X Sg bands and anomalous isotope shift will be reported later. The frequencies of the spectral lines were fitted to a Dunham-type expansion

S

n ~V9,J9zV 0J0! 5 ( Y ik V9 1 ik

D

1 i ~ J9 ~ J9 1 1!! k 2

S

2 S Y lm V0 1 lm

D

1 l ~ J0 ~ J0 1 1!! m , 2

where F is the transition frequency; Y’s are the Dunham Copyright © 1998 by Academic Press

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TABLE 5 1 1 6 Assignment and Transition Frequencies (in cm21) of the A1S1 u –X Sg System of Li2

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TABLE 5—Continued

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TABLE 5—Continued

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TABLE 5—Continued

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TABLE 5—Continued

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TABLE 5—Continued

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TABLE 5—Continued

constants; v and J are vibrational and rotational quantum numbers, respectively. A total of 9 Dunham constants for the X 1 S 1 g state and 13 Dunham constants for the A 1 S 1 u state were used in the fitting. The total of 22 Dunham constants can reproduce 976 transitions with a standard deviation of 0.0079 cm21, which is quite satisfactory compared with the experimental uncertainty of 0.005 cm21. Figure 2a shows the data field for the X 1 S 1 g state. Figure 2b is the data field for the A 1 S 1 u state. Basically, we used the data for the range of vibrational quantum numbers v 0 5 0 to v 0 5 1 1 8 for the X 1 S 1 g state and v9 5 0 to v9 5 24 for the A S u state. The highest rotational quantum number used in the fits was J 5 43. The Dunham constants and the fitting errors of the X 1 S 1 g state and A 1 S 1 u state are listed in Tables 1 and 2, respectively. The corresponding RKR curves are given in Tables 3 and 4. The transition frequencies used in the least-squares fitting are shown in Table 5. The Kratzer relation offers a test of the consistency of the molecular constants. For the A 1 S 1 u state the fitted and calculated Y02 values are 21.0240E 2 5 and 21.0265E 2 5, respectively, with a discrepancy of 0.24%. For the X 1 S 1 g state the same comparison gives Y02 values of 21.34140E 2 5 (fitted) and 21.34109E 2 5 (calculated). In this case the error is within 0.02%. To determine the electronic isotope shift of the A 1 S 1 u state of 7Li2 and 6Li2, which is an indication of a breakdown of B–O approximation, we need accurate potential minima for both isotopomers. However, due to the correlations between Dun-

ham constants, the fitted constants will depend on the Dunham constants set chosen and the data set available; therefore the actual uncertainty will be substantially larger than the fitting error of the constant. We chose the present Dunham constants set because it gives smaller standard deviation of the fit while the errors of the fitted constants remain small (,10%). If we take the Y00 corrections of both the upper and the lower state into account, the present fit gives a value of the A 1 S 1 u state potential minimum Te 5 14068.043 cm21 for 6Li2. If we vary the choice of Dunham constants included in the fit, from the present case to the Dunham constants used by Kusch and Hessel (14) and also vary the data set from v9 , 25 to v9 , 9, the variance of Te value in the worst case can be as much as 0.031 cm21. We take this value as the uncertainty due to the choice of Dunham constants and the range of upper state vibrational levels included in the fit. By including the Y00 corrections, Kusch and Hessel’s (14) result for 7Li2 (which is more similar to our case in that their v9 included in the fit is also less than 25) gives Te 5 14068.203 cm21. If we assume their value of Te has similar uncertainty to ours, we suggest that 1 1 the 7Li2 and 6Li2 A 1 S 1 u –X S g system has an electronic isotope shift of 0.160(70) cm21 at the equilibrium internuclear distance. The quoted uncertainty here includes both the fitting error and the uncertainty due to different choices of Dunham constants and data set. The atomic limit isotope shift from the 2p–2s atomic transition is 0.351346(20) cm21 (21). These two values are comparable but not identical. This indicates that there is a slight breakdown of the B–O approximation and it is internuclear distance dependent.

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1 1 Li2, A 1 S 1 u –X S g SYSTEM, SUB-DOPPLER, POLARIZATION SPECTROSCOPY

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1 1 The RKR curves of A 1 S 1 u and X S g states are given in Tables 3 and 4, respectively. For the A 1 S 1 u state, the values for the inner and outer turning points of vibration, Rmin and Rmax, agree with those for Linton’s curve (15) to the third digit after the decimal point. After adding the Y00, the vibrational energies Gv,J50 agree with Linton’s result within 0.03 cm21. The number of digits given in our RKR potential curve is larger so that errors resulting from truncation can be avoided in numerical integration of eigenvalues using the RKR curve. The term values calculated from these two curves agree very well (within 0.04 cm21) with those calculated from Dunham constants given in Tables 1 and 2. The minima of the RKR curves for the different isotopes are 7 slightly shifted. For the X 1 S 1 g state this shift is Re( Li2) 2 6 1 1 Re( Li2) 5 0.00026(7) Å. For the state of A S u the shift is Re(7Li2) 2 Re(6Li2) 5 0.00023(11) Å. This is an additional indication of the breakdown of the B–O approximation, since within this approximation the potential energy curves should be identical for different isotopes.

CONCLUSIONS

We have determined new precise molecular constants for the 1 1 Li2 A 1 S 1 u –X S g band system. These constants are based on high-resolution single mode cw laser polarization spectroscopy of this system. The new constants predict the 6Li2 A 1 S 1 u – X1 S1 transitions with higher accuracy than was previously g possible. Our analysis also indicates that there is a noticeable anomalous isotope shift due to the B–O approximation breakdown for the lithium isotopomers (22). 6

ACKNOWLEDGMENTS We wish to thank Professors Li Li, Colan Linton, William Stwalley, and Robert Le Roy and Drs. Mingguang Li, Bing Ji, and Kenneth Urbanski for helpful discussions. We are also grateful to Dr. Stiliana Antonova and Mr. Guenadiy Lazarov for their help with the experiment, and to Ed Kaczanowitz and Steve Stevenson for technical support. This work was supported by NSF.

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