High-Resolution Laser Spectroscopy of theA3Π1u←X1Σg+System of I2with a Titanium:Sapphire Ring Laser

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

182, 271–279 (1997)

MS967216

High-Resolution Laser Spectroscopy of the A 3P1u R X 1S g/ System of I2 with a Titanium:Sapphire Ring Laser Tokio Yukiya, Nobuo Nishimiya, and Masao Suzuki Department of Electronic Engineering, Tokyo Institute of Polytechnics, Iiyama 1583, Atsugi City, Kanagawa 243-02, Japan Received March 12, 1996; in revised form September 12, 1996

The Doppler-limited absorption spectrum of the vibrotational lines in the A 3P1u R X 1S /g system of I2 was measured in the region from 11,200 to 12,450 cm01 using a Ti:sapphire ring laser. The Q-branch lines of J Å 10 to 100 belonging to the £* R £9 Å (26 * Ç 45 * ) R 0 9, (19 * Ç 45 * ) R 1 9, (16 * Ç 45 * ) R 2 9, (16 * Ç 42 * ) R 3 9, and (22 * Ç 31 * ) R 4 9 progressions were assigned. The hyperfine splittings were observed at the vibrational states around the near-dissociation limit. The unperturbed line positions were obtained by first order approximation for the high-J rotational state. The values of n 0Q , B £* f 0 B £9 , D £* f 0 D £9 , and H £* 0 H £9 were determined using a least-squares fitting procedure. The spectroscopic constants of T £* , B £* f , D £* f , and H £* f of £* Å 16 Ç 45 were calculated with the aid of the Dunham expansion parameters of the X state and were compared with those reported by D. R. T. Appadoo et al. (J. Chem. Phys. 104(3), 903 (1996)). q 1997 Academic Press 1. INTRODUCTION

The electronic spectrum relating to the A state of the I2 molecule was first studied by W. G. Brown in 1931 (2). The band spectrum was not resolved, however, until the end of 1970’s due to the restrictions on the resolving power and sensitivity of the spectrometer used. The absorption spectrum of the A–X system was reported in 1979 by R. A. Ashby (3). Ashby measured the vibrational structure of this band using a grating spectrometer in the wavelength region of 800–1300 nm and reported the vibrational constants in his paper with C. W. Johnson (4). Gerstenkorn et al. (5) also gave the vibrational assignment for the A 0 X system detected at the 1300 nm region in 1981. The rotational spectroscopic constants of the A state were firstly reported by K. S. Viswanthan et al. (6) based on the measurement of the emission system at the 277 nm region. They made the assignment of the vibrational fine structures of the £* Å 5– 19 levels and calculated the spectroscopic constants of T *£ , B *£ , D *£ , and H *£ up to £* Å 35 using the RKR method. The direct measurement of the absorption spectrum of the A–X system using a high-resolution Fourier transform spectrometer has been reported by Gerstenkorn et al. in the wavenumber region of 7220 to 11,200 cm01 (7). They measured the spectrum by heating the absorption cell to increase the population densities at the higher vibrational and rotational states. The spectroscopic constants have lately been reported by D. R. T. Appadoo et al. based on the analysis of the £* Å (0 Ç 35) R £9 Å (3 Ç 17) vibrotational bands (1). They presented the parameters defining the exponential near dissociation expansions for the calculation of the spectro-

scopic constants and gave the spectroscopic constants up to the near dissociation limit of £* Å 50. Spectroscopies using lasers have rarely been adopted, as in the case of the B–X system. X. Zheng et al. investigated the b – A system using a frequency-doubled tunable dye laser. The population belonging to the rotational states of the ground vibrational levels of the A state was increased by pumping the free jet cooled to 5 K using an Ar–F laser and the rotational constant of the £9 Å 0 state was determined (8). T. Ishiwata et al. investigated the fine structures of the 1g(1D) – A 3P1u –X 1S g/ double resonance system and determined the spectroscopic constants of T *£ , B *£ , D *£ , and q *£ for the £* Å 9, 12, and 21 states (9). They also reported the vibrational levels and rotational constants calculated by the RKR method. As laser spectroscopy using a CW laser promises to enable determination of very accurate spectroscopic constants, we became interested in investigating the absorption spectrum of the A–X system using a Ti:sapphire ring laser oscillating in the wavelength region of 700–1000 nm. The measurement in the region from 810 to 860 nm where the very dense absorption signals belonging to £9 Å 0, 1, 2, 3, and 4 are detected at room temperature is important for the wavelength standard since the absorption spectra of the A–X systems of ICl and IBr become weak. The A–X system of I2 is too weak to be detected at room temperature by a spectrometer of a lower resolving power and the cell must sometimes be heated to increase the molecular density, although the absorption lines detected by a heated cell are distorted by the stronger lines belonging to the B–X system. The rotational fine structures and the hyperfine structures by nuclear spin interaction

271 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.

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FIG. 1. Block diagram of the Ti:Sapphire ring laser spectrometer.

can be resolved without being disturbed by the neighboring lines of the B–X system by the measurement at a room temperature. Our research, independent of the work by D. R. T. Appadoo et al. (1), is to determine the spectroscopic constants from £* Å 16 to the dissociation limit by observing the progressions from the lower vibrational states of £9 Å 0, 1, 2, 3, and 4 in the X state and to compare them with the ones calculated by the near dissociation expansion method. The research in the wavelength region is suitable since the spectrum are not disturbed by the hot band of the B–X transitions at the room temperature. The hyperfine splittings are our second concern since the eQq1 and eQq2 values of the A state are expected to depend on the vibrational quantum number and to converge to zero at the near dissociation limit (10, 11).

beam was used to get fringe signals with a spacing of 0.01006 cm01 . The confocal e´talon was constructed with a fused quartz pipe of 250 mm length and two spherical mirrors with focal length of 250 mm. The absorption and the fringe signals were detected by PIN diodes. The third beam was focused into the optical fiber of a wavelength-meter (Anritsu MF9630A) with an accuracy of {0.5 ppm.

2. EXPERIMENTAL DETAILS

The experimental setup constructed is schematically shown in Fig. 1. A Ti:sapphire ring laser (Coherent 89921) pumped by an argon ion laser (Coherent Innova 90) was used as an optical source. The laser beam was divided into three beams. The first beam was introduced into a 1.5mabsorption cell of 4 cm diameter, in which I2 gas purified by sublimation was charged at saturated pressure at room temperature. An effective pass-length of 12 m was obtained using a multipass technique as shown in Fig. 1. The second

FIG. 2. Recorder trace of the absorption lines in 11,717 cm01 –11,720 cm01 region.

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THE A R X SYSTEM OF I2

273

FIG. 3. The second derivative line profile of Q branches in the A–X system at the high vibrational levels of the A state. (a) The observed absorption lines of the Q(20) and Q(21) in the £* R £9 Å 40 R 2 band. (b) Line profiles simulated by using the Doppler width of 0.0048 cm01 . The wavenumbers of 0.007, 0.010, 0.015, and 0.02 cm01 denote the width of the frequency modulation, respectively.

A coarse wavelength setting on the order of 0.1–0.05 nm was done by tuning the BRF using a DC servo motor controlled by an error signal proportional to the difference between the present value of the wavelength in a PC (NEC PC9801VX) and that read out from the wavelength-meter. A continuous tuning range of 30 GHz was attained by applying step signals generated from a digital function generator to the galvo motor driver. The thin e´talon was also electrically controlled to get a good single mode operation. The laser frequency was modulated by a sine wave of small amplitude. A modulation frequency of 15 Hz was adopted in consideration of the response time of the galvo motor. The modulation width was estimated to be 200–300 MHz. The second derivatives of the absorption lines and those of the fringe signals were detected with phase sensitive amplifiers. Then these were AD-converted. The digital sig-

nals from the wavelength-meter were sent to the PC through a GP-IB bus and numerically averaged by synchronizing with every step of the sweep signal from a digital function generator and the peak of the fringe signal was assigned with reference to these values. As the tuning ranges of the laser were so narrow as to look around the band contour, we compiled the spectral fragments of about 1 cm01 with the fringe markers by using the PC and determined the line wavenumbers. The value indicated by the wavelength-meter was calibrated against the two-photon signal of Rb at 788 nm (12). The averaged values for sampling times of 100 agreed with those reported within the average deviation of 0.02 ppm. We also estimated the errors accompanying the frequency modulation by changing the modulation width. The value interpolated using fringe signals agreed with the averaged

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TABLE 1 Energy Splittings for Nuclear Quadrupole Coupling Effect of Identical Nuclei under the High- J Approximation

value obtained by locking the laser frequency to the absorption line within the average deviation of the wavelengthmeter. We estimated the accuracy of the absolute line positions to be 0.005 cm01 , which was almost three times the standard deviation, by considering the linewidth and the signal-to-noise ratios of the measurement. The trace of the absorption lines in the 11,717–11,720 cm01 region thus recorded is shown in Fig. 2. This trace was reproduced by compiling the five fragments which were continuously tuned in 0.8 cm01 ranges. The traces were quite different from the Atlas recorded using a heated cell at a higher temperature of 7907C (13).

stronger. The Q-branch lines belonging to the higher vibrational state of £* Å 30, however, split into the doublet or triplet as shown in Fig. 3a. Since the nuclear hyperfine splittings at the higher rotational level of J Å 20 are approximately independent to the rotational quantum number, we determined unperturbed line position using the relation given for the identical nuclear coupling 1 DneQq e / f Å ( 0 eQq *1 { eQq *2 ){Y *1 { Y *2 } 2 0 ( 0 eQq 91 ){Y 91 { Y 92 }

[1]

Å ( DeQq e / f ){Y *1 { Y *2 },

3. RESULTS AND DISCUSSION

The Q-branch lines were clearly distinguished from the P- and R-branch lines in the dense absorption spectrum since the nuclear hyperfine splittings were narrower than the Doppler width, and the line intensities were several times

where Y1 and Y2 are the Casimir’s function. The Y *1 { Y *2 values and the degeneracies of the hyperfine levels for the high J approximation are listed in Table 1 (14–16). Assuming the Doppler width and the quadrupole coupling constant

FIG. 4. The average line splittings of the even J values of each vibrational level.

FIG. 5. Fortrat diagram for £* R £9 Å (26 * –45 * ) R 0 9.

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FIG. 6. Fortrat diagram for £* R £9 Å (19 * –45 * ) R 1 9.

275

FIG. 8. Fortrat diagram for £* R £9 Å (16 * –42 * ) R 3 9.

DeQq f to be 0.0048 cm01 (HWHM) and 02450 MHz, respectively, we calculated the overlapping line profiles of the six components for the even and odd J values as shown in Fig. 3b. Since the spectral resolution depends on the modulation width, we calculated the line profiles by changing modulation width from 0.020–0.007 cm01 . The line splittings of 0.01470 and 0.01670 cm01 for Q(21) and Q(20), respectively, shown in Fig. 3a are close to the line profiles calculated by assuming a modulation width of 0.015 cm01 . The average line splittings of the even J values are shown in Fig. 4 and estimated to be 0.016 { 0.002 cm01 . We estimate the DeQq f value to be 2400 { 300 MHz, almost equal to that reported for the X state (17). The unperturbed line position could be determined as the center of gravity of the observed hyperfine components within the errors of wave-

length measurement. However, as the line splittings were clearly resolved in the even J transitions by comparison with those of the odd J, we sometimes omitted the unresolved odd J lines from the following least-squares analysis. The rovibrational levels of the A and X state are given by

FIG. 7. Fortrat diagram for £* R £9 Å (16 * –45 * ) R 2 9.

FIG. 9. Fortrat diagram for £* R £9 Å (22 * –31 * ) R 4 9.

E £A*J * Å T *£ / B *£ {J * (J * / 1) 0 V 2 } 0 D *£ {J * (J * / 1) 0 V 2 } 2 / H *£ {J * (J * / 1) 0 V 2 } 3

[2a] and E £X9J 9 Å G 9£ / B 9£ {J 9 (J 9 / 1)} 0 D 9£ {J 9 (J 9 / 1)} 2 / H 9£ {J 9 (J 9 / 1)} 3 ,

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[2b]

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YUKIYA, NISHIMIYA, AND SUZUKI

TABLE 2 Spectroscopic Constants of Q Branches for £* R £9 Å (26*–45*) R 09, (19*–45*) R 19, (16*–45*) R 29, (16*–42*) R 39, and (22 *–31*) R 49, in the A–X System

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TABLE 2 —Continued

277

TABLE 3 Spectroscopic Constants of the A State Calculated by a Global Least-Squares Fitting Procedure

in cm01 and 2.5s in parentheses

where the effective rotational constant B *£ splits into B *£ f and B *£e Å B *£ f / q£ owing to the V-type doubling in the A state. The Q-branch line positions are given in the power series of J(J / 1) as nQ (J) Å n 0Q / DB£ J(J / 1) 0 DD£ J 2 (J / 1) 2 / DH£ J 3 (J / 1) 3 ,

[3]

where the effective constants n 0Q , DB£ , DD£ , and DH£ are those given in terms of the spectroscopic constants of the flevel and the X state: n 0Q Å T *£ 0 G *£ 0 B *£ f 0 D *£ f 0 H *£ f á T *£ 0 G *£ 0 B *£ f , [4a] DB£ Å B *£ f 0 B 9£ / 2D *£ f / 3H *£ f á B *£ f 0 B 9£ 0 2D *£ f ,

[4b]

DD£ Å D *£ f 0 D 9£ / 3H *£ f á D *£ f 0 D 9£ ,

[4c]

and DH£ Å H *£ f 0 H 9£ .

[4d]

With the aid of the T *£ and B *£ values reported for the A state (6, 9) and G 9£ and B 9£ for the X state (18–20), we assigned the £* R £9 Å (26 * –45 * ) R 0 9, (19 * –45 * ) R 1 9, (16 * –45 * ) R 2 9, (16 * –42 * ) R 3 9, and (22 * –31 * ) R 4 9 series in the region of 11,200–12,450 cm01 . The total number of bands assigned amounted to 114 and the number of rotational lines was approximately 3700. Our line positions assigned at lower vibrational level than £* Å 34 agreed satisfactorily with those calculated using the spectroscopic constants given by Appadoo et al. (1). The line positions assigned for £* Å 35 and £* Å 36 deviated slightly from the calculated ones within the absorption linewidth. As these deviations increased greatly for high vibrational states of £* Å 37, we were forced to make the assignment using a bootstrap method. The P- and R-branch lines were not assigned because the line positions were not clear due to the hyperfine splittings and the weaker line intensities. The fortrat dia-

grams for these assignments are shown in Figs. 5, 6, 7, 8, and 9, where the rotational quantum numbers assigned are indicated by the / marks. The bands for £* £ 25 in the £9 Å 0, £* £ 18 in the £9 Å 1, £* £ 15 in the £9 Å 2, and £* £ 43 in the £9 Å 3 series could not be assigned because of the poor S/N. The bands for £* £ 16 in the £9 Å 3 and £* £ 21 in the £9 Å 4 were out of the wavenumber region TABLE 4 The Correlation Factor of the Spectroscopic Constant for £* Å 25

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FIG. 10. The relationship between T £* and the vibrational level.

investigated. The bands belonging to the higher vibrational level of £* § 46 could not be found. The weaker lines in the wavelength region shorter than the band origin £* R £9 Å 45 R 0 were difficult to assign. One may search for levels higher than £* Å 45 using a longer absorption cell. The effective constants of n 0Q , DB£ , DD£ , and DH£ in Eq. [3] were calculated using a least-squares fitting method. The centrifugal distortion constants of DL£ and higher order terms were fixed to zero since the correlation between DH£ and DL£ was 0.99. The results are listed in Table 2. The lines of the lower rotational states of J Å 10 were not included in this fitting to avoid bringing in errors from the nuclear hyperfine splitting since the high-J approximation could not be used. The DH£ term was fixed to zero in the (16 *, 17 * ) R 3 9 and (22 * –25 * ) R 4 9 series because the lines higher than J Å 60–70 were not measured. In the £* Å 45 level, the DH£ term was also fixed to zero. The rotational parameters of the A state could not be independently determined without measurement of the P- and

FIG. 11. The relationship between B £* f and the vibrational level.

FIG. 12. The relationship between D £* f and the vibrational level.

R-branch lines. We could, however, determine the constants except for the V-type doubling constant q£ from the Q-branch lines since several authors have reported the spectroscopic constants of the X state by analysis of the B–X system. The spectroscopic constants of T *£ , B *£ f , D *£ f , and H *£ f in the A state were then calculated from the rotational lines belonging to the same £* state by a least-squares fitting procedure using the Dunham expansion parameters of the X state (20). The H *£ term in the £* Å 45 bands were omitted since the standard error was greater than the H *£ value determined. The correlation factors between the spectroscopic constants for £* Å 25 are shown in Table 4 as an example. The results for the £* Å 16 to 45 levels are listed in Table 3. The standard deviations in these least-squares fittings were around 0.002 cm01 as listed in the same table. The observed and calculated line wavenumbers for all the bands studied have been placed in the Depository of Unpublished Data, and are available from the Editorial Office upon request. The differences between the wavenumbers calculated by Ap-

FIG. 13. The relationship between H £* f and the vibrational level.

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padoo et al. (1) and by this work are shown in Figs. 10 to 13. The agreement in the vibrational state of T £* is quite reasonable. The differences in the rotational constant begin to increase at vibrational states higher than 40 and at the £* Å 45 state it becomes almost 20% smaller. It is considered that the coefficients for the near dissociation expansion for B *£ f were calculated using the experimental values up to £* Å 35. The centrifugal distortion constants of D *£ f seem to deviate from the calculated ones for higher vibrational state than £* Å 45, while H *£ f deviates more rapidly around £* Å 37. 4. CONCLUSION

The A–X system of the I2 molecule was measured in the 11,200–12,450 cm01 region and the Q-branch lines belonging to the 114 bands were assigned. By use of the spectroscopic constants of the X state, T *£ , B *£ f , D *£ f , and H *£ f values in the A state of the vibrational levels of £* Å 16 * –45 * were determined. The spectroscopic constants and the line positions were compared with those calculated using the parameter determined by Appadoo et al. from the analysis of the lines observed in the 7,200–11,200 cm01 region. It was found that the differences between the results of the two methods were within the standard errors for £* Å 16–35. However, the line positions calculated using the parameter of Appadoo et al. (1) began to deviate from the observed positions as the vibrational quantum number increases from £* Å 37. High-resolution laser spectroscopy of the wide tuning range of 1250 cm01 revealed the band structures in the quite dense spectrum around 11,600–12,450 cm01 region and will give further information on the near-dissociation limit. Assignments of the P- and R-branch lines are now expected

for the analysis of the V type doubling constant and the nuclear hyperfine structure. REFERENCES 1. D. R. T. Appadoo, R. J. Le Roy, P. F. Bernath, S. Gerstenkorn, P. Luc, J. Verge`s, J. Sinzelle, J. Chevillard, and Y. D’Aignaux, J. Chem. Phys. 104(3), 903 (1996). 2. W. G. Brown, Phys. Rev. 38, 1187 (1931). 3. R. A. Ashby, Canad. J. Phys. 57, 698 (1979). 4. R. A. Ashby and C. W. Johnson, J. Mol. Spectrosc. 84, 41 (1980). 5. S. Gerstenkorn, P. Luc, and J. Verge`s, J. Phys. B. 14, L193 (1981). 6. K. S. Viswanathan, A. Sur, and J. Tellinghuisen, J. Mol. Spectrosc. 86, 393 (1981). 7. S. Gerstenkorn, P. Luc, and J. Verge`s, ‘‘Atlas du spectre d’absorption de la molecule d’iode, Vol O, 7,220–11,200 cm01 ,’’ Laboratoire Aime´ Cotton, CNRS II, Orsay, 1993. 8. X. Zheng, S. Fei, M. C. Heaven, and J. Tellinghuisen, J. Mol. Spectrosc. 149, 399 (1991). 9. T. Ishiwata, H. Takekawa, and K. Obi, J. Mol. Spectrosc. 159, 443 (1993). 10. R. Bacis, M. Broyer, S. Churassy, J. Verge`s, and J. Vigue´, J. Chem. Phys. 73(6), 2641 (1980). 11. C. M. Western, T. J. Slotterback, J. R. Johnson, D. W. Pratt, and K. C. Janda, J. Chem. Phys. 98(3), 1826 (1993). 12. F. Nez, F. Biraben, R. Felder, and Y. Millerioux, Optics Comm., 432 (1993). 13. S. Gerstenkorn, J. Verge`s, and J. Chevillard, ‘‘Atlas du spectre d’absorption de la molecule d’iode, Vol. III, 11,000–14,000 cm01 ,’’ Laboratoire Aime´ Cotton, CNRS II, Orsay, 1982. 14. H. M. Foley, Phys. Rev., 747 (1947). 15. M. Kroll and K. K. Innes, J. Mol. Spectrosc. 36, 295 (1970). 16. N. Nishimiya, T. Yukiya, and M. Suzuki, J. Mol. Spectrosc. 163, 43 (1994). 17. R. P. Hackel, L. A. Hackel, and S. Ezekiel, Phys. Rev. A, 1342 (1980). 18. P. Luc, J. Mol. Spectrosc. 80, 41 (1980). 19. J. W. Tromp and R. J. Le Roy, J. Mol. Spectrosc. 109, 352 (1985). 20. S. Gerstenkorn and P. Luc, J. Phys. 46, 867 (1985).

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