Vol. 6, No. 11/November 1989/J. Opt. Soc. Am. B 1975

Doppler-free ultraviolet excitation spectra of C 1I-X 12 inNa2 by modulated population spectroscopy

G.-Y. Yan, B. W. Sterling, T. Kalka,* and A. L. Schawlow

Department of Physics, Stanford University, Stanford, California 94305-4060

Received April 28, 1989; accepted July 12, 1989

The C II,, state of Na2 has been studied in detail by cw UV Doppler-free excitation spectra from its ground state,simplified by modulated population spectroscopy. 270 levels of e parity and 180 levels of f parity with 11 v 35and 8 S J 70 were measured with high resolution. The observations reveal that many of the e levels with 15 v S24 are perturbed. A likely candidate for the perturbing state is the (3)'1j+ state. A set of Dunham coefficients wasdeduced to fit the spectroscopic data after deperturbation and used to construct the Rydberg-Klein-Rees potentialfor the C 'lHu state. In addition, A-type doubling of the state was observed directly.

INTRODUCTION

Many molecular Rydberg states of Na2 have been exploredby laser spectroscopic techniques.'-8 Studies of the statesprovide experimental tests of theoretical calculations.9Since the ground state of Na2 has g parity and most of thetechniques that were used to study the Rydberg states in-volved two-photon processes, the explored Rydberg statesare mainly of g parity. Information about high-lying unger-ade states is still lacking. However, UV emission, terminat-ing on the ground state, originates only in ungerade states inthis system because of selection rules. Detailed study ofungerade Rydberg states is therefore an attractive and prac-tical subject.

One of the ungerade states, the C I,, state, was studiedrecently by laser fluorescence spectroscopy techniques. 7"10

The studies corrected the previous vibrational assignmentsand provided constants for the state, which were deducedfrom spectroscopic data of its lower vibrational levels. Foreach of the vibrational levels, only a few rotational levelswere observed, owing to the lack of a tunable narrow-bandUV laser. In this paper we report the first observation toour knowledge of UV Doppler-free excitation spectra of theC 1lIu-X 'Zg system. A slightly modified Coherent 699-29ring dye laser with an intracavity frequency-doubling crys-tal, operating in AutoScan mode, provided coherent UVradiation. Modulated population spectroscopy was used tosimplify the excitation spectra."1 Population of a lowerlevel (v", J") of the X 12' state was modulated by a seconddye laser tuned to a known strong visible transition A Z'(v',J')-X (v", J"). Signals of excitation transitions, origi-nating in the modulated level of X 'g(v", J"), were extract-ed when the ring laser scanned.

Each of rotational levels in the C 'lHu state has two compo-nents that are due to the A-type doubling. One with theparity of (-1)J is called the e level; the other with the parityof -(-I)J is the f level.'2 For the X Z+ state, a rotationallevel has the parity of (-I)J. A transition occurs only be-tween two rotational levels with different parities, i.e., -+ or + - -. Thus Q branches (AJ = 0) excite moleculesinto levels off parity only in the C lIIu-X 1 system, where-as P and R branches (J = 1) populate levels of the e

parity. In our experiment, 270 levels of e parity and 180levels off parity with 11 v < 35 and 8 < J < 70 in the C 'Hustate were measured with an accuracy of 0.03 cm-'. Ener-gies of the levels ranged from 31 100 to 33 300 cm-'. A-typedoubling in the C 'Hu state has been observed directly. Apefis positive. For vibrational states with 15 v 24, mostrotational levels of e parity were perturbed drastically. Themost likely candidate for the perturbing state is the (3)1'u+state. In addition, it was also observed that some levels of fparity and their adjacent levels of e parity were both per-turbed slightly over the observed regime. This could becaused by perturbations due to other states. After deper-turbation, a set of Dunham coefficients was deduced andused to construct a rotationless potential for the C 'llu state.

EXPERIMENT

The experimental setup is shown schematically in Fig. 1. ACoherent 699-29 ring dye laser ran with Kiton Red dye andan intracavity frequency doubler (LiIO3, Coherent Option7500-01). It provided cw UV radiation. The nominal band-width of UV output was 1 MHz rms. Originally, a specialoutput coupler with high reflectivity was installed, insteadof the normal one, to maximize the second-harmonic genera-tion. Also, the original beam splitter was replaced by aspecial one designed to reflect enough light into the refer-ence cavity of the dye laser. The laser output power in thevisible was several milliwatts. This was not strong enoughfor use of the built-in wavemeter. In addition, the extreme-ly strong beam inside the cavity saturated two detectorsseverely. These detectors monitor reflected light from thebirefringent plate and the thin talon. Signals from thedetectors are fed into the interface of the 699-29 computercontroller as error signals for AutoScan operation. Thus theuse of intracavity frequency doubling prevented the ringlaser from working in AutoScan mode. We replaced thespecial output coupler mirror by one with slightly lowerreflectivity (R 98% near 640 nm) and used the originalbeam splitter to increase the visible output to several tens ofmilliwatts. To avoid saturation of the two detectors, twopolarization sheets were placed in front of them as attenua-

0740-3224/89/111975-04$02.00 © 1989 Optical Society of America

Yan et al.

1976 J. Opt. Soc. Am. B/Vol. 6, No. 11/November 1989

(599.21) -~ - AOM --dye laser ,. ' ,: :-_

beam 1(visible)

monilor (6~~~~~~ ~~~~99.29)beam 2 (UV) dye laser------- intracavity

doubled

photodiode beam 3

block v (visible)

1b-o :::k in e: x.- mzr ::

Fig. 1. Schematic diagram of experimental setup. AOM, acousto-optic modulator; PMT, photomultiplier tube.

E

I--,

0-

D

4- 0 0 Original Mirror

O 0 Replaced Mirror

0

2

100 Se 00

0 i i i I i 316 318 320 322

Wavelength (nm)

Fig. 2. Comparison of tuning curves of intracavity frequency-dou-bling dye laser with different output coupler mirrors.

tors. Orientations of the polarizers were adjusted such thattwo detectors provided nominal peak-to-peak signals of 4-6V. After the minor modifications, the dye laser with theintracavity frequency doubler worked in 699-29 AutoScanmode, except that each scan was performed over an intervalnot greater than 2 cm-', beyond which UV output droppedsignificantly because of phase-matching-angle walk-off.Figure 2 shows a portion of the UV tuning curve for oursystem. The open circles in the figure represent the curvebefore the modifications. Although UV power was lowered,the modifications provided many conveniences in tuningand measuring frequencies as well as recording signals.Lowering the transmission of the output coupler could in-crease the UV output. With 2% transmission, the leakage ofvisible radiation was 40-60 mW over the tuning region. Afew tens of milliwatts of visible output is, however, enoughfor both the wavemeter and the reference cavity. We didnot attempt to optimize the system because of the lack ofavailable mirrors.

For lower-level population modulation, a Coherent 599-21dye laser operated with Rhodamine B. Typical output pow-er of the laser was near 80 mW. It was tuned to excitetransitions A 12+(v', J')-X 1'g (v", J"), according to calcula-tions with previous constants for the two states.'3 Visible

fluorescence was directed into a 0.75-m grating spectrometerand recorded with a Hamamatsu R1333 photomultipliertube and a photon-counting system. The fluorescence spec-tra were used to determine the excitation transitions unam-biguously. The spectral resolution of the spectrometer was-0.02 nm. The 599-21 dye laser was then tuned to thecenter of the excitation transition by maximizing nonreson-ance fluorescence easily within 0.005 cm-'. The visiblebeam and the UV beam counterpropagated through a crossoven, which contained Na and operated at 400-450oC withAr buffer gas at a pressure of 1 Torr. The visible beam waschopped by an acousto-optic modulator (Intra-ActionAOM-50) at 100 kHz. When the UV beam was tuned toexcite Na molecules into levels (v, J) of the C 'lII state fromthe depopulated lower levels X 1'g (v", J"), modulated UVfluorescence originating in the levels of C lII(v, J) waspicked up by a 1P28 photomultiplier and a lock-in ampifierat the chopping frequency. A spatial filter and a MellesGriot UG-11 UV filter were placed in front of the photomul-tiplier to reject visible light and scattered UV light. UVfluorescence, following two-photon or two-step transitionsof visible photons from the depopulated levels, had an oppo-site phase with respect to that of the signals and appeared tobe a constant background. It did not influence our observa-tions at all.

Although modulated population spectroscopy simplifiedthe excitation spectra, some satellite lines from J" ± 2, J" ±4 survived to be observed. Some of the satellite lines weremuch stronger than their parent lines, which were perturbedand weakened. For those lines, observations were per-formed twice with P-branch and R-branch excitations orexcitations from lower levels of different vibrational states.When the ring laser scanned, the UV excitation spectra andfluorescence spectra of I2 were displayed simultaneously ona monitor. The built-in wavemeter could then be checkedat any time against the I2 spectra. This ensured that theaccuracy of measuring fundamental frequencies was lessthan 0.006 cm-'. Uncertainty of measured energies of levelswas safely estimated to be 0.03 cm-', including drift of the599-21 laser and uncertainty in determining energies of thelower levels.

ANALYSIS AND DISCUSSION

270 e-parity levels and 180 f-parity levels of the C ll,, statewere measured. Vibrational and rotational quantum num-bers of the observed levels ranged from 11 to 35 and 8 to 70,respectively. The energies of the levels are located between31 100 and 33 300 cm-'. Figure 3 shows deviations betweenmeasured and calculated values, using Verma's constants,10

versus v for both e levels and f levels with certain rotationalquantum numbers. For the f levels of J = 50, the deviationsincrease monotonically and smoothly with v up to 5.5 cm-iexcept for v = 12. This increase indicates that the constantsshould be refined to fit the higher vibrational levels. For thee levels of J = 49 or J = 51, the deviations also climbmonotonically as v increases. But deviations for some vvalues jump up or down by 1 cm-' or even more. The elevels are more or less perturbed. We then measured rota-tional levels systematically with 8 < J S 70 for each of thevibrational states with 14 < v < 24. Figure 4 illustrates thedeviations of e levels and f levels versus J(J + 1) - 1 for v =

Yan et al.

,):e.5Z4-

Vol. 6, No. 11/November 1989/J. Opt. Soc. Am. B 1977

5 .0S *~~~~~~~~~~4 *J=50 g

3 *-

2

0-0~~~~~~

1 0*

210 12 14 1 6 18 20 22 24 26 28 30 32 34 31

v Value(a)

60 0

5 800 J=49 80J= 51 8

3 8

2

0~~~~0 0oo8o°O

10

2 I | I l l l I l l10 12 14 16 18 20 22 24 26 28 30 32 34 36

v Value

(b)

Fig. 3. Deviations between measured and calculated energies ofvibrational-rotational levels with certain J values versus v for (a) flevels of J = 50, (b) e levels of J = 49 and J = 51.

17. Obviously, only levels of e parity near J = 49 are per-turbed strongly. This is consistent with Fig. 3. The devi-ations versus J(J + 1) - 1 for v = 15 are shown in Fig. 5..Two crossing points appear near J = 39 and J = 62. As for v= 17, the levels of f parity near the crossing points are notperturbed. This fact indicates that the perturbations comefrom a 12 state. Figures 4 and 5 also show A-type doublingdirectly.

The C 'flu state could be perturbed by several states overthe energy regime. Matrix elements of perturbations areproportional to [J(J + 1)11/2 for the heterogeneous perturba-tions. Coefficients of [J(J + 1)]1/2 in the perturbation ma-trix element, ranging from 0.007 to 0.027 cm-' for the vibra-tional states of 15 < v < 24, were obtained after deperturba-tion. Rotational constants of the perturbing states are lessthan those of the C II. state at corresponding crossingpoints by roughly 0.02 cm-'. For some crossing points,extra lines were observed. They were used to confirm thedeperturbations and the rotational constants of the perturb-ing states deduced from the deperturbations. Most likelythe perturbations are mainly caused by the (3)1'+ state.

In addition to perturbations of e levels only, perturbationsof bothf levels and e levels were observed for some vibration-al states. These perturbations were very weak: shifts ofperturbed levels were measured to be a few tenths of a wavenumber. We did not deperturb these data, because the

measurement was insufficiently accurate to permit us to dothis. These points were dropped in later fittings.

After deperturbation, 190 e levels and 170 f levels wereseparately used for least-squares fittings to deduce the Dun-ham coefficients. All the data that we measured had vvalues above 10. The dangers of fitting based only on dataat high v values are well known. Fortunately, some Ar-ionlaser and Kr-ion laser lines have been matched with 18transitions of the C flI-X 1'g system, involving 18 levels ofthe C lII, state with 0 • v < 8 and 12 < J < 124.7 Half ofthese levels are of e parity, and the rest are of f parity.These were added to our measured data for the fittings.Although the laser lines are not exactly at the frequencies ofthe transitions, deviations were not crucial for the fittingsbecause many of the data used were measured with highaccuracy. The fittings were satisfactory, i.e., reproductionsof the measured levels were within the measurement uncer-tainty. Only deviations for a few levels involved with thetransitions of laser lines are -0.2 cm-', even though estimat-ed standard deviations for both fittings were less than theuncertainty of measurement, 0.03 cm-'. Dunham coeffi-cients for the C III, state are tabulated in Table 1. AVef ispositive. This illustrates that the main interactions are withthe low-lying (2)'Z+ state, although the perturbations ob-served may be caused by the (3)12+ state, which lies above

0.8

0.4-

0

0

cm

0.0

-0.4-

-0.8

-1.2-

-1.60 1000 2000 3000 4000

J(J+ 1)-iFig. 4. Deviations between measured and calculated energies ofvibrational-rotational levels for C fl1u with v = 17 versus J(J + 1) -1.

1 .2

0.8

E

0

0U,

cm

0.4-

0.0*

-0.4+

-0.8-

-1.210 1000 2000 3000 4000 5000

J(J+1)-iFig. 5. Deviations between measured and calculated energies ofvibrational-rotational levels for C fl1u with v = 15 versus J(J + 1) -1.

0

0000 00

cV 040 000 o* ***.**** *.0

00

e level* f level

0

0

e level

* f level 0

000 0

. MSDCP o0 ° ° o 0 oe 0 **** * *

00

I I I l0

Yan etal.

1978 J. Opt. Soc. Am. B/Vol. 6, No. 11/November 1989

Table 1. Dunham Coefficients for the C 'II, Statea

Yio = 1.165936E2 (2.7e - 2) Y02 = -5.070452E - 7 (5.3e - 9)Y20 = -6.694904E - 1 (3.8e -3) Y12 = 2.0695175E - 9 (2.2e - 10)Y30 = 9.9059784E - 4 (2.4e - 5)Y40 = 1.3201365E -4 (7.Oe - 6) Y03 = 3.1720898E - 12 (2.2e - 13)Y50 = -1.796947E -6 (7.6e -8)

Yo = 1.1672307E - 1 (3.5e - 5) AqO = 1.6869E - 4Y1,, = -9.525076E - 4 (6.4e - 6) Aq, = -0.266744E - 4Y2, = 4.1082414E - 6 (4.7e - 7) Aq2 = 1.4443339E - 6Y3 = 3.6991288E - 8 (1.le - 8) Aq3 = -2.2602288E - 8

T = 29621.66 (6.7e - 2). Yi, is for e levels only, other coefficients are taken as mean values of e levels an

3.40

3.35

E 3.30

° 3.25

3.20 \3.15

3.10U)o 3.05

3.00

2.952.5 3.0 3.5 4.0 4.5 5.0

Nuclear Separation (,Fig. 6. Rotationless potential for the C

Table 2. Rotationless Potential for th

R (A) Te (cm-') R (A)

2.60 33285.41 4.202.80 31686.24 4.403.00 30604.68 4.603.20 29969.08 4.803.40 29677.14 5.003.545 29621.66 5.203.60 29628.57 5.403.80 29758.86 5.604.00 29979.12 5.80

the C 'II, state. A Rydberg-Klein-Rees rC 1lI, state constructed with the Dunhanshown in Fig. 6 and tabulated in Table 2.

The (3)12;' state has not yet been observeexperiment or in IR Fourier-transform specing two-photon transitions.5 The internuchthe state at equilibrium is -4.2 A. It is difiNa molecule into the state directly from the

,q= Yi,(e)- Yl(f);d f levels.

ed levels of the ground state in our system. But informationabout the state can be obtained from the C 'lu-X '4g tran-sitions indirectly, if the C Hlu state is mainly perturbed bythe state. Research investigating this possibility is current-ly in progress.

ACKNOWLEDGMENTS

We are grateful to Bruce Peuse of Coherent, Inc., for provid-ing the replaced output coupler mirror. This research wassupported in part by the National Science Foundation undergrant NSF PHY-86-04441 and in part by the U.S. Office ofNaval Research under contract ONR N00014-87-K-0265.

B. W. Sterling is an Office of Naval Research predoctoralfellow.

* Permanent address, Rafael, Armament DevelopmentAuthority, Azmon, Israel.

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2. S. Martin, J. Chevaleyre, S. Valignat, J. P. Perrot, M. Broyer, B.5.5 6.0 6.5 Cabaud, and A. Hoareau, Chem. Phys. Lett. 87,235-239 (1982).

3. Li Li, R. W. Field, and Qingshi Zhu, in Advances in LaserScience-II, Proceedings of the Second International Laser

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30277.90 can, Can. J. Phys. 62, 1543-1562 (1984).30614.41 6. G. Delacretaz and L. W6ste, Chem. Phys. Lett. 120, 342-34830974.02 (1985).31342.74 7. C. Effantin, J. d'Incan, A. J. Ross, R. F. Barrow, and J. Verges, J.31716.55 Phys. B 17, 1515-1523 (1984).32091.00 8. P. Niay, P. Bernage, and H. Bocquet, J. Mol. Spectrosc. 128,32465.84 502-508 (1988).32836.26 9. G. H. Jeung, J. Phys. B 16, 4289-4297 (1983); Phys. Rev. A 35,33198.69 26-35 (1987).10. K. K. Verma, T. H. Vu, and W. C. Stwalley, J. Mol. Spectrosc.

91, 325-347 (1982).11. M. E. Kaminsky, R. T. Hawkins, F. V. Kowalski, and A. L.

Potential for the Schawlow, Phys. Rev. Lett. 36, 671-673 (1976).12. R. N. Zare, Angular Momentum (Wiley Interscience, New York,

a coefficients is . .. 1988), p. 308; J. M. Brown, J. T. Hougen, K.-P. Huber, J. W. C.

Johns, I. Kopp, H. Lefebvre-Brion, A. J. Merer, D. A. Ramsay, J.d directly in our Rostas, and R. N. Zare, J. Mol. Spectrosc. 55, 500-503 (1975).troscopy follow- 13. M. M. Hessel, Laser Molecular Physics Section, National Bu-

reau of Standards, Gaithersburg, Maryland 20899 (personalear separation of communication, 1976). The coefficients were tabulated on pp.ficult to excite a 21-22 of M. E. Kaminsky's Ph.D. dissertation, Ginzton Labora-=rmally populat- tory Rep. No.2531 (Stanford University, Stanford, Calif., 1976).

Yan et al.