two-photon excitation cross section of the b ? x(0,0) band of co measured by direct absorption

1988 J. Opt. Soc. Am. B/Vol. 16, No. 11 /November 1999 M. D. Di Rosa and R. L. Farrow

Two-photon excitation cross section of theB — X(0,0) band of CO

measured by direct absorption

Michael D. Di Rosa and Roger L. Farrow

Combustion Research Facility, Sandia National Laboratories, M.S. 9055, P.O. Box 969,Livermore, California 94551-0969

Received April 26, 1999

We report new measurements of the two-photon absorption rate in the B X(0, 0) band of CO, as determinedfrom absorption spectra obtained with Fourier-transform-limited pulses of well-characterized spatial profile.By comparing measured absorption spectra of the CO Q branch near 230 nm with a nonlinear model for thepulse attenuation, we derive the spectrally integrated cross section s0

(2) . The space- and time-dependentmodel considers two-photon absorption followed by one-photon photoionization of the excited state. TheQ-branch spectral profile is simulated with previously measured coefficients of collisional broadening and shift.Remarkably, for modest irradiances of 80–350 MW/cm2 at the focus, attenuations of 10% and greater at theQ-branch peak were observed in a single pass through neat CO at pressures of 12–33 kPa. Our result for thespectrally integrated cross section, averaged over five experiments, is s0

(2) 5 (1.5 1 0.7/20.2) 3 10235 cm4.© 1999 Optical Society of America [S0740-3224(99)01511-8]

OCIS codes: 300.6390, 300.6410, 300.6420, 300.6540, 300.1030.

1. INTRODUCTIONRecently developed optical methods for the sensitive de-tection of CO use two-photon excitation to populate theupper electronic states, avoiding the need for excitationwavelengths in the vacuum ultraviolet. As diagrammedin Fig. 1, CO can be detected through the visible-wavelength fluorescence excited by two-photon absorptionin the B X band.1 Two 230-nm photons promote tran-sitions within B X(0, 0), and detection of the laser-induced fluorescence (LIF) proceeds by collection of theblue-to-green fluorescence in the angstrom bands (B→ A). Alternatively, in the method of resonance-enhanced multiphoton ionization, CO can be detected bythe ions (or electrons) that are produced by absorption ofa third photon at 230 nm in a photoionization step thatconnects CO–B(v 5 0) to an energy 2.15 eV above theionization potential. Both two-photon LIF and 2 1 1resonance-enhanced multiphoton ionization are appliedextensively to the point-specific detection of CO inflames.2–8 In either method, absolute cross sections fortwo-photon absorption and photoionization are essentialfor relating signals to molecular concentrations.

Recently9 we measured the cross section for photoion-ization of CO–B(v 5 0), in agreement with Looneyet al.,10 whereas previous estimates had ranged over 3 or-ders of magnitude.10–12 The two reported rate coeffi-cients (a, defined Section 2) for two-photon excitation ofthe B X(0, 0) band are similarly separated. Througha rate-equation analysis of LIF and resonance-enhancedmultiphoton ionization signals obtained at low pressure(7 Pa), Bergstrom et al.12 determined that a 5 13 10227 cm4/W at the peak of the two-photon Q branch.Tiee et al.13 found that absorption at the Q-branch peakcould be observed readily at modest pressures (2–13 kPa)

0740-3224/99/111988-07$15.00 ©

in transmission measurements and determined a signifi-cantly smaller rate coefficient of a 5 1 3 10230 cm4/W.The disparity cannot be explained by the different pres-sure regimes of the measurements. However, the mea-surement of nonlinear rate coefficients such as a requiresa full temporal and spatial characterization of the excita-tion source, which is often a difficult task and can be aprime source of uncertainty.

Here we report new measurements of the two-photonexcitation spectrum of the B X(0, 0) band of CO, whichwe performed in the manner of Tiee et al.13 by recordingthe single-pass absorption of laser pulses, tuned near 230nm, through a cell containing CO. By using nearlytransform-limited pulses and recording images of spatialprofiles, we greatly minimized the usual ambiguities incharacterizing the excitation light. From measured spec-tra of a, we derived the spectrally integrated cross sections0

(2) that is intrinsic to the two-photon B X(0, 0) band.

2. FORMULATIONFollowing the treatment of Saxon and Eichler,14 we writefor the two-photon absorption rate W @s21#

W 5 s~2 !~ I !2, (1)

where s (2) [cm4 s] is a two-photon rate coefficient and I[cm2 s21] is the photon flux density, related to the irradi-ance I [W/cm2] by

I 5 I/\vc , (2)

where vc [s21] is the center radial frequency of the laserfrequency distribution. The alternative form of the ratecoefficient of a [cm4/W],

1999 Optical Society of America

M. D. Di Rosa and R. L. Farrow Vol. 16, No. 11 /November 1999 /J. Opt. Soc. Am. B 1989

a 5 s~2 !/\vc , (3)

arises from the equivalent definition of W through

W 5 aI2/\vc . (4)

The spectrally integrated two-photon cross section, s0(2)

[cm4], is related to s (2) by

s~2 !~2vc! 5 s~2 !~Vc! 5 s0~2 !G ~2 ! (

J9

FJ9 (J8

SJ8J9~2 !

3 E2`

`

fJ8J9~j 2 VJ8J9!g8~j 2 Vc!dj, (5)

where J8 and J9 index, respectively, the rotational levelin the upper and the lower states, FJ9 is the (Boltzmann)fraction of molecules in state J9, SJ8J9

(2) is the two-photonrotational line strength for the transition J8 J9 of(two-photon) frequency VJ8J9 , and fJ8J9 [s] is the transi-tion line-shape function. Functions SJ8J9

(2) and fJ8J9 arenormalized so that

(J8

SJ8J9~2 !

5 1, (6)

E2`

1`

f~V!dV 5 1. (7)

The integral in Eq. (5) takes into account a finite spectralwidth of excitation through the function g8(V) [s], whichis related to the spectral distribution g(v) of the laserpulse through the convolution

g8~V! 5 E2`

1`

g~j!g~V 2 j!dj, (8)

with g(v) subject to

E2`

1`

g~v!dv 5 1. (9)

Photon statistics of the excitation pulse, through thesecond-order intensity correlation factor15 G (2) of Eq. (5),also influence the two-photon rate coefficient. G (2),

Fig. 1. Energy diagram with process relevant to CO detectionthrough two-photon excitation of B X.

which is often a source of uncertainty because of unresolv-able temporal fluctuations in the excitation pulse, equals1 for the transform-limited pulses used here.

At the rate of W [Eq. (1) and Fig. 1], two photons areabsorbed by the resonant transition and a third photonwill photoionize the upper state, depending on how effec-tively the photoionization rate (Ri of Fig. 1) competeswith rates of relaxation mechanisms. The differentialloss of I/cm along the propagation coordinate z, under theassumption of weak excitation, is then

~] I/]z !loss 5 2ns~2 !~ I !2S 2 1s iI

s iI 1 QD , (10)

where n [cm23] is the (assumed constant) number densityof the ground state, s i [cm2] is the cross section of photo-ionization, and Q [s21] is the sum of radiative (AB→A1 AB→X) and collisional (Qelec) relaxation rates of theupper state. We assume that the radial (r) and the tem-poral (t) variations of I at any axial location are given byGaussian distributions according to

I~r, z, t ! 5 ~4 ln 2/p!3/2

3~E/\v!exp$24 ln 2@~r/D !2 1 ~t/t!2#%

tD2 ,

(11)

where E [ E(z) is the local pulse energy, t is the FWHMduration of the pulse, and D [ D(z) is the local beam di-ameter (FWHM). We compute the axial variation of Dassuming Gaussian-beam propagation,

D~z ! 5 D0@1 1 ~z/zR!2#1/2, (12)

with the Rayleigh range zR determined from

zR 5 ~p/2 ln 2 !@D02/l#, (13)

where D0 is the FWHM diameter of the focused beam.Consistent with Eq. (12), the origin of the z axis is locatedat the beam focus.

The assumption of Gaussian functions persisting withbeam propagation for the spatial and temporal profiles isan approximation in view of the nonlinear (quadratic) de-pendence of the absorption rate on the irradiance [Eq.(4)]. Over the spatial and temporal extent of a pulse, thenonuniform absorption rate is greatest within the coreand acts to broaden the spatial and temporal distribu-tions progressively as the beam propagates. For the caseof 10% net absorption, a level that was typically achievedin our experiments, we determined through separate cal-culations that the assumption of Gaussian-beam propaga-tion underestimates the t and D of the transmitted beamby 6% and underpredicts s0

(2) by 5%. Given other, muchlarger uncertainties in the experiment, this error is ac-ceptably small.

Spatial and temporal integration over (] I/]z)loss of Eq.(10) yields the differential loss of energy

dE/dz 5 E2`

1`E0

`

~] I/]z !loss2prdrdt, (14)

where cylindrical symmetry is assumed. On substitutionof Eqs. (11)–(13), Eq. (14) expands to


dE/dz 5 2ns~2 !I2EH 3 2 R 1 R2~2p!21/2

3 E0

`

ln F1 12A2

Rexp~2T2!GdTJ , (15)

where

T 5 ~4 ln 2 !1/2~t/t!, (16)

I2 is the average photon flux:

I2 5 ~2 ln 2/p!3/2E/\vc

tD2 , (17)

and R is a ratio of the rates of relaxation to photoioniza-tion according to

R 5Q

s iI2

. (18)

We note that I2 , when it is squared, provides the squaredaverage photon flux

~ I2!2 5 F ~1/E !E2`

1`E0

`

~ I !22prdrdtG2

,

which may be used in place of I2 in Eq. (1) for calculatingan average excitation rate. Useful analytic expressionsfor E(z) are readily derived in limits of zero photoioniza-tion [R → `; Eq. (18)] and zero quenching (R 5 0),which reduce Eq. (15) to

dE/dz 5 2H 2 R → `

3 R 5 0 J @ns~2 !I2#E. (19)

For a beam focused at the center (z 5 0) of an absorptionpath of length 2L, Eq. (19) becomes

1/Et 2 1/Ei 5 H 2 R → `

3 R 5 0 J @ns~2 !/\vc#

3 ~tD02!21~2 ln2/p!3/22zR tan21~2L/2zR!,

(20)where Et and Ei are the transmitted and incident ener-gies, respectively. Beam absorption by a two-photon pro-cess therefore occurs mainly over 2zR , the confocal pa-rameter of the beam.

Absorption spectra are simulated through numericalintegration of Eq. (15), incorporating Eqs. (5)–(13) and(16)–(18). The rotational line strengths SJ8J9

(2) are deter-mined from Chen and Yeung16 for the case of linear po-larization and with their ratio F/E set to 23. That ratiois based on the polarization ratio s ll /scc 5 300 measuredby Tjossem and Smyth17 for the two-photon transitions ofCO B X. Essentially, SJ8J9

(2)5 1 for the Q-branch

(J8 5 J9) transitions considered here, designated Q(J9).Zero-pressure line positions VJ8J9 are obtained forQ(0) –Q(14) from the measurements of Drabbels et al.18

The remaining VJ8J9 are calculated through availablespectroscopic constants.18–20 At pressure P [atm], a tran-sition is shifted by d 3 P and homogeneously broadened(in FWHM) by 2g 3 P. For the case here of self-collisions, coefficients d and 2g are assigned the

J9-independent values 20.21 and 0.74 cm21 atm21, re-spectively, as provided by preliminary analyses of mea-surements that we intend to report elsewhere. The tran-sition line shape ( fJ8J9) is obtained through a Voigtprofile21 that combines the Doppler broadening, collision-induced broadening, and collision-induced shift of thetransition. We also take into account a minor ac Starkshift and broadening of the transition owed to the photo-ionization process. The former is proportional to I by thecross section ss 5 7 3 10218 cm2 (Ref. 9); the latter in-creases the homogeneous width by s iI (FWHM). We sets i 5 1 3 10217 cm2 (Ref. 9) and Q 5 (1/tB) 1 (kP),where, for CO-B(v 5 0), tB 5 21 ns is the radiativelifetime22,23 and k 5 6.0 3 109 s21 atm21 is the rate coef-ficient for quenching by CO.1,2,12,24 We obtain the pa-rameters t, D0 , and the FWHM of g(v) of the excitationpulse from independent measurements, leaving s0

(2) asthe only variable of Eq. (15).

3. EXPERIMENTAs depicted schematically by Fig. 2, the experiments re-corded the absorption of pulsed light, tunable over thetwo-photon Q branch of CO B X(0, 0) at 230 nm, thatpassed 14.8 cm through a static cell. The cell was cappedwith fused-silica windows and filled with CO of 99.99%purity to pressures of 50–250 Torr (7–33 kPa). The UVexcitation pulses were nearly transform limited in band-width and were generated as follows: Continuous-wave,single-frequency light at ;690 nm from a tunable ringdye laser was pulse amplified through a three-stagepulsed-dye amplifier (PDA) that was pumped at 20 Hz bythe second harmonic of an injection-seeded Nd:YAG laser.Pulses from the PDA were then frequency tripled throughtwo b-barium borate crystals to provide the 230-nm light.Portions of the continuous-wave light were sent to awavemeter (not shown) to assist with nominal tuning andto a temperature-stabilized, confocal etalon [of 750-MHzfree spectral range (FSR)] backed by a photodiode to pro-vide a register of relative laser frequency while the spec-tra were recorded. The temporal evolution of the excita-tion pulse, recorded with a detector of 1-GHz bandwidth,appeared structureless and smooth, reflecting the gener-ally Gaussian shape of the injection-seeded pulse thatwas pumping the PDA. A fit of the recorded pulse shapeto a Gaussian function yielded t 5 6.9 ns for the FWHM.The spectral width of the UV excitation pulse was 120MHz, as determined in a previous study.9

Approaching the cell, the excitation light passedthrough a spatial filter consisting of a 50-mm pinhole atthe focus of an f 5 10 cm lens followed by an f 5 20 cmrecollimating lens. The beam then passed through avariable attenuator consisting of a half-wave (l/2) platebefore a MgF2 Rochon polarizer, from which the verticalpolarization was selected. Energies were adjustablefrom 0 to 200 mJ/pulse, and the beam was focused at thecenter of cell with an f 5 100 cm lens. Both before andafter the cell a portion of the beam was reflected (s plane)off a fused-silica wedge and focused ( f 5 10 cm) onto apyroelectric detector, providing signals Si and St thatwere proportional to the incident (Ei) and the transmit-ted (Et) pulse energies, respectively.


Fig. 2. Configuration for measuring single-pass, two-photon absorption spectra. Signals Si and St are proportional to the incident (Ei)and the transmitted (Et) pulse energies, respectively.

With the cell evacuated, the ratio St /Si varied lessthan 1% over the full range (25–200 mJ/pulse) of incidentenergy and had negligible (,0.5%) modulation with laserfrequency from etaloning of cell windows. Signal Si wasconverted to Ei through measurements of the averagepower of the incident beam and the known pulse repeti-tion rate of 20 Hz. Beam parameter D0 was evaluatedfrom spatially calibrated, 53-magnified images of the fo-cused waist recorded by a CCD camera. Although theywere nearly round, the images were fitted to a surface ofelliptical cross section as composed by the multiplicationof two orthogonal Gaussian functions. With correlationcoefficients (r2) of >0.99, the fits provided FWHM widthswa and wb along the major and minor axes, respectively.Beam ellipticity, defined as wa /wb , was 1.08 or less.Beam diameter D0 was determined from (wa 3 wb)0.5

and was typically 80 mm. As based on D0 5 80 mm, acalculated confocal parameter of 2zR 5 13 cm [Eq. (13)],and measured absorptions of typically 10%, the 15-cmpath of the cell was sufficient to yield 60% of the maxi-mum absorption attainable with a cell of infinite length[by Eq. (20)].

4. ANALYSISAs suggested by Eq. (20), we recorded beam absorption bythe relation of (1/Et 2 1/Ei) for its proportionality to s (2)

and for its immunity from fluctuations in Ei to the extentthat photoionization contributes a consistent or consis-tently small fraction of the net absorption. A measuredspectrum (crosses) that covers rotational linesQ(0) –Q(15) of CO B X(0, 0) is shown at the top ofFig. 3 with a vertical scale of (1/Et 2 1/Ei), here calledthe reciprocal difference. On the horizontal scale of two-photon frequency, data were acquired every 0.003 cm21 as10-shot averages of (1/St 2 1/Si) } (1/Et 2 1/Ei), where

(1/St 2 1/Si) was measured for each shot. The cell con-ditions were 130 Torr (17 kPa) of CO at 294 K, D0 equals68 mm, and Ei varied smoothly with frequency about anaverage of 83 mJ/pulse by 615%. The peak of the spec-trum corresponds to 13% absorption. Photoionization ac-counts for 25% of the total absorption (short of the maxi-mum possible contribution of 33%), as estimated from Q,

Fig. 3. Measured two-photon absorption spectra, displayed bythe reciprocal difference 1/Et 2 1/Ei as proportional to s (2) (seetext). Conditions were 294 K and 130 Torr (17 kPa) CO, withexcitation pulses of ;80 mJ/pulse and 6.9-ns width focused to 68mm. Top, comparison of the data (crosses) with the best-fitsimulation (solid curve), produced for s0

(2) 5 1.0 3 10235 cm4.Bottom, residual of the fit.


D0 , the average Ei , and a photoionization irradiance av-eraged over the I2 distribution of the excited-state popu-lation.

Numerical integration of Eq. (15) over the length of thecell produced the simulated spectra (solid curve) also seenat the top of Fig. 3. With all other parameters of Eq. (15)assigned, only the integrated cross section s0

(2) was variedin a least-squares fit of the simulation to the data. Themeasured spectrum was shifted horizontally for best fitwith the simulation, which served as the frequency refer-ence. A small baseline adjustment of the measured spec-trum of less than 1% of the peak signal was also permit-ted. In the simulation, the measured variation of Ei withfrequency was represented by a smoothly varying func-tion, and g8(V) [Eq. (8)] was represented by a Gaussiandistribution with a 170-MHz FWHM. Compared withthe transition widths, which have at minimum a FWHMDoppler width of 6 GHz, the laser was essentially mono-chromatic. For the data of Fig. 3 we obtained a best-fitcross section of s0

(2) 5 1.0 3 10235 cm4. The residual dif-ference between the data and simulation appears at thebottom of Fig. 3. Whereas it is not ideally flat about zero,the structure of the residual is particularly minor consid-ering that the simulation was varied in magnitude only.The simple Voigt-profile construction of the simulationthus appears to describe the measured spectrum ad-equately.

Table 1 summarizes the results of five trials performedon separate days, where for each trial the alignment of la-sers and optics, and the resultant D0 , were separately es-tablished. For each trial, the measured D0 and the rangeof pressure (P) and Ei used are listed. Whereas we couldreadily generate a collinear green beam from B → Astimulated emission,12,25 these conditions were avoidedwhen spectra were recorded. For each trial, typicallyfour to five spectra were recorded. Each spectrum of atrial was acquired for a different combination of P and Ei

and was reduced to s0(2) . The rightmost column of Table

1 gives the trial-averaged cross section. The error ofroughly 625% in the measurement includes calibrationuncertainties in establishing Ei and D0 and a (usuallysmall) component that arises from uncertainties in theabsorption baseline.

To investigate systematic errors in the determinationof s0

(2) , we varied D0 from 64 to 99 mm, Ei from 25 to 135

Table 1. Conditions and Measured Two-PhotonCross Sections of Five Separate Trials, Including

Final (Trial-Averaged) Cross Section

D0(mm)

P(kPa)

Ei

(mJ/pulse)Ipeak

(MW/cm2)a

s0(2)

(310235 cm4)

64 7–27 50 150 1.5 6 0.468 7–17 25–135 65–350 1.0 6 0.369 13 50–95 130–240 1.4 6 0.486 8–16 35–85 57–140 1.7 6 0.499 13–33 40–100 49–120 1.8 6 0.5

Cross section 1.5 1 0.7/20.2b

a Calculated from (4 ln 2/p)3/2E/tD02.

b See text for explanation of range.

mJ/pulse, and P from 7 to 33 kPa. We found that the fiveresultant cross sections overlap within experimental un-certainties, lending confidence in the model and the ex-perimental approach. The mean is 1.5 3 10235 cm4, witha standard deviation of 0.2 3 10235 cm4. A source of sys-tematic error, however, might still rest with the assump-tion of diffraction-limited propagation [Eq. (12)]. Mea-surements of the beam profile at either end of the cellshowed that the averaged entrance and exit diametersmay have exceeded that calculated through D0 and Eq.(12) by as much as 20%. This greater divergence of theactual beam from D0 we describe through a zR decreasedby roughly 20%, which by Eq. (20) signifies a shorter in-teraction length of two-photon absorption and an increasein s0

(2) by ;15% in compensation to recover the measuredabsorption. Our measured s0

(2) might then underesti-mate the true cross section by 15%, to which we add thepreviously mentioned 5% error incurred for use of a pre-scribed envelope of propagation. We allow that the crosssection could exceed the greatest trial-measured value byas much as 20% and report s0

(2) 5 1.5 1 0.7/20.23 10235 cm4, which also appears in the last row ofTable 1.

5. DISCUSSION AND CONCLUSIONFor comparison with our measurement of s0

(2) 5 1.53 10235 cm4 we convert the conflicting rate constants ofthe two earlier studies12,13 to the basis of G (2)s0

(2) .Through Eqs. (3) and (5), and by their stated experimen-tal conditions, the rate constant a 5 1 3 10227 cm4/W ofBergstrom et al.12 translates to G (2)s0

(2) ' 5 3 10234

cm4. The a 5 1 3 10230 cm4/W reported by Tiee et al.,13

which is smaller by 3 orders of magnitude, leads to a simi-larly smaller G (2)s0

(2) ' 5 3 10237 cm4. The second-order coherence factor of G (2), although it is unknown foreither case, we may reasonably confine to 2–3 (Refs. 26and 27) for the combinations of dye-laser and harmonicgeneration that were used to generate the 230-nm light.Because of this uncertainty in G (2), and also in the re-ported a, we emphasize that the derived cross sections areestimates to effect an order-of-magnitude comparison.We then find that our measurement of s0

(2) 5 1.53 10235 cm4 presents an intermediate value, beingroughly a factor of 100 greater than the result of Tieeet al. and a factor of 10 smaller than the result of Berg-strom et al.

With allowance for their (unstated) uncertainty, weconsider our measurement to be in reasonable agreementwith the result of Bergstrom et al.12 The rather largedisagreement with Tiee et al.13 is surprising, as their ratecoefficient was obtained from absorption measurements,as in our experiment. Unfortunately, Tiee et al. did notdescribe the analysis of their absorption data, nor didthey provide experimental details sufficient for a separateanalysis. Using Eq. (15), we reproduced the absorptionmeasurements of their Fig. 4, obtained for CO pressuresof 0.7–13 kPa and a cell 35 cm long. Their laser pulses,focused into the cell by an f 5 50-cm lens, were stated tohave an energy of 500 mJ and a duration of 4 ns FWHM.The spectral width of the laser and, more critically, the


focused spot size were unspecified. From fitting the LIFexcitation spectrum of their Fig. 3, we determined aGaussian spectral width of 1.4 cm21 FWHM for the laser(taking into account Doppler, collisional, and ionizationbroadening). We assumed that the focused waist (D0)might reasonably have been 50 to 600 mm FWHM. Overthis range in D0 the result was a range of cross sectionsG (2)s0

(2) of 0.041–1.5 3 10235 cm4, with the largest crosssection corresponding to the largest waist. Our measure-ment would then agree with that of Tiee et al. if D0' 600 mm could be supposed.

In Fig. 4 we plot curves of the peak excitation rates (2)/G (2) of the B X(0, 0) band versus laser spectralwidth (FWHM Gaussian) for several CO pressures from 0to 1 atm. These curves were calculated through Eq. (5)for a temperature of 295 K and with s0

(2) 5 1.53 10235 cm4. Both Doppler and collision-induced broad-ening (for the case of self-collisions) were includedthrough the Voigt profiles used for fJ8J9 . As expected,

Fig. 4. Variation of the peak two-photon rate coefficient of COB X(0, 0) with pressure and laser spectral width (FWHMGaussian) at 295 K. Curves are generated from Eq. (5) withs0

(2) 5 1.5 3 10235 cm4 and with Doppler and collision broaden-ing (CO environment) taken into account.

Fig. 5. Variation of peak two-photon rate coefficient of CO B← X(0, 0) with temperature and laser spectral width (FWHMGaussian) at 1 atm. Curves are generated from Eq. (5) withs0

(2) 5 1.5 3 10235 cm4 and with Doppler and collision broaden-ing (N2 environment) taken into account.

the peak excitation rate decreases as the excitation spec-trum broadens from increasing pressure and laser spec-tral width. Figure 5 gives curves of peak s (2)/G (2) versuslaser spectral width for a fixed pressure of 1 atm and sev-eral temperatures relevant to the detection of CO inflames. The curves are calculated similarly to those inFig. 4, except that the collision broadening is based on theCO dilute in N2, the relation for which we intend to reportelsewhere. Average excitation rates (W) can be calcu-lated from the s (2)/G (2) of Figs. 4 and 5 by use of known orassumed beam parameters [of G (2), E, t, and D] in the ex-pression

W 5 @s~2 !/G ~2 !#G ~2 !~ I2!2,

where I2 is given by Eq. (17).For all but low-pressure applications, quantitative ap-

plication of two-photon excitation of CO B X will addi-tionally require knowledge of collision-broadening coeffi-cients, collision-induced shift coefficients, and collider-specific quenching rates over a wide range oftemperatures. Experiments on the collision broadeningand shift of CO B X(0, 0) lines are in progress in ourlaboratory.

ACKNOWLEDGMENTSThis study was supported by the U.S. Department of En-ergy, Office of Basic Energy Sciences, Division of Chemi-cal Sciences. The authors are grateful to Paul Schraderfor his expert technical assistance.

R. L. Farrow’s e-mail address is [email protected].

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two-photon excitation cross section of the b ? x(0,0) band of co measured by direct absorption

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