Reactive collision dynamics by far wing laser

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study of chemically reactive molecular collisions in an at- tempt to elicit ... K + HgBr2 + wL ---+KBr + HgBr* and .... structure. The collisional redistribution profile of Fig. 3 (a) was obtained from the spectrally and temporally integrated emission on ...
Reactive collision dynamics by far wing laser scattering: Mg+H2 P. D. Kleiber, A. M. Lyyra, K. M. Sando, V. Zafiropulos, and W. C. Stwalley Citation: J. Chem. Phys. 85, 5493 (1986); doi: 10.1063/1.451560 View online: http://dx.doi.org/10.1063/1.451560 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v85/i10 Published by the American Institute of Physics.

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Reactive collision dynamics by far wing laser scattering: Mg + H2 P. D. KleiberB) Department 0/ Physics and Astronomy, University 0/ Iowa, Iowa City, Iowa 52242-1294 A. M. Lyyra,a) K. M. Sando, V. Zafiropulos,a) and W. C. Stwalley8).b) Department o/Chemistry, University 0/ Iowa, Iowa City, Iowa 52242-1294

(Received 12 June 1986; accepted 11 August 1986) We have measured the far wing absorption profiles ofthe MgH 2 collision system leading to both the nonreactive formation of Mg· and into two distinct final rotational states of the reaction product MgH (v" = 0, J" = 6, 23). We have observed qualitatively expected behavior including a pronounced red wing in the reactive absorption profile indicating strong reaction probability on the excited attractive potential surfaces. We have also observed novel aspects of the excited state dynamics including reactive vs nonreactive channel competition effects and a strong far blue wing reactive absorption suggesting significant reaction probability even for trajectories on the repulsive surfaces. We have developed a simple theoretical model to semiquantitatively explain our experimental results. This model uses standard quasistatic theory to estimate the absorption probability as a function of detuning between levels of MgH2 and with assumed nonreactive vs reactive branching ratios, accounts for the subsequent evolution on the excited potential surfaces. This theory correctly predicts the overall shapes of the profiles and in general gives reasonable predictions for the relative magnitudes of the wing intensities.

I. INTRODUCTION

A. Atom-atom collisions

The study of the profiles of pressure broadened atomic spectral lines has a long and interesting history. 1-12 In large measure this interest has resulted from the fact that spectral line shapes yield important information concerning the underlying atom-atom collisional interactions. From the early work of HoItzmark, 1 Jablonski, 2 Condon, 4 and others, it is well established that the far wing absorption profiles of pressure broadened transitions are quite sensitive to the detailed shape of the intermolecular potential curves formed in the collision. In particular, in the Born-Oppenheimer, FranckCondon limit an absorption event is considered to occur at a fixed internuclear separation between states of the "quasimolecule." In the far line wing, i.e., for lal ~ 'Tc- I where a = ({U L - (Uo ) is the frequency shift or detuning of the radiation from the asymptotic atomic resonance and 'Tc is roughly the duration of a "hard" collision, the quasistatic absorption profile is related to the probability of finding a particular atom-perturber pair at a fixed internuclear separation (Ro) such that the quasimolecular potential curves are shifted into resonance with the probe radiation field. The result of this very simple model gives the frequency dependent absorption probability k(a) as

k(a)o:41rR~e-V.(Ro)/kT

[dV(R)] , dR Ro

(1)

where V(R) = Ve (R) - Vg (R) is the excited state-ground state difference potential, Ro is the Condon point of absorption [where V(Ro) = fza] and the exponential term gives a ground state Boltzmann factor. Here Ve (R) and Vg (R) are a) b)

Also Iowa Laser Facility. Also Department of Physics and Astronomy.

the collisional energy shifts from the excited and ground atomic states, respectively, and each vanishes as R-oo. In the mid-1970's, Gallagher and co_workers,10-12 in an important series of papers, showed how these basic ideas could be used to obtain accurate maps of the quasimolecular potential curves by carefully inverting the temperature dependent absorption or emission line wing profiles of collision broadened lines. These techniques are most useful for isolated lines and binary atom-atom collisions. More recently Cooper, Burnett, and co-workers, \3-16 extending the experiments of Carlsten, Szoke, and Raymer,17 have shown how final Zeeman state specific measurements of the far wing absorption profiles not only are sensitive to the form of the potential curves at the point of absorption, but also yield important information concerning the dynamical evolution of the collision from the point of absorption to a particular final asymptotic channel. Theoretical modeling by Julienne and Mies 18.19 of the experimental results of Alford et al. 16 on alkaline earth-rare gas collision systems has clearly demonstrated the sensitivity and importance of these techniques. It should also be noted, however, that while these experimental results can be used for such rigorous and accurate tests of semiclassical or quantum dynamical calculations using model potential curves, relatively simple theoretical arguments based on an intuitive molecular reorientation model 20 also give very reasonable and appealing agreement with the experiments. B. Molecular collisions

Gallagher has extended these far wing line profile techniques to the case of nonreactive atom-molecule collisions (Na + N 2 ), though with somewhat limited success. 21 In these situations, it is no longer generally possible to invert

J. Chem. Phys. 85 (10).15 November 1986 0021-9606/86/225493-12$02.10

@ 1986 American Institute of Physics

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Kleiber et al. : Far wing laser scattering

the line profile data to obtain the potential surfaces since there will usually be many points on the surface (corresponding to different internuclear separations and orientations) which will contribute to the signal at a given detuning. Nevertheless, as pointed out by Gallagher, the wing profile data yields stringent tests of model potential surfaces, and can give useful qualitative information about the nature of the collisional interaction. 21 Polanyi has suggested applying similar techniques to the study of chemically reactive molecular collisions in an attempt to elicit information concerning the short lived reaction complex or "transition state. ,,22 Following these suggestions, Arrowsmith et al. have obtained far wing "emission profile" measurements from the chemiluminescent reaction N a2 + F --+ (Na 2F) t --+ NaF + Na * under molecular beam conditions. 23 The far wings ofNa atomic "D" line emission give information which is sensitive to the exit channel surfaces of the (Na-NaF) complex. Those results allow qualitative interpretation of the pronounced red wing as due to classical satellite emission [a minimum in the difference potential ofEq. (1)] between the excited and ground states of the (Na 2F) intermediate. Brooks and co-workers have also performed laser absorption experiments in the "reaction complex" for the reactions 24 K + HgBr2 +

w

L

---+KBr + HgBr*

and K + NaCI +

w L ---+Na* +

KCI.

In each case, quantitative theoretical modeling has been difficult primarily because of extreme signal-to-noise limitations in these molecular beam experiments. In a recent paper we have presented preliminary results of our experiments on far wing laser absorption into the MgH2 collision complex. 25 The process may be written symbolically as (see also Fig. 1)

Mg(3 ISo) + H 2---+(MgH 2 ), ( MgH 2) + W L ---+ (MgH2 ) *

(2a) (2b)

followed by (MgH 2) *---+Mg* (3

Ipn

+ H2

(2c)

(MgH 2 )*---+MgH(u",J") +H.

(2d)

or

Note that the ground state reaction ofMg and H2 to form the corresponding hydride is substantially endoergic ( - 25 000 cm - I) and is therefore unfavorable in the absence of laser pumping. If, however, a laser is coupled into the transient (MgH2) complex, the system can be pumped to an excited potential surface of the quasimolecule where subsequent chemical reaction is highly probable. 26 In our previous discussion 25 we presented the far wing absorption profiles leading to both the nonreactive channel [Mg*(3 Ipn formation] and into a specific vibrationalrotational final state MgH (u" = 0, J" = 23) of the reactive channel. In this paper we will expand upon those measurements including results from a different rotational state of the MgH product which might be expected to demonstrate markedly different behavior. We will also discuss qualitatively the implications of these results for our understanding of the dynamics of this excited state reactive collision and will present a semiquantitative comparison of these experimental results with a very simple theoretical model based on approximate potential curves and a classical model of the collision dynamics. We believe the experimental data are sufficiently precise to allow very sensitive and detailed tests of more accurate semiclassical or quantum theoretical calculations based on complete ab initio potential surfaces and we hope this paper will stimulate work in that direction. The MgH2 system offers a number of advantages for these studies: Its "small size" makes theoretical modeling tractable, indeed ab initio potential surface calculations have

LlF ( 520nm)

COLLISIONAL FLUORESCENCE ( 285 nm )

FIG. I. Representation of the MgH2 reactive collision energetics as a function of reaction coordinate. The dashed curves in the "transition region" allow qualitative indication of a possible reaction pathway and are taken from Ref. 28.

1

Mg ( 3 So) + H2 H

Mg +

I H

H

H

Mg~1

H

/ Mg

Mg

"

REACTION COORDINATE

H

H

+

"

H

J. Chem. Phys., Vol. 85, No.1 0, 15 November 1986 Downloaded 17 Jan 2013 to 155.247.53.178. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

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Kleiber et al. : Far wing laser scattering

been performed, and the kinetics of the excited state reaction Mg*(3 IP~)

+ Hr-+-MgH + H

EXPERIMENTAL ARRANGEMENT

(3)

have already been extensively studied in a beautiful series of "state-to-state" experiments by Breckenridge and Umemoto. 26.27 In particular, Breckenridge and Umemoto find that the reaction is entrance channel controlled occurring with very large (i.e., essentially gas kinetic) cross sections. Early theoretical work by Jordan and co-workers,28 and more recently by Chaquin et al. 29 has given some insight into the nature of this excited state reaction; it has been argued that the process occurs preferentially through C 2v geometry via the strongly attractive 1 IB2 level of (MgH 2)*. Such a result would suggest a strong broad red.wing in the reactive collision absorption profile and a relatively weaker blue wing. These qualitative predictions will be discussed below in Sec. V. Furthermore, Breckenridge and Umemoto have observed a nonstatistical bimodal rotational popUlation distribution in the MgH product and have proposed an interesting intuitive picture of its origin.27 They suggest that the dominant high rotation component is primarily due to side-on attack ofthe Mg* (3 I P ~ ) onto the H2 bond via the I B2level, while the weaker low rotation component contains a significant fraction of end-on attack geometry. If these arguments are correct, these preferred geometries can be used to greatly simplify the theoretical modeling for our experiment by limiting the required orientational averaging. These arguments also yield different quantitative predictions for the reactive absorption profiles leading to either high rotational product states or low rotational product states. II. EXPERIMENTAL ARRANGEMENT

The experimental setup, based on a standard pumpprobe technique, is shown in Fig. 2. A frequency-doubled and -tripled 30 Hz Nd:Y AG laser [Quanta Ray DCR2A30 (3) ] is used to simultaneously pump two pulsed dye lasers (Quanta Ray PDL-IE). The pump dye laser is operated with a mix of Rhodamine 590 and Rhodamine 610 laser dyes in an oscillator-amplifier arrangement. The tunable output near 570 nm is frequency doubled in an angle-tuned KD*P crystal to the region near 285 nm. Typical energies of the ultraviolet pulses are - 200 ItJ in a 5 ns pulse. The laser is linearly polarized ( - 85% ) and has a spectral bandwidth of -0.03 nm. The probe dye laser is operated with Coumarin 500 laser dye in the A-X band region ofMgH near 506 nm. The typical output energy is 500ltJ in a 5 ns pulse and the laser spectral bandwidth is -0.03 nm. The beam intensities in the interaction region can be estimated to be - I MWI cm2 for the pump and -10 MWIcm 2 for the probe laser. The probe pulse is optically delayed by 7 ns from the pump laser pulse and the two beams are softly focused with a 50 cm quartz lens to overlap at the oven center. As discussed in the Appendix, this probe delay is short enough to minimize the effects of secondary collision processes leading to the formation of MgH, as well as rotational relaxation of the MgH product.27 The oven is a five-armed stainless-steel cross allowing spectral observation perpendicular to the laser axis and si-

FIG. 2. Block diagram of the experimental arrangement.

multaneous temperature measurement with a stainless-steel encased thermocouple inserted directly into the oven. A slight depression in the oven center was filled with magnesium metal (99.95%) and the oven was heated to -700 K as indicated by the thermocouple. Due to temperature gradients between the heated arms of the oven and the Mg reservoir at the oven center, vapor pressure curve estimates of the density using the thermocouple temperature are too high. We have measured the Mg atom density directly using a Rayleigh scattering technique described in Ref. 30 and discussed in detail in the Appendix. These measurements yield typical Mg densities in our experiment of [Mg] = 1 X 1013Icm 3 ± 50%. The oven was filled with a hydrogen buffer gas at a typical pressure of 4 Torr as determined by a Wallace Tieman gauge. The probe laser was tuned in the MgH X 2l: + A 2n(0,0) band to the RI (23) transition at 506.5 nm or to the R I (6) transition at 516.1 nm. We could then detect the relative population of either the (v" = 0, J" = 23) level or the (v" = 0, J" = 6) level of MgH formed in the collision process. Note that the probe-laser intensity was easily sufficient to saturate the transition. These levels were chosen somewhat arbitrarily although the particular choice of a high rotation and low rotation product stems from the dynamical arguments concerning their possible correlation with different entrance channel orientations discussed above. The spectral output of the oven was collected with a two lens optical system and focused onto the slit of a McPherson 0.35 m scanning monochromator equipped with a 1200 lineslmm holographic grating. The f number of the detection system was limited by the oven geometry to f 18. The monochromator was calibrated for absolute wavelength using a quartz-Fe hollow cathode lamp. The monochromator

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Kleiber et a/. : Far wing laser scattering

could be used to detect either the Mg·(3 IP~-3 ISO) resonance emission at 285.2 nm or the P(25) or P( 8) LIF lines from theA 2n_x2~+ (0,0) band of MgH. The light signal was detected with an electrically cooled S-20 (EM! 9659QB) photomultiplier tube. The detector signal was then fed directly into a boxcar averager-gated integrator system (Stanford Research Systems model SRS 250) operated in the active base line subtraction mode. The output was averaged over -1500 laser pulses, amplified electronically, and displayed on a chart recorder. The pump-laser intensity was monitored with an energy detector and the far wing profiles were normalized to constant incident energy. III. EXPERIMENTAL RESULTS

The major results of this work are given in Fig. 3. The far wing profiles show the relative populations in (a) the

NON REACTIV[ ABSORPTION PROFILE

NON REAC TlVE ABSORPTION PROFI LE

[Mg"]

00..-

Mg· (3 IP~) level (absorption into the nonreactive channel), (b) the MgH (v" = 0, J" = 23) level, and (c) the MgH (v" = 0, J" = 6) level (corresponding to absorption into final state-specific reactive channels) as a function of pump laser detuning from the Mg resonance line (a = UJ L - UJ o ). In Fig. 3 the absorption profiles have been multiplied by a factor a2 to expand the scale and enhance the structure. The collisional redistribution profile of Fig. 3 (a) was obtained from the spectrally and temporally integrated emission on the Mg· resonance line while the reactive collision profiles of Figs. 3 (b) and 3 (c) are obtained from the integrated probe laser induced fluorescence (LIF) signal. Also shown in Fig. 3 are the results (solid lines) of a simple semiquantitative theoretical model described in Sec. IV. For each case the solid error bars allow an estimate of the random uncertainties and give the standard deviation from the mean ofa large number of runs (typically N=15-

[Mg")

RED WING

o~_

I

-",

-,..,

"r

"~

0.1 L----...I_L..l....J....J...LL!...l-_-'---'--.L-"-...L.LUJ -10 -100 -1000

BLUE WING

I

0.1

1000

10

6Icm")

(b) [MgH I v", O.

J", 23))

FIG. 3. Experimental far wing laser absorption profiles (points) for the MgH2 reactive collision system. (a) Mg(3 'P~ - 3 'So) collisional fluorescence signal; (b) MgH (v" = 0, J" = 23) laser induced fluorescence probe signal; and (c) MgH (v" = 0, J" - 6) laser induced fluorescence probe signal as a function of laser detuning [1:1 = (w L - w o )] from the Mg atomic resonance transition. The profiles have each been multiplied by a factor 1:1 2• See the text for details. Also shown are the theoretical model results (lines).

REACTIVE ABSORPTION PROFI LE

REACTIVE ABSORPTION PROFILE

[ MgH I v", 0, J", 23)) BLUE WING

RED WING

"'

>

J:

J:

'" :::;;;'"

:::;;;

~

~

0.1

-100

-10

6

-1000

10

1000

(em")

FIG. 5. Relative branching ratio for the reactive [MgH (UN = 0,1" = 23) 1 and nonreactive [MgH* (3 IP~)] exit channels as a function of laser detuning.

FIG. 6. Bluewinglred wing asymmetry for the [MgH (UN = 0,1" = 23) 1 reactive absorption profile.

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Kleiber et al. : Far wing laser scattering

RED WING

~

I

'" '"

~

~

~

~

0.1

-100 t; (em-')

-10

-1000

FIG. 7. Relative branching ratio for the low rotational [MgH (v' = 0, J' = 6) I and high rotation [MgH (v' = 0, J' = 23) I reaction product. The dashed line assumes no correlation between product rotational distribution and excitation wavelength. The solid curve assumes that product rotation is determined entirely by entrance channel geometry, the low rotation state correlated with C ~, geometry and the high rotation state with C2 , geometry.

with C2v geometry and the low rotational product state with C co v geometry. The dashed theoretical curve in Fig. 7 is the expected result for the case where the rotational product distribution is completely uncorrelated with the entrance channel excitation process. This limit is chosen to agree with the resonance excitation result of Breckenridge and U memoto. 26 These two limiting models clearly bracket our experimental results and while it is not possible at present to differentiate between these two extreme cases given the inadequacies of the theoretical models, the results certainly suggest some correlation between final rotational product state distribution and entrance channel geometry. We hope future work aimed at improving the experimental precision and extending the detuning limits will shed additional light on these questions. VI. CONCLUSIONS

We have measured the far wing absorption profiles of the MgH2 collision system leading to both the nonreactive formation of Mg· and into two distinct final rotational states of the reaction product MgH (v" = 0, J" = 6, 23). We have observed qualitatively expected behavior including a pronounced red wing in the reactive absorption profile indicating strong reaction probability on the excited attractive potential surfaces. We have also observed novel aspects of the excited state dynamics including reactive vs nonreactive channel competition effects and a strong far blue wing reactive absorption suggesting significant reaction probability even for trajectories on the repulsive surfaces. We have developed a simple theoretical model to semiquantitatively explain our experimental results. This model uses standard quasistatic theory to estimate the absorption probability as a function of detuning between levels of MgH 2 • A very simple dynamical model, with assumed non-

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reactive vs reactive branching ratios accounts for the subsequent evolution on the excited potential surfaces. Our potential curve data is taken from the work of Chaquin et al. 29 and is limited to fixed geometries in the symmetric orientations; these limitations allow only rough comparisons between theory and experiment. This theory correctly predicts the overall shapes of the profiles and in general gives reasonable predictions for the relative magnitudes of the wing intensities. We conclude that the ab initio potential curves of Chaquin et al. 29 are probably reasonably accurate over the range of this experiment tl. :s 500 cm -1 (R ~ 3.2 A). The most significant discrepancies between theoretical and experimental results may be due to a poor long range form of the theoretical potentials, or to our simplistic dynamical model. We believe our data is sufficiently precise to allow for quantitative comparisons with a more sophisticated theoretical model and hope this work stimulates interest in that direction. ACKNOWLEDGMENTS

We wish to gratefully acknowledge helpful discussions with W. H. Breckenridge. This work was supported in part by the National Science Foundation under Grant No. CHE 83-13352 and in part by the Petroleum Research Fund under Grant No. PRF 15244G. APPENDIX: TECHNICAL EXPERIMENTAL DETAILS Density measurements/system calibration

We have used a light scattering calibration technique described in Ref. 30 to obtain an absolute calibration of our detection system efficiency allowing accurate measurements of the absolute magnesium density and rough estimates of the absolute product densities. These measurements will be important in estimating possible systematic errors and background effects. The observed nonresonant Rayleigh Scattering signal (S) from a rare gas of density N is

S = (}N(ki:ro )IL , where kL is the wave number of the laser, Yo is the nonresonant polarizability of the gas, IL is the laser flux (photons/ cm 2 s -1), and () is a constant describing the detection system efficiency (including geometrical factors, transmission functions, detector efficiencies, etc.). () relates the scattering intensity (in photons/cm3 pulse) to a particular signal (in Coulombs) on the gated integrator storage capacitor. Since the Rayleigh scattering signal S can be measured at a known rare gas pressure, and the quantities kL> Yo' and IL are known or can be measured, an accurate determination of the detection system efficiency () can be made for a given experimental arrangement. For our case the minimum detectable signal corresponds to (S) min ~ 1 X 104 (scattered photons/ cc pulse). Assuming the LIF probe transition is saturated and for reasonable fluorescence branching ratios, this minimum signal corresponds to a detection limit of roughly [MgH (v", J")]-3XIOS/ccpulse for the product state density. The near resonant Rayleigh scattering signal from Mg atomic vapor of density No is given approximately by

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5502

Kleiber et al. : Far wing laser scattering

So

= eNo [(dcik1 )/h 2C4 ] (l/A2)IL'

where do is the dipole moment for the resonance transition and we have assumed the laser detuning A is large compared to the atomic linewidth such that the Rayleigh signal can be easily resolved from the atomic fluorescence. By comparing the scattering signals from a known pressure of rare gas in a cold oven, to that obtained at a fixed detuning from the Mg atomic resonance transition in a heated oven, the density (No) of Mg can be accurately determined: No = N(So/S) (foA 2/dci)h 2C4 • This technique leads to a measured Mg density in our experiment of [Mg] = 1 X 1013Icc ± 50%. The absolute reaction product state density can also be roughly determined using these techniques. Obviously the result will depend on experimental conditions and particularly on laser detuning. To be specific in the following discussion, we will assume typical operating conditions (T = 700 K, [Mg] = 1 X 1013Icc, [H 2 ] = 4 Torr) and arbitrarily choose a particular detuning A = - 47 cm - I (red). In this case the reaction product state density can be determined from the measured LlF signal for our calibrated detection system, by assuming the probe transition is saturated, and by using the Honl-London factors for the transition of interest to estimate the branching ratio for the fluorescence step. Thus the product densities become [for A= -47cm- 1 (red)] [MgH (v"

= O,J" = 23)] ~ 6X 106/cm3 pulse

and [MgH (v" = O,J" = 6)]

~4X

106/cm3 pulse.

Due to experimental difficulties (e.g., estimating pumpprobe beam overlap) and because we have neglected excited state collisional quenching, this result should be regarded as a rough lower limit on the actual product state density. To determine the total product density, we require the final state branching ratios at this detuning. Assuming the measured final state energy disposal results of Breckenridge and Umemoto (Fig. 7 of Ref. 27) hold for this off-resonant excitation, we can roughly determine a lower limit for the total reaction product (summed over final rotational and vibrational states) as [MgH] ~ 3X lOs/cm 3 pulse for this example. Discussion of systematic uncertainties

Radiative trapping Under these conditions of Mg density, the line center Mg* resonance emission is radiatively trapped. It has been demonstrated by Carlsten, Szoke, and Raymer 17 that the effect of radiative trapping of this collisional fluorescence is to lower the overall signal level by allowing increased collisional quenching of the upper state and diffusion of the excited atoms out of the detection region during the long radiative lifetime, without significantly modifying the absorption profile. We have verified these results by checking that the nonreactive collisional fluorescence profile shapes [Fig. 3 (a) ] are independent of Mg density and H2 pressure under our operating conditions to within our uncertainties. The LIF measurements of the reactive absorption are not affected by radiative trapping.

Radiative trapping effects make an absolute measurement of the Mg* density somewhat uncertain. However, it is important to note that a significant fraction of the resonance fluorescence is emitted during the laser pulse and is therefore ac Stark shifted outside the resonance absorption linewidth; this alleviates somewhat the radiative trapping problem and hence its effect on the overall signal level is mitigated. Under typical operating conditions and again at a laser detuning of A = - 47 cm- I (red) the Mg* density is thus roughly estimated as [Mg*] -1 X lOs/cm3 pulse.

TherlnalequiHbriulnconcentraUons The reaction of ground state Mg( 3 ISO) with H2 to form MgH is substantially endoergic. The thermodynamic equilibrium concentration of MgH under the conditions of this experiment can be estimated34 at [MgHlthermal _10 5 / cm 3. This concentration is, of course, spread over a large number of rotational levels at - 700 K. The largest thermal density corresponds to the state v" = O,J" = 9, the most probable J value. The expected popUlation of this level is [MgH (v" =0, J" =9)]thermal _104/cm 3 which lies well below our minimum detection limits. Therefore, no equilibrium MgH should be detected in our state specific LlF measurements and this was verified experimentally.

Alnplified spontaneous elnission A possible source of systematic error in these measurements could be amplified spontaneous emission (ASE) from the UV pump laser contributing to the observed line profiles; this contribution would be particularly important at large laser detunings if significant ASE overlapped the transition resonance. We have measured the laser wing ASE background level of the near-UV pump laser to be < 10- 7 of the peak laser signal at ± 5 nm detuning. The optical depth at line center in this experiment is _10+ 3 • Thus it is clear that no ASE at the Mg-resonance line will reach the interaction region at the oven center. We have also verified that the observed signals from both Mg* and MgH vanish if the oscillator cavity of the pump laser is spoiled.

NonHnearprocesses We have previously observed and studied a series of very interesting nonlinear processes occurring in near resonantly pumped alkaline earth vapors 35- 37 leading to strong photoionization, self-focusing, parametric amplification, and stimulated atomic emission under some conditions. It is, of course, imperative to ensure here that any such possible nonlinear phenomena do not influence our line shape results. The lowest order nonlinear processes of concern in this experiment are multiphoton ionization and self-focusing effects. The near resonant two photon ionization rate can be estimated using Refs. 38 and 39 to be Y2PI ~ 104 S - I under typical operating conditions in this experiment (lL -lMW/cm 2) and for A-20 cm- I . This rate drops rapidly (- 1/A2) for larger detunings and hence any possible systematic effects due to laser nonlinearities should be most significant near line center. For our laser pulse

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Kleiber et al. : Far wing laser scattering

[MgH] vS IL

.-J

~

.-J W

a::

• 0.1

FIG. 8. Linearity of reaction product with pump laser power.

Secondary collision processes We believe the largest source of systematic uncertainty in these experiments results from the two collision process

(1'p - 5 X 10- 9 s), and [Mg] -1 X 1013 /cm3, the ion density can then be estimated as [Mg+]-[Mg]y2Pl1'p

-5X lOs/cm 3 pulse. Assuming an effective two body recombination rate40 a - 10- \0 cm3/s, subsequent excited state reaction will be much too slow to lead to significant formation of MgH product during the short pump-probe delay time. Also under the conditions reported in this experiment, we have observed no evidence of self-focusing or any other nonlinear beam propagation effect which might influence our results. However, for detunings a $ 10 cm - I, magnesium densities [Mg] ~ 10 14/cm3, or laser powers I L ~ 5MW/ cm 2, we can observe the onset of self-focusing, parametric mixing, and other nonlinear processes. These effects obviously limit the range of our experimental parameters. The processes of interest in Eq. (2) should be linear in pump laser power; this is experimentally demonstrated in Fig. 8 for typical operating conditions over the range oflaser intensities from 0.3-5 MW Icm 2 • These checks were carefully repeated at each data point to ensure linearity.

Mg + H2 + fwJ L -Mg·

+ H2

followed by Mg·

+ H 2-MgH + H.

An upper limit on the rate for this excited state reaction can be obtained using the measured total quenching cross section u Q = 31 A2 of Breckenridge and Umemoto. 26 Thus the rate of secondary collisions Y2c = NH2 vUQ $ 4.8 X 107 S-I for our typical operating conditions. For an effective pumpprobe delay time 46 teff -4 ns, the probability ofa secondary collision is P2c - Y2c teff $ 0.19. Again this should be regarded as a rough upper limit. As an example we use the approximate Mg· density at a = - 47 cm -I (red) to roughly estimate the total MgH density due to secondary collisions under typical operating conditions: [MgH]2c -Y2cteff [Mg·] $ 2X 107 / cm3 pulse. This upper limit value should be compared to the lower limit for [MgH]

Mg-Mg collisions and dlmer absorption Our typical operating densities [Mg] -1 X 1013Icc are sufficiently low to eliminate effects due to both diatomic magnesium (Mg2) absorption and Mg-Mg resonance collisions. In particular we can estimate34 the thermal equilibrium dimer fraction at 700 K as [Mg 2]1[Mg] - (10- 9 ) corresponding to a dimer density [Mg 2] - 105/ cm3 under our typical operating conditions. This value is much too small to significantly contribute to our measurements. The Mg-Mg resonance collision broadening rate can be estimated41 from YMg-Mg = kf~e2 No/2m where k is a constant of order unity (k = 1.532 for this case),42 fo = 1.84 is the known oscillator strength for the Mg resonance transition,43 and No is the atomic magnesium density. This results in the value YMg-Mg =9 X 106 s - I for the resonance collision rate.

[ Mg H ] vs [ Mg ] .-J

~ .-J W

a:

• I~--~~~~~~~--~~~~~~

10'2

10'3

10'4

[Mg](Cm 3 )

FIG. 9. Linearity of reaction product with magnesium density.

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Kleiber et al. : Far wing laser scattering

5504

I

~ 100 [ MgH] vs [ H2 ] ...J

6=-47cm- 1


Z



~

10

...J W 0::

FIG. 10. Linearity of reaction product with hydrogen pressure.

under the same conditions [MgH) ~ 3X lOs/cm 3 pulse. For this example, the total contribution due to these secondary collision processes should be S 0.07. The process of interest in this experiment should be linear in H2 buffer gas pressure while the two collision process discussed above is quadratic in H2 pressure. In Fig. 10 we show the results of an H2 pressure linearity test at 1 I::J.. = - 47 cm- (red) and under otherwise typical conditions. The LIF signal is linear in H2 pressure over the range 1-10 Torr. The possible systematic contributions in the measured MgH signal discussed in this section are shown by the dashed error bars in Figs. 3 (b) and 3 (c). They are most significant at small detunings where the relative [Mg·) density is largest and become negligible compared to the statistical uncertainties at larger detunings.

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J. Chem. Phys., Vol. 85, No.1 0, 15 November 1986 Downloaded 17 Jan 2013 to 155.247.53.178. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions