J.C.S. Faraday I, 1980,76, 30-42Construction of a Kinetic Model for the Iodine CHJPhotodissociation LaserCalculation of Cross-sections and comparison with ExperimentBY ANGEL COSTELA, JUAN M. FIGUERA, MARGARITA MART~N, JUAN M. PBREZInstituto de Quimica Fisica " Rocasolano ",C.S.T.C., Serrano 119, Madrid-6, Spain.AND LUIS VALLEReceived 20th November, 1978The known dependence of the reactivity of the methyl radical formed in CH31 photolysis uponirradiation wavelength has been explicitly introduced in an attempt to derive a kinetic model of theCH31 laser. The model was used to derive the cross-section for stimulated emission, u3+4 =5.6 x lo-'' cm2, in accordance with other reported values. Furthermore, the model gives a quantita-tive estimate of the final product concentrations, the effect of sulphur hexafluoride, the time-dependentbehaviour of the laser and the gain.These are all in reasonable agreement with previously deter-mined experimental results.Since the first reported laser emission in the flash photolysis of CH31 and CF31,'a variety of iodides have been shown to yield population inversion and laser action.However, only a few have the characteristics suitable for high energy operation (e.g.,for nuclear fusion investigation). From the photochemist's point of view two of thedesired features are: high yield of excited iodine atoms, I(2P4), shown in this workas I*, producing proportionally high population inversions (AN) and slow quenchingof these excited atoms. These characteristics have been studied for a variety ofsystems [e.g., ref.(2)]. With this background, attempts to construct kinetic modelsthat would pruvide additional information about the laser operation and quenchinghave been numerous. For example, a kinetic model has been proposed to interpretI2 formation in the flash photolysis of CH31 ; this suggests that the reaction,is of considerable importance.stress the role of quenching ofI* by the initially formed radicals. The high decomposition yields found undercertain conditions have been ascribed to pyrolysis.6* The rapid thermal equilibra-tion implied by this mechanism is explained by vibrational energy transfer from thehot radicals to the substrate. However, our preliminary report * on wavelengtheffects and repetitive operatiun of the CH31 laser introduces new observations thatthe reported models cannot explain.In particular, the pyrolysis hypothesis is toocrude ; a better approximation is required which takes into account the influence onsubsequent kinetic events, of the amount and type of energy (i.e., vibrational,translational, etc.) initially imparted to the photofragments. In this paper anattempt is made to develop an improved model. The different reactivities of vibra-tionally and translationally excited methyl radicals have been explicitly introducedinto the laser kinetic model and maximum use has been made of the data on elementaryreactions available in the literature. The number of arbitrarily chosen parametersI* +CH31 + CH3-+12,Other models used for CH31 and CF31 lasers 4 93COSTELA, FIGUERA, M A R T ~ N , PBREZ AND VALLE 31has been kept to an absolute minimum.On this basis we have tried to develop amodel for the CHJ laser that will approximate its time-dependent behaviour andpredict the after-lasing products and the gain, under different conditions of diluentgas pressures and illumination.The data presented indicate that the proposed model not only rationalizes previousresults but can yield information about some important laser parameters. Thecalculated cross-section for I* emission using this model agrees with the availableexperimental data. The results obtained have encouraged us to apply a similarapproach to lasers of more practical interest.THE MODELKINETIC MECHANISM USED IN THE MODELIn order to construct and probe the new model we have made extensive use ofexperimental data from ref.(8). The predictions made were compared to experi-mental results for the following cases: (A), methyl iodide with photolysis atil > 220 nm ; (B), as (A) but with the full arc of the Xe lamp ; (C), methyl iodidewith SF, in the ratio 1 :9 at ;Z > 220 nm and (D), as (C) but with the full Xe arc.Some of the observed laser parameters are sensitive to experimental conditions(cleanliness of windows and mirrors, alignment, etc.) and therefore exact agreementbetween calculation and experiment cannot be expected. We will return to thispoint later.The basic hypothesis from which the model is developed is the generation ofmethyl radicals with different kinds and amounts of energy according to the photolysiswavelength used.It will be shown later that this is supported by the availableexperimental data on CH31 photolysis. At wavelengths longer than 220 nmphotolysis of CH31 forms mainly low energy translationally excited methyl radicals ;on the other hand, below 220 nm the formation of highly energetic, vibrationallyexcited methyl radicals predominates. These radicals have different chemicalreactivities. The vibrationally excited radical is the more reactive, abstracting Hvery easily (E, = 9 kcal mol-l), while the main reaction of the translationallyactivated radical is recombination with other radicals. Evidence in favour of thesehypotheses is found in reported laser data and in results from stationary CHJphotolysis and photofragmentation spectroscopy.O Following this line of axgu-ment we first developed a model for the simplest case in which only translationallyexcited methyl radicals were formed (i.e., the case in which the photolysis is atil > 220 nm). Once this model performed satisfactorily we extended it to cover theexperiments performed with the full arc of the Xe flash lamp.For photolysis at wavelengths longer than 220nm the mechanism can be re-presented by reactions (1)-(19) of table 1. In the following discussion, reactionnumbers are those used in table 1 ; this table also includes the rate constants used inthe calculations and pertinent references.The process is initiated by the flash photolysis of CH31 when, for A > 220 nm,translationally excited methyl radical (CH,.), and atomic iodine ( R 90 % is excited2)are produced, reaction (1).The excited iodine can contribute to the laser emission,reaction (2), or it can be deactivated by collisional quenching with the substrate,reactions (3) and (4), or with other products, reactions (5)-(9).The quenching of I* by reactions (3)-(6) has been extensively studied 11-14 andwell established rate constants can be introduced into the model.Donobue and Wiesenfeld l1 found that the combined effects of reactions (7) and(8) on laser emission is five to ten times that of the alkyl iodide. They estimate32 IODINE CH3I PHOTODISSOCIATION LASERTABLE PHYSICAL AND CHEMICAL PROCESSES INCLUDED IN THE CH31 LASER MODELlengths are present processes (20)-(24) are included.Processes (1)-(19) are used for photolysis at wavelengths > 220 nm ; when shorter wave-processrate constant source/molecule-l cm3 s-l or footnote)(reference numberhv(1) CH3I + (CH3)t+I*(I)A > 220 nm(2) I* + I + ~ V a' = i 3 1 5 m(3)(4)I* + CH3I + I2 + CH3*I*+ CH3I + I+ CH3I( 5 ) I*+I2 + I+I,(6) I*(+ M) -+ I(+ M)(7) I*+ CH3- -+ I+ CH3-( 8 ~ ) I*+CH3*(+M)+ CH,I(+M)(8b)(9)(10)(1 1)(12)(13) I+I+CH3I+ Iz+C&I(14) I+I+I2 + 212(15) I+I(+ M) + I2(+ M)(16) CH3*+CH,*(+M) + C2H6(+M)(17) CH3*+12 + CH3Ii-I(18a) CH3*+I(+ M) + CH,I(+ M)(1 8b)(19) CH2I*+ CH21- + C2H4+12(20) cH31 + (CH3-),+1* i12 < 220 nm(22) (CH3.),+CH3I+ CH3-+CH31I*+ (CH3*)t -+ I+ CH3.(CH,*)t+ CH31 + CH4+ CH2I(CH,*)t+ CH31 + CH3*+ CH31(CH,*)t(+ M) 4 CH3*(+ M)hv(21)(23) (CH,*)v(+M)+ CH3*(+M)(24) (CH3*)v +I*+CH3* +I(CH,*)V+ CHJ + CH4+ *CHpI1.33 x 10-134.3 x 10-132 .4 ~ 10-173.6 x 10-l11 . 6 ~ 10-l21 . 6 ~ 10-l22.5 x 10-l12.5 x 10-l21 . 1 6 ~1 . 1 6 ~ 10-l21 . 6 ~ 10-133.1 x 10-312 . 5 2 ~ 10-304.1 x 10-333 . 6 6 ~ 10-l18.3 x1 . 1 6 ~1.5 x 10-lo2.5 x2.5 x1.ox 10-l12.5 x(a) Pure CH31 (Le., M = CH31); (b) same reaction, but M = SF6 (experiments withC&I-/SF6 in the ratio 1 :9) ; (c) estimated in this work, see text ; (d) used for estimation ofthe final ethylene concentration, assuming that (19) is the only CH21- reaction (it is notincluded in the kinetic scheme); (e) in cm6 s-l.k , +k, w 5 x cm3 molecule-l s-l.Palmer and Padrick obtained a similarvalue for k,. Of course, the presence of inert gases will influence k8 and the cor-responding reaction with ground state iodine. We will return to this point later.The quenching of I* by activated radicals, reaction (9), may play an importantrole when the substrate pressure is low and there is no inert gas present. The rateconstant for this process has been taken to be slightly higher than for the analogousreaction with thermal methyl radicals.In calculations for the cases without inert gases the combined effect of reactions(7)-(9) has been made roughly equal to that reported by Donohue and Wiesenfeld.llThe rate constants for translationally excited methyl radicals, reactions (10)-(12)COSTELA, FIGUERA, M A R T ~ N , P ~ R E Z AND VALLE 33have been deduced from our previously reported experiments.The formation ofz 1.5 % of methane allows us to estimate the rate constant for reaction (10) to beabout 1/70 of that for collisional radical deactivation with CH31. This rate constantfor collisional deactivation is given by Z/N, where 2 is the collision rate and N isthe number of collisions required to decrease the energy of the radical to < 1 kcalmol-l. The fraction of energy lost per collision, AE/E, may be obtained from theexpression, AE/E = 2mlm2/(ml+m2)2 where ml and m2 are the masses of thecolliding entities. The rate constants kll and k12 can be estimated.15Recombination reactions and the reaction of I2 with thermalized methyl radicalscomplete the model, reactions (13)-( 19).Reaction (19) is considered negligible andhas not been included in the kinetic model. This assumption is obviously unjustifiedin the case of massive photodecomposition but under such conditions the wholemechanism would be too complicated to be amenable to analysis. The inclusion ofreaction (19) is, however, necessary to explain the presence of ethylene in the photolysisproducts. These products may be of no importance during the laser emission, butthe model gives a rationale for their formation and also an estimate of their finalconcentrations.Reliable data are available for reactions (13)-(17), 6-20 consequently only reaction(18) need be discussed. The values available for the rate constant for this methylradical and iodine recombination differ by two orders of magnit~de.~.11* 21 Thisdifference and the crucial role of reaction (18) in the photodecomposition forced us tothink caxefully about this process. In other alkyliodides this rate constant has beenfound to be similar in magnitude to that for the alkyl radical recombination.22However, in CF31 a strong pressure dependence has been Some experi-mental data 24 helped to clarify this point. The CH31 photodecomposition quantumyield measured in our laboratory for the flash photolysis at 6 Torr for A > 220 nm,under the same conditions as used in the laser experiments, was found to be slightlybelow 0.9. This indicates that 10-15 % of the CHJ photolysed recombines to theoriginal substrate (the primaxy photodecomposition of CH31 has QD = 1).WhenSF6 is present in the ratio 9/1 the experimental OD is lowered to M 0.25; this isascribed to the effect of SF:, on recombination [reactions (8) and (18)]. These dataprovide the ratio of recombination to C2H6 to recombination to CH31. As themethyl recombination is well established, a good estimate for the other recombination(k18 + k,) can be obtained. The ratio k18/k8 can be deduced from the effects of theserate constants on the population inversion. The individual rate constants can thenbe obtained.When the full xenon arc is used, CH31 photolysis at A < 220 nm [reaction (20)lmust be added to the model. This process forms excited iodine I* and groundstate I and vibrationally excited methyl radical, (CH,.),.This radical may abstracthydrogen, reaction (21), or be collisionally thermalysed by the substrate, reaction (22),or by some inert gas, reaction (23). Finally, we have to include the analogue ofreaction (9), i.e., the quenching of I* by (CH,.),, reaction (24).The values of k21-k23 are based on the results of Callear and Van der B e ~ g h . ~ ~The ratio methane :ethane found indicates similar rates for abstraction and de-activation (i.e., kzl M kz2) in pure CH31 [see also ref. (26)]. The effect of SF6 onthis experimental ratio allows (k22/k23) to be estimated.PHOTON DENSITY RATE EQUATIONFour different processes that affect the photon density should be included in thisequation : spontaneous and stimulated excited iodine emissions, ground iodine1-34 IODINE CH3I PHOTODISSOCIATION LASERabsorption and cavity losses.The first is only important as a laser trigger; it wasneglected, but a small photon density was allowed at all times.The cavity losses, f, defined as WF/ Wl = 1 -f( W, and WI are the fkal and initialintensities, respectively), were estimated at 26 % for light travelling a complete cyclewithin the cavity. Losses for the numerical integration program could be definedas a rate constant of photon density + decrease (loss coefficient) : -d+/dt = p+.Integration over the time needed by the light to complete a cycle in the cavity,assuming intensity and photon density to be proportional, yields the equation :where L is the cavity length and the other symbols have their usual meaning.Thevalue of p obtained was 112 ,us1.The definition of the cross-section to be used in the photon density equationrequires some discussion, especially in connection with the hyperhe levels involvedin the transition.The collisional mixing or cross-relaxation between the upper hyperfine levels ofthe iodine transition is expected to be much slower than for the lower levels.27However, the results of Alekseev et aZ.28 show that cross-relaxation between theupper levels can be essentially complete at sufficiently high pressure and that oscillationof the F = 3 3 4 transition totally suppresses the other possible hyperfine transitions.If we assume that cross-relaxation is faster than any other process affecting thepopulations and that the hyperfine level populations are distributed according tolevel degeneracies, them we may write :where + is the photon density ; t, the time ; c73-,4, the cross-section for the I; = 3 3 4transition; gt=3 and g$=,, the degeneracies of the F = 3 and F = 2 levels of theexcited iodine; I* and I the total populations of the upper and lower levels, withtotal degeneracies g* and g, respectively ; and b, the loss coefficient.PUMPING SIMULATIONThe sum of two lorenzians, normalized and having the parameters described intable 2, gives an adequate representation of the flash (see fig.1). The total lightTABLE 2.-PUMPING SIMULATION AT 500 Jtime dependent proiileparameter of the lorenzian used aabsorbed photon density/photons ~ r n - ~I I1 A > 220 nm 1 < 220 nmf.w.h.m./,us 7 7.5 1.41 x 10l6 7.5 x 10l6time of maximumlps 10 22a Experimental data, ref. (8) and (24) ; normalization of the simulated curve to theexperimental flash was performed below 30 ,us where the match between them is goodCOSTELA, FIGUERA, M A R T ~ N , PBREZ AND VALLB 35quanta absorbed at A > 220 nm was determined in our laboratory, the quantumyield of I* used was 0.92.2 At A > 220nm both the quantum yield (taken asThe values used are givenin table 2. We have checked the dispersion for these figures (A > 220 nm) whichcan be introduced in the model and still give a reasonable description of the experi-mental results. Total decomposition is sensitive to the light absorbed and the laserpulse width to the I* quantum yield.We have observed that changes of -130 % inthe number of absorbed photons and about half of that for the I* quantum yield canbe tolerated by our model.= 0.5) and the light absorbed had to be estimated.0 5 10 15 2 0 25FIG. 1.-Flash profile introduced into the model (see text), dashed line. Experimental flash used,from ref. (S), solid line.NUMERICAL INTEGRATIONProgram DESUB 2 9 was used for the numerical integration of the differentialequations. The method is based on fitting the approximations to a rational functionof the discrete interval h and subsequent extrapolations to zero interval size, h = 0.Rational extrapolation is applied to a modified midpoint integration rule.ps and the con-centrations of the products were printed every 0.1 ps.On completion of the integra-tion, the program plots the evolution of the dependent variables against the inde-pendent variable.Some problem emerged in the first attempts to use the program. The integrationof the equations was initially unsteady; the computing time was excessive and theprogram did not converge. These difficulties are mainly due to the sudden and largechanges in the photon density value with time. The routine behaviour was consider-ably improved by using a relative error concept as the convergence criterion insteadof the initial standard error. However, attainment of adequate stability required theimposition of two restrictions, unless the photon density exceeded a minimum valueand the population inversion reached a threshold, rate of photon density change wastaken as zero.In ordinary conditions the initial integration step was 0.1 36 IODINE CH31 PHOTODISSOCIATION LASERMass balance was not explicitly introduced into the equation; therefore, itcould be used as a check on the reliability of the computed results.We found thatwith the program used, which gave concentrations to three significative figures, thesum of the rounding errors was higher than the mass balance deviation. Thisevidence suggests that the routine accumulative errors are < 0.1 %. Initial conditionswere those used in the experiments. *RESULTS AND DISCUSSIONDECOMPOSITION PRODUCTSThe products should properly be referred to as products formed in the flashphotolysis of CH3T, because their formation is not sensitive (within the errors ofcalculated and experimental data) to the attainment of laser oscillation in the experi-ment.Therefore, the products are unaffected by the rate of photon density changeand consequently by the cross-section for stimulated emission. For this reasoncross-sections are discussed later.The concentrations of CHJ and the main photodecomposition products, C2H6,CH4 and I,, are plotted against time in fig. 2 and 3. From the asymptotic characterof the resulting graphs (excluding I,) it can be deduced that the reaction after 30 p sis near completion. Therefore, values calculated at 30 p s can be considered a goodapproximation to final values and are compared with experimental results in table 3.The agreement between experimental and calculated values is reasonable.The model quantitatively explains the effects of the different factors that play arole in CH31 decomposition.Thus, the high level of decomposition found onirradiation without a filter or inert gas is shown by the model to be the consequence of2 0 LI I I 1 I i I0 5 10 15 20 25 30tlNFIG. 2.-Photochemical CH3I laser. Calculated methyl iodide concentration plotted against timefor the four cases studied. (-a - -), case (A), CH31, h > 220 nm ; (- - -), case (B), CH31, full Xearc ; (-), case (C), CH31/SF6 in the ratio 1 /9, h > 220 nm ; (- o - o), case (D), CH31/SF6 inthe ratio 1/9, full Xe arcCOSTELA, FIGUERA, M A R T ~ N , P I ~ R E Z AND VALLE 373.02.52.01.51.00.50 5 10 15 20 25 300 5 10 15 20 25 30 0 5 10 15 20 25 30tlPSFIG.3.-Photochemical CH31 laser. Calculated time evolution of the generated products, eachgroup of curves corresponds to one of the cases studied. (A), CH31, A > 220 nm ; (B), CH31,full Xe arc ; (C), CH3I/SF6 in the ratio 1 /9, h > 220 nm ; (D), CH3I/SF6 in ratio the 1 /9, full Xe arc.TABLE 3 .-MODEL CALCULATIONS OF THE CH3I LASER DECOMPOSITION PRODUCTSresults are given as percentages ofthe initial methyl iodide concentrationCH31 C2H6 CH4 C2H6conditions' calc. ref. (8) calc. ref. (8) calc. ref. (8) calc. ref. (8)(A) CH31, J. > 220nm 5.53 6.01 2.24 2.97 0.08 0.08 0.04 -(B) CH31, full uc 42.46 56.68 5.29 6.20 15.14 19.32 7.57 12.47(C) [CH3II/[SFc,I = 1.9,J.> 220 nm 2.77 1.83 1.18 0.90 0.008 0.03 0.004 -(D) [CH3Il/[SF,I = 1.9,full arc 10.15 9.35 4.09 3.57 0.77 0.89 0.39 0.66' Corresponding to the four cases studied in ref. (8)38 IODINE CH3I PHOTODISSOCIATION LASERtwo factors, (a) an important increase in light absorption (CH31 absorbs very stronglyat 3, < 220 nm) and (b) the role of the vibrationally excited methyl radical [reactionThe effects of wavelength and inert gases are, as seen in table 3, adequatelyreproduced by the program. The strong influence of SF6 on iodine-methyl radicalrecombination [reaction (8) and (18)] is noteworthy. The agreement between theresults and the calculated values is not surprising since the model was constructedusing the experimental results to introduce some of the unknown rates.Whatshould be stressed is the ability of the model to reproduce other laser parameters,such as gain, cross-section and time-dependent behaviour, under a variety of experi-mental conditions (see below).(201.POPULATION INVERSION CALCULATIONThe population inversion has been defined as AN = I* - (g*/g)I. The calculatedAN in the absence of laser emission is plotted against time in fig. 4. In these calcula-tions the rate of change of the photon density is made equal to zero and thereforethe calculated values of AN are not dependent on the cross-section, as mentionedpreviously.tlWFIG. 4.-PhotochedcaJ CHJI laser. Calculated population inversion in each case studied.(- - .), case (A), CH31, X > 220 nm ; (- - -), case (B), CH31, full Xe arc; (-): case (C),CH31/SF6 in the ratio 1 /9, A > 220 nm ; (- o - o -), m e @), CH31/SF6 in the ratio 119, fullXe arc.The values of several positive and negative contributions to AN when AN is amaximum are given in table 4.The most relevant features of these data are discussedbelow. Although in every case quenching by CHJ is the quantitatively dominantdeactivation factor, the other contributions largely determine the shape of the ANcurves. Thus, full arc photolysis of CH31 is characterized by an early maximum inAN [see curve (B), fig. 41. The formation of strong I* quenchers, mainly I2 andmethyl radical, causes a sudden decrease in AN when the pumping by the flash isintense (and still increasing).The introduction of SF6 has dramatic effects; ACOSTELA, FIGUERA, MARTfN, PkREZ AND VALLE 39(curve D) attains a higher and longer lasting maximum. This is not due directlyto the reduction in photodecomposition products as might be expected (see table 3),but to the combined effects of SF6 on the deactivation of" hot " methyl radicals andthe subsequent reaction of these radicals with I to reform the substrate [reaction (18)].This removal of I favourably influences the value of AN. Obviously, these effectsare strongly diminished if radiation with 3, < 220 nm is suppressed; both primarydecomposition and formation of " hot " radicals being drastically reduced, SF6 isalso less active. These trends are present in the results.TABLE 4.-cALCULATED RATES (molecules ~ r n ' - ~ S-' X OF DIFFERENT PROCESSES THATAFFECT THE POPULATION INVERSION AT A MAXIMUMquenching I* positivecontributionsto ANquencherreact ionbconditions" CH31(3-4) I2 CH3*(7-8) CH3,-+ CH3,m pumping (18)(A) CH31, 3, > 220nm 3.9 0.51 0.28 0.02 4.75 0.24(€3) C&I, full arc 10.0 2.7 1.3 1 .o 12.8 2.6(c) [CH3a/[SF61 = 1/993, > 22Onm 3.57 0.57 1.21 0.002 4.44 1.17(D) [CH3II/[SF6] = 1/92full arc 10.4 4.2 6.7 0.04 11.4 10.3-" Corresponding to the four cases studied in ref.(8) ; see table 1 for reaction identifi-cation.CALCULATION OF CROSS-SECTION A N D GAINThe cross-section of stimulated emission is one of the most important laserparameters and was required for the calculation of the laser's time-dependent charac-teristics.Its calculation employing our calculated values of AN was considered animportant achievement of the model and a positive check of its performance.The small signal unsaturated gain, G, can be calculated as :where AN,,, is the maxima of the AN curve (see fig. 4). The other symbols and theunderlying assumptions have been described previously.As previously explained, the calculated AN do not depend on C T ~ ~ ~ . Therefore,by introducing into eqn (25) the calculated AN,,, [fig. (4)] and the experimentallyobserved gain [determined under conditions for which eqn (25) holds], the value of03+4 can be calculated.This procedure was applied to the simplest case, CH31 with il > 220 nm. Inthis case the number of reactions and the number of undetermined rate constantsare a minimum; it should therefore provide the most accurate results.The cross-section was calculated to be 03+4 = 5.6 x This cm2 at 6 Torr of CH3140 I 0 D I NE CH3I P HOTODI SSO CI AT ION LASERTABLE 5.-MODEL CALCULATED GAIN AND CROSS-SECTION OF THE CH3I LASER AND COMPARISONWITH SOME EXPERIMENTAL VALUESconditionsa63'4 gainb/10-18cm2 calculated ref. (8)(A) CH31, 2. > 220nm 5.6'(B) CH3T, full arc 5.6 1.87 1.9(C) [CH31]/[SF6] = 1/9, A > 220 nm 3.9 1.44 1.6(D) [CH31]/[SF6] = 1/9, full arc 3.9 2.54 2.1a Corresponding to the four cases studied in ref. (8) ; see text for definition and methodsof calculation ; Zuev et aL30 give a value of 5.2 at 7 Torr CF31.DBtlwFIG. 5.-Experimental (-) and calculated (---) time-dependent behaviour of the laser.(A)CH31, h > 220 nm ; (B) CH31, h > 165 nm ; (C) CHsIISF6, A > 220 nm ; (D) CH3I/SF6,h > 365nmCOSTELA, FIGUERA, MARTfN, PeREZ AND VALLE 41value can be compared with the value of Zuev et aL30 for 7.6 Torr of C3F,I, cr3 j4 =5.2 x 10-l8 cm2 (calculated from their values for the bandwidth, 0.419 GHz, and thespontaneous emission coefficient, A = 5 s-l). Our value at 6 Torr can be extra-polated to the case in which SF6 is present, using a sF6 broadening factor of5 MHz T ~ r r - l , ~ l giving o3 j4 = 3.9 x cm2. Using these values for the cross-section we can calculate the gain for the different cases considered from eqn (25),see table 5. Clearly, the calculated value for case (A) has no significance as thecalculation is merely the reverse of that made to evaluate For the other cases,the agreement between calculated and experimental results is good, being slightlyworse for the cases in which SF6 is present.However, these small discrepancies arewithin the errors than can be expected from this approach to the problem.CALCULATION OF THE LASER EMISSION TIME-DEPENDENT CHARACTERISTICSUsing the cross-sections calculated above we can now consider the time-dependentbehaviour of the laser which, as mentioned previously, is highly dependent on theseparameters. Calculated and experimental time profiles of laser output are plottedin fig. 5. The experimental reproducibility of laser initiation and duration is fair ;however, reproducible intensities are difficult to obtain since small differences inalignment cause large differences in intensity.In addition the time constant of thelaser detector is x 1 ps and with this resolution the results reported in ref. (8) onlyrepresent the envelope of a combination of peaks for which the fine structure is notavailable. To these limitations must be added the crude kinetic description of thecomplicated phenomenon of laser emission.Taking into account these intrinsic difficulties, the calculations give a fair agree-ment with experiment The narrow, fast decay signal of CH31 photolysed with thefull arc, curve (B) of fig. 5, is reproduced quite accurately. The widening of thepulse produced by either removing the short wavelengths, curve (A), adding SF6,curve (D), or both together, curve (C), is approximately reproduced.This indicatesthat the AN calculations are basically sound, since their time evolution is, togetherwith the cross-sections, the source of the time-dependent behaviour of the laser.We axe grateful for the numerous suggestions and criticisms of Prof. R. M. Utrilla.A. C. and M. M. held Fellowships from the C.S.I.C.; L. V. from the InstitutoEspaiiol de Emigracibn. This research was partially supported by the Comisi6nAsesora de Investigacih Cientifica y TCcnica.l J. V. V. Kasper and G. C. Pimentel, Appl. Phys. Letters, 1964,5,231 ; J. V. V. Kasper, J. H.Parker and G. C. Pimentel, J. Chem. Phys., 1965,43,1287.T. Donohue and J. R. Wiesenfeld, Chem. Phys.Letters, 1975,33,176 ; T. Donohue and J. R.Wiesenfeld, J. Chem. Phys., 1975, 63, 3130.D. M. Haaland and R. T. Meyer, Int. J. Chem. Kinetics, 1974, 6, 297.V. Yu. Zalesskii, Soviet J. Quantum Electronics, 1975, 4, 1009.R. E. Palmer and T. D. Padrick, J. Chem. Phys., 1976,64,2051.V. Yu. Zalesskii and E. J. Moskalev, Soviet Phys. J.E.T.P., 1970,30, 1019.E. V. Arkhipova, B. L. Borovich and A. K. Zapol’skii, Soviet J. Quantum Electronics,6, 686.A. Costela, J. M. Figuera, M. Martin and L. Valle, Chem. Phys. Letters, 1978, 53,478.G. M. Harris and J. E. Willard, J. Amer. Chem. SOC., 1954,76, 4678.lo S. J. Riley and K. R. Wilson, Disc. Furaduy Soc., 1972, 53, 132.T. Donohue and J. R. Wiesenfeld, J. Phys. Chem., 1976, 80,437.l2 R. J. Butcher, R. J. Donovan, C. Fotakis, D. Fernie and A. G. A. Rae, Chem. Phys. Letters,1975, 30, 398.197642 IODINE CH3I PHOTODISSOCIATION LASERl3 D. H. Burde and R. A. McFarlane, J. Chem. Phys., 1976, 64, 1850 ; D. H. Burde, R. A.McFarlane and J. R. Wiesenfeld, Chem. Phys. Letters, 1975, 32,296.l4 R. J. Donovan and D. Husain, Trans. Faraday SOC., 1966, 62, 1050 ; R. J. Donovan and D.Husain, Ann. Report Chem. SOC. Ser. A, 1971, 68.l5 J. G. Calvert and J. N. Pitts, Jr., in Photochemistry (John Wiley, N.Y., 1966), p. 648.l6 R. Engelman, Jr. and N. R. Davidson, J. Amer. Chem. SOC., 1960,82,4770.l7 D. L. Bunker and N. R. Davidson, J. Amer. Chem. SOC., 1958,80,5085.l8 J. A. Blake and G. Burns, J. Chem. Phys., 1971,54, 1480.l9 F. K. Truby and J. K. Rice, Int. J. Chem. Kinetics, 1973, 5,721.2o M. C. Flowers and S. W . Benson, J. Chem. Phys., 1963,38, 882.21 S. W. Benson, in 23ermochemicaZ Kinetics (John Wiley, N.Y., 1968), p. 67.22 C. C. Davis, R. J. Pirkle, R. A. McFarlane and G. J. Wolga, I.E.E.E. J. Quantum Electronics,23 T. Ogawa, G. A. Carlson and J. C. Pimentel, J. Phys. Chem., 1970,74,2090.24 J. M. Figuera and L. Valle, unpublished work.25 A. B. Callear and H. E. Van der Bergh, Chem. Phys. Letters, 1970,5, 23.26 J. R. Majer and J. P. Simons, A h . Photochem., 1964,2, 137.27 E. A. Yukov, Soviet J. Quantum Electronics, 1973, 3, 117.28 V. A. Aleskseev, T. L. Andreeva, V. N. Volkov and E. A. Yukov, Soviet Phys. J.E.T.P., 1973,29 P. A. Fox, in Mathematical Sofware, ed. J. R. Rice (Academic Press, London, 1971), p. 477.30 V. S. Zuev, V. A. Katulin, V. Yu. Nosach and 0. Yu. Nosach, Soviet Phys. J.E.T.P., 1972,35,31 W. Fuss and K. Hohla, Z. Natwforsch., 1976,31a, 569 ; H. J. Baker and T. A. King, J. Phys. D,1976, 12, 334.36, 238.870.1976,9, 2433.(PAPER 8/2016