Intra-and Intermode Vibrational Energy Flow in CH 3 F Excited by Irradiation with an intense CO 2 Laser : A Non-Linear Vibrational Relaxation

The vibrational relaxation mechanism of CH3F whose v3 mode is excited by a transversely excited atmospheric (TEA)CO2 laser-pulse has been discussed on the basis of observation of the laser-induced fluorescence (LIF) of the v3 overtones and of the C-H stretching modes and kinetic analyses. The time-evolved LIF in the 3-/zm region was found to be dependent significantly on the laser fluence; at a low fluence (<0.01 J cm-2), the emission intensity increased almost exponentially with a rate similar to the one determined in the experiment with a Q-switched laser, while at a higher fluence (>0.1Jcm-2) the emission rose much faster to form a peak which decayed quickly before a second broad peak appeared. In the wavelength-resolved fluorescence measurement, it was found that the kinetics of population in the v4 level were similar to those in the 3v3 level, while those in the Vl, 2v5, v2 + v5 and 2v2 levels behaved in a way different from those in the v4 level. These observations lead to the conclusion that the laser energy poured into the v3 mode flows to the v4 level directly through 3v3 as well as by the successive interand intramode V-V energy transfers, i.e., v3--+ v6--+v2, vs--+ 2(v2, vs)--+ Vl--+ v4. A model calculation of the relaxation kinetics, including the direct V-V energy transfer between two 3v3 and v4 levels, could reproduce the 3-/xm emission data. Another significant finding is a non-exponential depopulation in the 2v3 level, the v4, Vl and other vibrational levels in the 3-/xm region in the final stage of the relaxation. The deactivation rate is larger for a higher level and is a decreasing function of time and is much larger than the V-T/R energy transfer rate determined in the


INTRODUCTION
In dealing with the mechanism of vibrational energy flow in polyatomic molecules whose specific vibrational mode is excited by laser irradiation, it has become the general consensus that the intramode vibration-to-vibration (V-V) energy transfer dominates the intermode V-V so that a local vibrational quasiequilibrium distribution is attained within the laser-pumped vibrational mode prior to establishment of the steady-state distribution among all modes, and that in the final stage of the relaxation, the vibration-to-translation/rotation (V-T/R) energy transfer occurs from modes having low fundamental frequencies. The former studies on the vibrational relaxation of a number of small polyatomic molecules support this mechanism and are reviewed in detail by Flynn1.
Of the polyatomic molecules, CH3F has been investigated the most intensively for its vibrational relaxation. Since the v3 C-F stretching mode of CH3F has the lowest vibrational frequency resonant to the CO2 laser line and the V-T/R relaxation is relatively slow, a large part of the energy pumped into the v3 mode by the CO2 laser irradiation is stored within various vibrational modes for a relatively long period. This implies that under a quasiequilibrium condition, a population distribution with a high vibrational temperature is realized in each mode, and CH3F could thus be one of the polyatomic molecules which are adequate for more detailed investigation of their intra-and intermode energy transfer mechanism on the basis of observations of laser-induced fluorescence (LIF).
According to the aforementioned general principle of vibrational relaxation, the CH3F molecules which have absorbed CO2 laser photons in the v3 mode transfer their energies to the v4 mode through the following pathway (see Figure  v3--+ v6--+ v2, v5--+ 2v2, 2v5 --+ vl--v4 (1) This mechanism was proved by Sheorey and Flynn 2 and Apkarian and Weitz 3 in the LIF measurement of CH3F excited by a Q-switched CO2 laser. Contrary to this, another pathway, which includes the intramode V-V ladder climbing within the v3 mode and the near-resonant intermode V-V energy transfer between 3v3 and v4: V3 "--+ 2V3--'+ 3Y3--+ 1/4 "+ 1/1 "-+ 2v2, v2 + 1/5, 2vs (2) has been proposed based on high-resolution spectroscopic data; this indicates that a number of rotational levels of the 31/3 state are strongly Coriolis coupled with those of the 1/4 state4. The main reason for preference of the pathway in Eqn (1) rather than that in Eqn (2) is that the populations in the bending overtones, 21/. and 21/5, are much larger than those in the 31/3 level and, moreover, that bending overtones and CmH stretching modes are coupled with each other by Fermi as well as Coriolis interactions' 6. In the pathway of Eqn (1), the population rate in the 1/4 level should not depend on the average number of CO2 laser 144 H. NAKANE AND S. TSUCHIYA photons absorbed per CH3F molecule. Nevertheless, Kneba and Wolfrum 7 found that the rise rate of the 3-/xm emission induced by irradiation of CH3F with the 9.6-/xm P(20) line of a TEA COe laser was much larger than that predicted by Eqn (1). A similar phenomenon which could not be explained by Eqn (1) was also reported by Sheorey and Flynne. When CH3F was irradiated by the focused beam of a Q-switched CO2 laser pulse, an initial fast rise of the 1/1, V 4 (CH stretching) emission occurred, which was followed by a partial decay and later by a second slower rise to a broad maximum. As a possible interpretation of this finding, it was suggested that a rapid increase of the population in the v, v4 / v3 level caused the initial fast rise of the 3-/zm emission. The present authors proposed the pathway in Eqn (2) as a mechanism to explain the aforementioned phenomenon found in the 3-/zm emission induced by irradiation of CHaF with a TEA CO2 lasers.
However, Forber et al. 9 opted for Eqn (1) as a dominant energy flow mechanism on the basis of the measurement of the vibrational temperature for each mode of 13CHaF excited by a TEA CO2 laser. More recently, Apkarian et al. 1 carried out a model calculation of coupled rate equations which were formulated based on Eqn (1) as well as Eqn (2) to conclude that the direct V-V transfer from 3v3 to Vl/V4 could not occur even under a strong laser excitation condition, since the vibrational heat capacity of the Vl, v4, 2v2, v2 + vs, 2v5 levels was too large to fill them from 3v3.
If the observed increase of the population rate in the Vl, v4 levels of CHaF molecules whose v3 mode is excited by a strong CO2 laser is attributed to the existence ofthe pathway in Eqn (2) as well as Eqn (1), the intermode V-V energy transfer from the 3v3 to the v4 level must be extraordinarily efficient. According to the established view of the collision probability of V-V energy transfer rates, its rate may not be large unless both the energy non-resonance, which must be transferred to/from translation/rotation, and the change in the number of vibrational quanta are minimized. Therefore, it would be of fundamental importance to clarify the mechanism of the intermode energy flow in CHaF molecules whose specific mode is excited by a strong CO2 laser.
In this paper, we report the measurements of the wavelengthresolved infrared (IR) fluorescence from CH3F whose v3 mode is excited by irradiation with a TEA CO2 laser and the kinetic analysis of the relaxation process. The main purpose of this study is to test whether the kinetics of the population in each vibrational level is dependent or not on an initial amount of the laser energy which is poured into the v3 mode of CH3F and to seek a more general vibrational energy flow mechanism which is applicable irrespective of the extent of laser irradiation.

EXPERIMENTAL
The v3 mode of CH3F in a gas cell was excited by irradiation with the 9.4-/xm P(20) line of a TEA CO2 laser (Lumonics, TE-102-2). The laser pulse energy was adjusted in the range of 0.7-0.01J by placing an appropriate number of polyethylene films (0.01 mm in thickness) in the pathway of the laser beam as an attenuator. The laser energy and the pulse shape were measured by a calorimeter (Gentec, Ed-500) and by a photon-drag detector (Rofin, 7400), respectively. The pulse was composed of a spike of 200-nm FWHM and a tail of 1.5 s duration when the laser medium was a mixture of He" CO2" N2 3" 1" 0.4 and the pulse repetition frequency was 2.5 Hz. The cross-section of the laser beam was reduced to the size of 9.5 6.5 mm by use of a ZnSe condenser lens, so that the laser fluence was increased up to 1 J cm-2.
The laser intensity was not completely homogeneous throughout the cross-section. In fact, the fluence distribution across the beam crosssection was determined by probing energy of the laser beam which passed through a pin-hole of 1 mm inner diameter by a pyroelectric energy meter. The result of this measurement indicates that it is a good approximation to assume the above size of the cross-section for homogeneous intensity of the laser beam.
Two types of gas cell were employed. The first one was designed according to the proposal of Manuccia and Franke111, and was employed for measurement of the dispersed LIF spectrum. The second was one for observing a time-evolved IR fluorescence at a fixed wavelength. Both systems were composed of a Pyrex glass cell (10 cm i.d. and 30cm in length) which includes two mirror systems" one for multiple reflection of the incident laser beam and the other for collection of the induced IR fluorescence. The latter mirror system was of the Welsh type12. In the first arrangement of the cell, five plane mirrors were placed inside the cell as a pentagonal column whose internal surfaces enabled the incident laser beam to traverse a long distance when the incident direction of the beam was slightly tilted from one perpendicular to the column axis. In this experiment, the incident laser beam reflected on the internal mirrors 24 times, its pathlength being about 1.5 m; at the end of the beam's traverse the laser intensity was attenuated to about one-half of the original value. Sice this attenuation was unfavorable for quantitative discussion of the fluorescence data, a second arrangement of the mirror system was employed; the laser beam was reflected only three times by two parallel plane mirrors placed 12 cm apart from each other, so that the attenuation of the laser intensity was less than 10%. The LIF collected by the Welsh mirror system was taken to a monochromator (f= 3.4) with a 4-/xm blazed grating of 300 groove mm-1 or to band pass filters for 3 and 5-/zm regions before illuminating an InSb photovoltaic detector (Fujitsu, IV200). The signal was initially treated by a current preamplifier (PAR, 181) whose frequency response was d.c. to 0.67 MHz (-3 dB), and this output was amplified by an amplifier (Brookdeal, 9454) with a bandwidth of 0.1Hz-3 MHz (-3dB). The final signal was digitized and accumulated by a data processor (Iwasaki, SM 1300). Normally, 1024 or 2048 data were averaged to improve the S/N ratio. The time response function of the detector system was determined to be about 3/xs by use of a GaAs IR emission diode which was pulsed by an electric square wave. Calibration of the sensitivity of the monochromator, including the detecting system, was made by a spectral measurement of the radiation from a homemade black body furnace. The discharge noise of the TEA CO2 laser was employed as a trigger pulse for timing the signal processing system; the time between the trigger and the CO2 laser pulse was determined to be 1.5-0.5/xs by monitoring the laser pulse by the photon-drag detector. The fluctuation of this delay time was disregarded because of the relatively long response time of the detector. Special attention was paid to reducing the discharge noise of the TEA CO2 laser which interfered significantly with the signal processing. The entire laser apparatus was covered by copper plates of 0.3 mm in thickness, and the LIF measurement system, including the monochromator, the detector and the current preamplifier, was also shielded by copper plates.
The sample gas of CH3F was a commercial gas (PCR) with a nominal purity of 97-98%, and was employed after repeated solidification at liquid N2 temperature. According to the mass spectroscopic analysis, the impurity content was less than 0.4%. The pressure of the sample The observed temporal behavior of the 3-/xm emission from CH3F whose v3 mode is excited by irradiation with a TEA CO2 laser, 9.4-/xm P(20) line, is shown in Figure 2 as a function of the laser energy fluence.
The data taken at a low fluence and reproduced in Figure 2(a) shows that the emission rises almost exponentially to a plateau, although a large discharge noise of the laser makes it difficult to trace the initial rise of the emission accurately. Disregarding the noise, it is seen that the rise rate is in the same order of magnitude as the one reported on the excitation by a Q-switched CO2 laser (cf. Figure 6(b) of Ref.
2). In contrast to this, as shown in Figure 2(b), increasing the fluence of the laser, the emission rises much faster to form a peak which is followed by a second broad peak. This observation is analogous to that found by Sheorey and Flynn 2 under focused irradiation with a Q-switched CO2 laser (cf. Figure 6(a) of Ref. 2). In the data of Figure 2(c) which has been observed at the highest fluence of this experiment, the emission forms a clear peak in the initial stage, while the second broad peak in Figure 2(b) changes to a shoulder of the initial peak.
The results shown in Figure 2 imply that we may not apply the energy flow mechanism of Eqn (1) to interpret the observed dependence of the 3-/xm emission of the laser fluence. According to the mechanism of Eqn (1), the vibrational relaxation proceeds towards a quasiequilibrium state, in which the population distribution in each mode is of the Boltzmann type. Therefore, populations in respective levels except those of the laser-pumped mode may not exceed the magnitudes defined by the quasiequilibrium condition. For example, populations in the Vl and v4 levels grow after the pulsed excitation of the v3 mode and approach the steady-state values with a rate defined by combination of the intra-and intermode V-V energy transfer rates and, thus, the rate must be much less dependent on the laser fluence than the observed one.
It has been suggested by Sheorey and Flynn 2 that a rapid accumulation of population in the vl + v3 or v4 + v3 level through the resonant process: results in an initial rapid rise of the emission due to the transition Vl + v3--v3. However, the population in the vl or v4 level is limited to the amount in equilibrium at room temperature, so that it would be difficult to explain the significant increase of the fluorescence intensity just after the excitation with a high laser fluence. Moreover, even if Eqn (3) contributes to the initial rapid rise of the 3-/xm emission, the emission intensity must exceed the initial value in the later stage since populations in the Vl and v4 levels should grow due to the mechanism of VIBRATIONAL ENERGY FLOW IN CH3F 149 Eqn (1). This expectation was not realized in the present experiment using strong laser excitation.
The observed phenomenon on the v3 emission of CH3F excited by the TEA CO2 laser may not be attributed to a multiple photon absorption. The 3-/zm emission of CH3F was induced by irradiation with only two CO2 laser lines, i.e. the 9.4-/zm P(20) and the 10.2-/zm R(20) lines. Of these lines, the latter induced the emission with its intensity being 1/100 that of the former. It is well known that the frequency of the 9.4-/zm P(20) line is near-resonant to the qQK(12)(K 1, 2) v 0--1 transition of the v3 mode13. Thus, the linear resonant absorption in the v3 mode must be the major factor which determines the initial condition of the laser excitation.
Dispersed fluorescence spectra of v3 overtone and CH stretching bands Figure 3 shows the time-resolved fluorescence spectra of the V3 overtone band taken at intervals of 0.01/xm. Since the wavelength resolution of the monochromator is not sufficient to separate each vibration-rotation line, the observed spectra of the v3 2 0, 3 2 and 4--2 transitions of the v3 overtone overlap with each other. The intensity of the spectral line for the vibration-rotation transition v'J'K'---, v"J"K" of a symmetric top molecule is described as where the notations are defined as follows: If the monochromator which is set at a wavenumber O) has a spectral slit functionf(wi, w), the observed emission intensity at this wavenumber is described as: states. Therefore, it is difficult to estimate the extent of the contribution of respective vibrational states to the observed fluorescence spectrum. Nevertheless, in a shorter wavelength region, the v4 vibration band is isolated from other bands due to relatively weak Fermi coupling with Vl vibration. Thus, it can be stated that the population rate in the v4 level in the early stage of the relaxation is larger than that in the Vl, 2v5, levels. In Figure 4 the observed spectral intensities in the wavelength range 3.2-3.3/xm are also found to be larger than those of the calculation. This might be attributable to a perturbation due to Coriolis coupling between the 3v3 and v4 state which has been pointed out already by Graner and Guelachvili5.
The time-evolved emissions of the v3 overtone and those in the 3-/zm region observed through the monochromator are shown in Figure 5.
The emission data at the three wavelengths in Figure 5 states, respectively, on the basis of Eqns (7a)-(7c). The 2v3 population increases quickly to a peak which decays with an initial large rate. The population in the 3v3 level behaves in a way similar to that in the 2v3 level. The time-evolved emissions at 3.29, 3.43 and 3.52 m are also shown in Figure 5(d)-(f). Referring to the spectrum given in Figure 4, the emission at the shortest wavelength can be interpreted as the contribution of population in the v4 level, while the data at the other two wavelengths are due to the densely overlapped emission bands from the vl, 2v5, 1/2 --1,'5 .and 2v2 level. The emission at 3.29/zm rises quickly to form a peak in the early stages of relaxation. This behavior is common to that observed in the v3 overtone. Emission in the longer wavelength region rises slightly after increase of the emission intensity at a shorter wavelength, reaching an almost constant intensity, although it does not form a clear peak. This finding implies that the kinetics for the v4 population are different from those of the other levels; Vl, 2v5, v2 + v5 and 2v2. These data will be discussed by comparison with the computer modelling of the relaxation kinetics. The average number of laser photons absorbed per CH3F molecule, (n), has been determined from observation of the intensity attenuation of the laser beam which passes through the CH3F gas in a cell 1 m in length. Figure 6 indicates that (n) is dependent on the laser fluence as well as on the pressure. The value of (n) is defined by: where Nis the number density of CH3F, and Nt6 and N are those in the ground and excited levels, respectively, which may interact with the laser field, I(t) is the laser intensity at time t, a is the absorption cross section, and co is the laser frequency. Using the reported values of the absorption cross-section 13 and the rotational relaxation rate constant 15 assuming that the qQ(12) and qQ2 (12) transitions to be resonant with the CO2 laser line, it was impossible to reproduce the data given in Figure 6 based on Eqn (8) combined with the kinetic scheme described later. This is probably due to the power broadening of spectral lines and the collision-assisted multiple photon absorption. A value of (n) exceeding 0.5 at higher fluences is attributable to the fact that CH3F excited to the v3 level makes collisional-rotational transitions to levels v -2 10 laser fluence J crK z which enable CH3F to absorb another photon to attain the 2v3 level during the laser pulse. This has been demonstrated in the CO2 laser irradiation of the CH3F/Ar mixture16. The laser frequency VL is 31 383905.6MHz determined by Chang13, and the rotation-vibration transition frequencies are obtained based on the molecular constants given by Freund et al. TM The pressure dependence of (n) is attributable to the collision broadening of the absorption spectral line and also to the collisioninduced rotational transitions which suppress saturation of the stimulated transitions. As shown in Table I, Table I is defined as follows, taking the collision broadening and the power broadening as well as the Doppler effect into account: where vi is the frequency of the ith line, 7p, the collision frequency, the Rabi frequency, fD(V', Vi), the Doppler line profile, and S, (83d3hc)lMil 2. Owing to multimode oscillation of the present TEA COe laser, the laser pulse is composed of a number of lines whose frequency distributes over a range as wide as I GHz. Assuming the Lorentz function to describe the frequency distribution of the COe laser line, the effective absorption cross section due to the ith transition of CH3F for the laser line is defined as" Oi('L) fcri(v)g(v)dv/fg(v)dv (12) where 9I is the mean frequency of the laser line. The average number of photons absorbed per CH3F molecule may be calculated by the equation" (n ) I[Oi(VL)I(t)/Nhf'L](lower /pper)dt (13) where Now'er and ]ower are the number densities of CH3F molecules in the lower and upper levels of the ith transition, respectively, and N is the total number density of CH3F. The summation in Eqn (13) must be made on respective transitions of the v3 vibration listed in Table I, and N values are the solution of the coupled rate equations that describe the stimulated transitions and the rotational and vibrational energy transfer collisions. If these rate equations are formulated for each population in respective levels of J, K states relating to the stimulated transition induced by laser irradiation, the number of coupled rate equations to be solved is very large, and it becomes physically unrealistic. Thus, we define a parameter which represents an average absorption cross-section for the v3 v"--v' transition as follows: Ov" Oi(L)fi/fi, (14) where3 is the fraction of population in the lower rotational level of the vibrational state v" for the ith transition. Assuming the average effective VIBRATIONAL ENERGY FLOW IN CH3F 157 (apparent) cross-section defined above, the kinetic equation is formulated to describe the laser-induced stimulated transitions and the collisional rotation as well as vibration transfer processes. It is assumed that a fraction of the population in the v" states possesses the absorption cross section of Eqn (12) and this fraction is a function of the laser fluence: f fo + aI(t), forv3=0 f aI(t) for v3 1 and 2 (15) where f0 is estimated to be 0.042 assuming the thermal rotational equilibrium distribution at room temperature, and I(t) is the laser power at time t, and a coefficient a is selected so that the calculated value of (n) fits with the observed values given in Figure 6. If the fraction f introduced in Eqn (14) is a certain constant value independent of the laser power, the calculated result of (n may not reproduce the experimental data which is a function of the laser fluence as well as the CH3F pressure. Thus, the laser stimulation scheme presented above is adopted to model the excitation and relation kinetics of laser-irradiated CH3F molecules. Excitation and relaxation kinetics Simultaneous differential equations are formulated to describe the excitation and relaxation kinetics of CH3F whose v3 mode is excited by irradiation with the 9.4-/xm P(20) line of the TEA CO2 laser pulse. The vibrational levels taken into consideration are summarized in Table II. For convenience, one vibrational level which represents both the v2 and v5 levels is assumed by introducing the increased degeneracy and is designated v25mthe energy level is the average of v2 and v5 weighted by their degeneracies. A similar treatment was taken for levels in the CH stretching region. Referring to the emission spectrum given in Figure 4, it is seen that one cannot discriminate respective contributions of the Vl, 2v2, v2 + vs, and 2v5 levels to the observed emission spectrum. Moreover, according to the high resolution spectroscopic studies, these vibrational states couple strongly with each other by Coriolis and Fermi interactions5'6. Therefore, five vibrational states are presented by one state v125 whose degeneracy is seven in the present model. The vibrational frequencies listed in Table II  In Table III, the energy transfer processes taken into consideration are summarized together with the non-resonant energy AE, and the rate constant assigned to each process. The energy transfer process may be categorized into three groups" intermolecular intramode V-V energy transfer, intra-or intermolecular intermode V-V, and V-T/R energy transfer. Of intramode V-V energy transfers, the energy transfer from v25 to 2v5 is the assumed to occur through the intermediate state of v2 / vs, since the 2v5 level is Fermi coupled and greatly shifted. The intermode V-V energy transfers considered here are all involved in the relaxation mechanism proposed by Sheorey and Flynn 2 and also by Apkarian and Weitz3, except for process [18] (in Table III) which is the direct energy transfer between 3v3 and v4. This latter process is assumed to occur collisionally and will be discussed later. V-T/R energy transfer is assumed to occur from v3 and v6 modes. Most of the rate constants for the energy transfer processes [1]- [23]  overestimated. For the other intramode V-V energy transfer rates, the value of 1 10 6 s -1 Torr -1 is assumed for the first step of the "up-theladder" process, since the rates for these V-V energy transfers must be close to the one for v25---> v2 + v5 which has been determined by Apkarian and Weitz 3 or to another intramode V-V energy transfer rate which is of the order of 10 6 s -Torr-. As for the intermode V-V energy transfers, based on the data of Sheorey and Flynn for v3---> v6 and v6---> v25, the other V-V energy transfer rates through the combination levels such as. 2v3---> v3 + v6, v3 + v6--> 2v6 etc. are also estimated by the Landau-Teller rule. For the intermode V-V energy transfers of 3 v3 <---> v4 and v4 <---> v25, the valueslistedinTable III are adoptedin thetrial calculation. The effect of the direct energy transfer from 3v3 to v4 and other states on the entire relaxation is one of the major subjects of this paper, so that the adequacy of these rate constants will be discussed later.
Taking the energy transfer processes [1]- [21] into account, the kinetic equations are formulated to describe the time-dependent population in each vibrational level among 14 levels in the course of the relaxation which starts by laser excitation of the v3 mode at the time origin. In the equations, the number density in ith level is denoted as Ni in which the level number is defined in Table I except in 0 which means the ground state. The total number density of CH3F is defined as N= i Ni. For the excitation process, it is assumed that a fraction of Ni(i O, 4, or 11) may interact with the laser radiation field of 9.4-/zm P(20) line, and that the average absorption cross sectionis common for the transition from the iv3 state to the Q" + 1)v3. If the parameter fis introduced as an equilibrium fraction of populations in these rotational levels of the relevant vibrational state, the rate equation for the population, N, in the rotational levels of the ith state which makes a stimulated transition to or from the kth state is formulated as follows: where j 1, 2 and 3 corresponds to the transitions of 0---> 1, 1 ---> 4 and 4--> 11, respectively, and krot is the rate constant of transitions from rotational levels interacting with the laser photon field to the other rotational levels, and is assumed to be a common value of The number density of the ground state may be derived by the relation 14 No N Z Ni.
(35) i=1 'These coupled differential Eqns (16), (21)-(34) were solved numerically by a Runge-Kutta-Gill method with the initial condition that the population distribution in respective vibrational levels at t= 0 is assumed to be in equilibrium at 295 K.
Comparison of kinetic calculation with LIF data In Figure 7, the calculated fractional population changes in the 2v3 and 3v3 levels induced by laser irradiation are shown together with the observed overtone emission from each state. Here, the observed emission intensities from 2v3 at the laser fluence of 0.7Jcm -2 are plotted so as to fit with the calculated ones in the later stage of relaxation. Thus, we may discuss the emission intensities from the 3v3 level relative to those from 2v3, and also the emission under a high fluence irradiation relative to those under a low fluence. Due to the relatively slow response of the IR light detecting system, the emission intensities were found to increase with a rate smaller than that calculated. However, the observed relative intensities and the decay rates of the 2v3 emission are in good agreement with the calculated fractional population change in 2v3 level based on the model including the direct 3v3 v4 V-V energy transfer. The observed population change in 3v3, which is defined as an emission intensity from the 3v3 level relative to that from 2v3, is larger by a factor of 1.5 than the calculated population change. Nevertheless, it may be stated that the present kinetic model calculation could reproduce the population kinetics determined by the LIF emission measurement. Referring to the spectral analysis of the 3-/xm emission band shown in Figure 4(d), the emission at the shortest wavelength 3.28/xm in this experiment is attributable to the v4 population, while the emission in the longer wavelength region, e.g. 3.52/zm is contributed from mainly 2v2, v2 + v5 and Vs. Figure 8  forms a peak at an initial stage which is reproduced in the calculation in spite of some disagreement in the increasing rate. This latter fact is probably due to insufficient response of the present IR light detecting system. The calculated v4 population in laser irradiation with a lower fluence, 0.097 J cm-2, is almost in agreement with the observed emission intensity, although its relative magnitude is too small by a factor of 1.5. This implies that the kinetic model given in Table III  Of the rate constants assigned to energy transfer processes listed in Table III, the magnitudes of k333,4 and kl,4 are most ambiguous. The energy transfer between v and v4 must be very efficient, because some rotational levels of these vibrational states are coupled with each other due to Coriolis forces and furthermore large dipole matrices are expected because of the intense absorption of the Vl and v4 bands.
Therefore, a large value, 1 x 106 s-1Torr-1, is assumed for a temporal value of k,4. The kinetic calculation was made assuming various values for k333,4 in the range of 1 x 105-1 x 10 6 s -1Torr-1. Comparison ofthe calculated time-evolved populations with the observed emissions from 2v3, 3v3, v4 and 1,'1/21;2/V2 q-1'5/2125 leads to the conclusion that k333,4 must be between 5 x 105 and 1 x 106s-1Torr-. Similarly, kl,4 was changed by a factor of five assuming the fixed value for k333,4 of 5 X 10 5 S -1 Torr-1. However the calculated time-evolved populations in relevant vibrational states were found to be relatively insensitive to the magnitude of this rate constant. Thus, it was concluded that the set of rate constants given in Table III was satisfactory for quantitative discussion on the relaxation mechanism.
In Figure 9, the experimental decay data of emissions from the 2v3, 3v3 and v4 levels in the final stage of the relaxation are presented. The intensities of the 2v3 and v4 emission are normalized in a way similar to that shown in Figures 7 and 8, so that one may discuss the population changes in 3v3 relative to 2v3 and also those of v125 to v4 using the calculated results given in Figure 9 as absolute values of the population changes in the respective states. Good agreement is seen between the observed emission decays and the kinetic model calculation in the later stage of relaxation. Clearly, the observed decay of populations in the 2v3, 3v3 and v4 states is much faster than the V-T/R transfer, and is not simply exponential; the decay rate is reduced gradually in the later stage and the decay of the 2v3 emission is slower than those in the other higher states, v125, v4 and 3v3. These observations are reproduced well by the present kinetic model calculation.
Relaxation kinetic scheme with versus without 3v3 v4 V-V energy transfer The kinetic rate Eqns (16), (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34), which are formulated based on the energy transfer processes given in Table III,  relaxation kinetics. In two mechanisms with and without the V-V energy transfer, the v4, Vl, and other nearby states are populated with almost the same rate. Population in v4 is slightly accelerated by inclusion of the 3v3 v4 V-V energy transfer, but the major part of the population is caused by the energy flow mechanism in Eqn (1). In the later stage of the relaxation, the calculations based on either mechanism result in the same population kinetics at the respective levels. The population in each level is reduced exponentially with the common rate, which is defined from the V-T/R energy transfer rates of v3 and v6 modes. Thus, in weak laser excitation of v3 mode, the vibrational energy flow from v3 to v4 and Vl and other nearby levels occurs mainly through Eqn (1) and the contribution of Eqn (2) is relatively small. In the case of strong laser excitation, a large energy is poured into the v3 mode, and the vibrational energy flow scheme from v3 to v4, vl, and other levels is dependent significantly upon whether the kinetic model includes the 3v3 v4 energy transfer or not. Without the V-V energy transfer, the population kinetics are essentially the same as those given in Figure 10(a). The vibrational energy flows from v3 to v2, v5 through v6 and finally to Vl and v4 keeping the quasiequilibrium population distribution within each vibrational mode. In the later stage of the relaxation, as shown in Figure 10 population in the v4 level is accelerated greatly due to the direct energy flow from 3v3 just after the laser excitation to reach a maximum. Then, the v4 population is reduced due to the intermode V-V energy transfer to Vl, 2v5, v2 + v5 and other nearby levels and also to v6, v2 and v5 modes via the 3v3 level since the excess energy accumulated in the v3 mode in the initial stage must be transferred to other levels. As already demonstrated in Figure 8, the observed emission data from v4 are in good agreement with the present model calculation.
Another significant finding in the kinetic model, including the 3v3 v4 V-V energy transfer, is that the vibrational quasiequilibrium population distribution may not be realized even in the final stage of the relaxation. In Figure 10(d), the population in each level decays in a non-exponential manner and the population ratio of certain levels is not constant during the course of the relaxation. On the contrary, in the case of weak laser excitation, as shown in Figure 10(b), the population distribution in the respective levels is in equilibrium at a single vibrational temperature in the final stage of relaxation; populations in all levels decay with the same rate, the V-T/R rate. Referring to Figure 10(d), it is seen that the non-exponential population decay is more significant in higher levels, v3 + /4, /3 + V125, /4, 33/3, and the populations in lower levels are reduced almost exponentially although the rate is larger than the V-T/R rate. This non-exponential population decay is caused by the existence of the 3v3 v4 V-V energy transfer. When this process is very efficient, a series of intermode V-V energy transfers occurs from 3v3 to 2v3 (see Figure 1) connecting levels which are located in between the two levels. This energy flow must occur if the relative population distribution in these levels exceeds the thermal one at room temperature, since the non-resonant energy of a V-V energy transfer process is transferred to/from translation and/or rotation whose energy distribution is in equilibrium at room temperature. After the successive intermode V-V energy transfers from the 3v3 to the 2v3 level, one quantum of the v3 vibration is transferred to translation and/or rotation. Further v3 quanta are lost if the intramode V-V pumping occurs within the v3 mode such as 2v3 + v3 3v3 + 0. The overall process is that proposed by Mandich and Flynn 2 for the vibrational relaxation of N20 and named a "catastrophic cyclic path". Since the cyclic path includes the intramode V-V energy transfer whose rate is a non-linear function with respect to the number density in a v3-excited level, the population decay in each relevant level must be dependent on the extent of the excitation .and be non-exponential against time. The decay rate is much larger than that of the V-T/R energy transfer which is a linear process.
The Coriolis interaction of high rotational levels of the 3v3 level with those of the v4 level has been pointed out by Graner4, who suggested an efficient energy transfer between 3v3 and v4 through Coriolis-coupled rotational levels. Later, his group carried out the intensive analysis of the high resolution spectrum in the 3-/zm region, '4(E), v(A), 2va(A), 2vs(A + E), v2 + y5(E)5'6. According to their analysis, 3v3, which lies 90cmhigher than v4, interacts with v4 leading to localized level crossing due to Coriolis coupling. Since the v2 and v5 fundamentals are only 8.4cmapart, their overtone levels are coupled by a strong Coriolis interaction and, thus, the same Coriolis coupling must be significant in 2v2 with v2 + v5 and in v2 + v5 with 2v5. Furthermore, a strong Fermi resonance is found in the Vl band since two parallel bands of equal intensity exist; the overtone level involved in the coupling is 2v or 2v5. The v4 band is relatively separate although a Fermi resonance between v4 and 2v5 must be taken into account. Thus, in the present kinetic model, only three levels, 3v3, v4 and v15, are introduced for the levels in the CH stretching vibration region. The conclusion derived in the former experiment s'16 was criticized by Apkarian et al. 1 According to their numerical solution of rate equations, which are formulated for seven excited vibrational levels, 13, V6, V2/VS, 2v3, 2(V2/V5), VX/V4, and 3v3, under the initial condition of 40% CHaF being in the v3 level and the remaining fraction in the ground level, the Vl/V4 level is populated quickly to reach a peak, while 2(VE/Vs) is not, even if the 3v3 Vl/V4 direct V-V energy transfer is included in the kinetic scheme. They attributed this to a small vibrational heat capacity of the 3v3 level relative to that of the Vl/V4 and 2(v2/vs) levels, and suggested that a pathway from 2v3 to 2(v2/vs) via Vx(V3 / v6, 2v6, v3 + v2/vs, etc.) contributed significantly to the population of the levels in the C--H stretching region. Their calculation was extended to the CH3F/Ar mixture, in which we demonstrated very efficient excitation of v4, Vl and other nearby levels in strong laser excitation6, and claimed that their model could not reproduce the rapid accumulation of population in these levels. Thus, they concluded that the 3v3 v4 direct V-V energy transfer could not contribute largely to the entire relaxation in strong laser excitation of CHaF at a low pressure (0.5 Torr) or in a mixture with Ar at a higher pressure (70 Torr). The present kinetic model is essentially similar to the one adopted by Apkarian et a/. 1, although seven excited levels in their model are replaced by 14 levels which include Vx in their notation. The rate equations describing the initial stimulation processes are not included in their model, but, instead, an initial excitation condition is assumed which is almost in accord with the present average number of photons absorbed at a fluence of 0.5 J cm -2 (see Figure 6). The only essential difference in the present calculation from that of Apkarian et al. is that their adopted rate constant for the Vl/V4 2(VE/Vs) V-V energy transfer is much smaller than that for the v4 v125 given in Table IIi. However, this value is possibly larger than those accepted normally because of a very strong interaction between the relevant levels that has been proved by high resolution IR spectroscopy5'6. For the kinetic However, this number has been measured to be as large as 6 in the mixture of 0.12 Torr CH3F and 120 Torr Ar at the laser fluence of 1 J cm-:z. Therefore, the assumed extent of their excitation is very much underestimated, and may not be the basis for discussion of the role of the 3v3 v4 V-V energy transfer in the relaxation. For the excitation and relaxation kinetics of CH3F or other molecules in a dense third body medium will be reported elsewhere. In the present kinetic calculation simulating the experimental data, it has been concluded that a cyclic series of the V-V energy transfers 2v3 vx 2'5/v2 q-Vs/2V2/v1 14 3V3 2'3 plays a significant role in the relaxation of CHaF whose v3 mode is highly excited. The conclusion derived by Apkarian et al. 1 that the 3v3 level may not contribute significantly to the filling of 2(VE/Vs) in either the low or high excitation regime is not consistent with the present finding of non-exponential decay of populations in higher vibrational levels in the final stage of relaxation. As shown in Figure 10(c) and (d), this phenomenon could not be explained by the mechanism without the 3v3 1,'4 V-V energy transfer process. The non-linear type relaxation found in the present experiment was also reported in the LIF kinetic studies 21 of COF2 whose v2 mode is excited by an intense CO2 laser. In weak laser excitation of COF2, which was carried out by Castleton and Flynn22, the LIF at 5/xm rose rapidly by the v2 2v2 intramode ladder climbing to reach a peak, which decayed biexponentially; the fast decay was assigned to V-V energy transfers from Vl, v2 to the other modes, while the final decay was due to the V-T/R process. Contrary to this, in strong laser excitation, the 5-/xm LIF of the final stage of the relaxation decayed non-exponentially; the rate defined from the decay slope became smaller in the later stage of relaxation. This observation is common to the present finding on v3-excited CH3F by the TEA CO2 laser, and might be caused by a mechanism similar to that proposed in this experiment.
The present experiment of strong laser excitation indicates that the mechanism in Eqn (1) must be supplemented by taking into consideration the intermode V-V energy transfers such as 3v3 v4. The kinetic model thus postulated should be applicable to more general cases in the wide range of the extent of laser excitation.
In order to test the applicability of the present kinetic model, the 3-/zm LIF was observed as a function of the laser fluence and compared with kinetic calculations. As shown in Figure 11, at the laser fluence of  Table III with the rate constant of the 3v3 v4 V-V energy transfer of 0(1), 0.46 J cm-2, the emission intensity increased rapidly to form a peak in the initial stage, while at 0.011Jcm -2 its increase is much slower showing an exponential growth. The numerical solutions of the kinetic Eqns (16), (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34) are also presented. The calculation was made by use of the rate constants listed in Table III  As pointed out previously, in the mechanism without the 3v3 v4 V-V energy transfer, the 3-/zm emission intensity increases after an induction period which is almost independent of the laser fluence.
Thus, to simulate the dependence of the 3-/xm emission intensity on the laser fluence, it is inevitable to introduce the 3v3 v4 V-V energy transfer in the mechanism. If the value of k333,4 is assumed to be 5 105S -1 Torr-1, the present kinetic model may reproduce the observed 3-/xm emission of CH3F laser excited with the fluence in the range of 0.01-0.5 J cm2.

CONCLUSION
When CH3F is excited in its v3 mode by irradiation with an intense CO2 laser pulse, the energy flow pathway from v3 to v4, Vl and other nearby levels has been proved to be the pathway in Eqn (1) combined with that in Eqn (2); the former is generally accepted in weak laser excitation, 1/3 16 12, 'V5 2v5, v2 + Vs, 2V2--1/1--1'4 (1) and the latter involves the intermode V-V energy transfer from the high overtone level, 3v3 to v4, which is Coriolis coupled: v3-2v3-* 3v3 v4--Vl--2v2, v2 + v5, 2v (2) The relaxation mechanism of CH3F in strong laser excitation is characterized by the above intermode V-V energy transfer.
In the initial stage of the relaxation of va-excited CH3F by strong laser irradiation, v4, Vl and other nearby levels are populated rapidly to reach a peak, which decays to a second broad maximum or to a plateau depending on the excitation condition. In the final stage of the relaxation, a quasiequilibrium vibrational distribution may not be 176 H. NAKANE AND S. TSUCHIYA established, since a non-linear type relaxation, which is composed of the successive V-V energy transfers from 3v3 to 2v3 through v4, vl, and other closely lying levels, is much more efficient for transferring the vibrational energy to the translation and/or rotation than the V-T/R energy transfer from modes having low vibrational frequencies.
The present kinetic mechanism of non-linear type relaxation could be generalized for the intermode vibrational energy flow of polyatomic molecules whose single mode is excited by strong laser irradiation. Intermode V-V energy transfers from high overtone levels of a laser-excited mode to singly excited levels of other modes play a significant role in causing non-linear relaxation kinetics which are quite different from those normally accepted under low excitation conditions.