The Mechanism of Occurrence of Dual Fluorescence in Intermediate Case Molecules as Viewed from Rotational Effects

Fluorescence decays of jet-cooled pyrazine excited at various positions of rovibronic transitions within the 0-0 band were measured by the use of a pulsed dye laser pumped by an excimer or a nitrogen laser. The experimental data thus obtained on the number (N) of the triplet states coupled to the initially excited singlet rovibronic state were analyzed and interpreted by the aid of computer simulation using an asymmetric rotor program. The results indicate that the extraordinarily great variation of N with excitation energy and unreasonably small values of N hitherto reported in the literature can be understood in terms of the conventional theory based on the singlet-triplet mixed state model which has been developed for elucidating the mechanism of the occurrence of dual fluorescence in intermediate case molecules. the fluorescence characteristics of under in a jet, analyzed the resulting experimental data by the aid of computer simulation using an asymmetric rotor program.


INTRODUCTION
Under collision-free conditions, molecules with intermediate case level structure, such as pyrazine 1'2 and pyrimidine3-5, are known to exhibit dual fluorescence consisting of fast and slowly decaying components, which give one and the same spectrum. The decay of the fluorescence can thus be expressed in the form: It) Cx exp (-t/r) + Ca exp (-t/r) (1) 213 where IF(t) means the fluorescence intensity as a function of time.
Here, and from now on, the subscripts 1 and 2 refer to the fast and slow fluorescence components, respectively. Hence, "t" < "t" 2 in Eqn (1): The biexponential decay of fluorescence in intermediate case molecules has been interpreted theoretically in terms of a singlet-triplet mixed state model. This model was first proposed by Lahmani, Tramer, Tric and Delory6'7, and was adopted by several groups of authors2-5'8-11. The basic ideas underlying the mixed state model are as follows6: (i) coherent excitation of mixed states, which result from coupling of an excited singlet (ro)vibronic state with a manifold of triplet (ro)vibronic states, prepares the singlet (ro)vibronic state concerned; (ii) owing to phase dismatching or dephasing, the initially prepared singlet (ro)vibronic state exhibits a fast exponential decay; (iii) this decay is followed by a quasiexponential slow decay due to a superposition of incoherent decays of individual mixed states.
The present paper deals with two problems concerning the mechanism of occurrence of the dual fluorescence in intermediate case molecules. One problem is that a new mechanism has recently been proposed by Kommandeur and his research group 12 to explain the results of their experiments on the effect of molecular rotation on the dual fluorescence. Their mechanism involves light scattering and is entirely different from the singlet-triplet mixed state mechanism by Lahmani et al 6. The other problem is concerned with the number of triplet states to which the initially prepared singlet state is effectively coupled. According to the mixed state mechanism, this number (N) should be significantly larger than unity. However, the values of N reported by more than a few authors for some excited rovibronic states of intermediate case molecules are close to, or even smaller than, unity.
In order to settle these problems, the details of which are given in the next section, we have re-examined the fluorescence characteristics of pyrazine under collision-free conditions in a supersonic jet, and have analyzed the resulting experimental data by the aid of computer simulation using an asymmetric rotor program.
IITAII.$ O1: THI IIOBI.III$ Let us consider an intermediate case molecule4-6. The lowest excited singlet electronic state and a lower-lying triplet electronic state of the molecule will be called $1 and T, respectively. A vibronic state in $1, which can be reached by optical excitation from the ground state, and a manifold of vibronic states in T will be denoted by IS) and {[Tj) }, respectively. The total energy widths of IS) and IT), denoted by 7s and 7r, respectively, are written as: where Fs and Fr represent radiative widths, and 7s R and R represent non-radiative widths, Fr and R being assumed to be independent of].
The coupling of IS) and {ITj) } leads to the following quasistationary mixed states" N j=l (4) with n 1, 2, N + 1. As was mentioned previously, N is the number of triplet vibronic states {IT}} to which IS} is effectively coupled. Owing to the above coupling, broadening of the IS) level occurs to give a linewidth denoted by Asr (fwhm). On the assumption that the triplet vibronic states {I T} } are uniformly spaced and that the coupling matrix elements are constant, independent of the index j, the broadening is represented by a Lorentzian line shape. In such a case, Asr is given by Asr 2;rV2srpr (5) where Vsr is the constant coupling matrix element, and pr is the density of the vibronic states {ITJ} }. In the foregoing descriptions, it has been presumed that vsrpr >> 1 (strong coupling). In the case of the Lorentzian line broadening, the number of effectively coupled triplet states, N, is given by N lf2j/pTAst (6) which, using Eqn (5), is rewritten as6'1'13.
N XZsp (7) The excited state which is initially prepared by coherent excitation of the set of mixed states { In) } is identical with the zero-order singlet state [S). The subsequent change in [S) content of the excited state can be described approximately as a sum of two exponential decays, corresponding to fast (coherent) and slow (incoherent) decays, as given by Eqn (1).
We assume here that N>> 1 and Asr>> Ys. The former relation follows from Eqn (7) and the relation VsrpT>> 1, and the latter is known to be valid for pyrazine13, pyrimidine 13  It may be noted here that integration of the first and second terms on the right-hand side of Eqn (1) with respect to between 0 and o gives Cl"g'l and C2r2, which correspond to (I) and q2, respectively. In the foregoing theoretical treatment, we have regarded the coupling states IS) and (] T) ) as vibronic without giving due consideration to the role of molecular rotation in the singlet-triplet coupling or in the electronic relaxation. However, the experimental value of PT is often too large to match the triplet vibronic density evaluated theoreto ically-5's-  (14) where Pr is the density of the vibronic states. Furthermore, by means of high-resolution emission spectroscopy, Baba el al. 5 observed that the fluorescence quantum yields of pyrazine and pyrimidine vapors vary greatly with the rotational level excited. Since then, several groups of authors 11 (2) only the slow fluorescence component is affected by molecular rotation. As has been mentioned, however, at least two problems remain to be settled. Kommandeur and.his coworkers 2 studied fluorescence characteristics of pyrazine in a supersonic jet, excited at various rovibronic transitions within the 0-0 band, using a pulsed and frequency-doubled dye laser as an exciting light source (pulse duration, several nanoseconds). The bandwidth of the laser (<0.1 cm-1) is such that the individual rovibronic absorption lines in the P and R branches, each of which is characterized by J' and is a superposition of all possible AK 0 transitions, can be resolved. They observed that the ratio of the pre-exponential factors C1/C2 (Eqn (1)) increases linearly with increasing J'.
In addition to the above observation, Kommandeur et al. found an interesting fact concerning the behavior of the magnitude of C1/C2. According to these authors, the value of C1/C2 resulting from excitation at the top of an absorption line in the P or R branch is an order of magnitude smaller than the one resulting from excitation at the bottom between that line and a neighboring line. Furthermore, on the side of the absorption line, the C1/Cz ratio has a value intermediate between those at the top and bottom. They observed such behavior of C1/C2 for various lines belonging to the P and R branches up to P(4) and R(9), the numbers in the parentheses denoting the J" values of the ground state.
According to Eqn (12), the above experimental results mean that the number of coupled levels N varies by a factor of more than 10 within a narrow wave number range of 0.2cm-1. Kommandeur regarded this as highly improbable, and considered that the fast component cannot be due to biexponential decay arising from intermediate case level structure, as it is conventionally understood from the viewpoint of the theory by Lahmani et al. Thus, he proposed an entirely new mechanism, i.e. the fast component actually originates from non-resonant light scattering (NRLS) 12. In his view, the azines, including pyrazine, are basically small molecules, and most of the experiments on the decay and quantum yield of the fast component can be explained when NRLS is included.
Recent experiments on the emission .decay of pyrazine with picosecond time resolution have shown that the fast component is a real fluorescence and is not due to light scattering11'35. The question will then be raised as to how one can explain the experimental results of Kommandeur et al2. It should be pointed out in this connection that the explanation by Kommandeur is based on the presumption that pyrazine can be treated satisfactorily as a symmetric top. In our opinion, the pyrazine molecule is actually an asymmetric top, and the deviation from the symmetric top may have an unexpectedly large effect on electronic relaxation processes in that molecule17.
We now turn to the problem of the number (N) of effectively coupled triplet states. This number is of crucial importance in the theory of Lahmani et al., as has been shown previously. For a molecule belonging to the intermediate case, the relation N>> 1, or at least N > 1, should be satisfied. The values of N that have been reported by several groups of authors for pyrazine are widely different from one another and, in some cases, the N values are smaller than unity. The situation can be seen by reference to Table I, in which the reported values of N are collected.
The value of N may change with the sample conditions such as pressure and temperature and also with the instrumental conditions such as the pulse duration or spectral bandwidth of the exciting light. Furthermore, the apparent value of C1/Ca would change with the response time or the time resolution of the detector system employed. In this study, therefore, we have directed particular attention to these experimental conditions.

EXPERIMENTAL
The experimental apparatus for measuring fluorescence-excitation spectra and fluorescence decays in a pulsed supersonic jet has been described elsewhere36. Pyrazine vapor of about 5 Torr seeded in helium (several hundred Torr) was expanded into a vacuum chamber at about 10 -5 Torr through the 400-/xm orifice of a nozzle.
In order to carry out selective excitation into rovibronic levels characterized by the rotational quantum number J', a tunable dye laser (Lambda Physik FL 2002 E) pumped by a XeCI excimer laser (Lambda Physik EMG 103 MSC) and combined with an angle-tuned etalon (free spectral range 1 cm-1) was used as an exciting light source with rhodamine 640 as the dye. The frequency of the dye laser was doubled by a potassium dihydrogenphosphate (KDP) crystal. The resulting ultraviolet (UV) pulses, which were used for exciting the sample, have a duration of 10ns and an effective bandwidth of 0.1cm-a. The wavelength of the UV light was scanned with a 0.02 cm -a step by using a portable computer (Olivetti M10).
A tunable dye laser (Molectron DL14) pumped by a nitrogen laser (Molectron UV22), which is the same as the one used as an excitation experimental conditions. The UV pulses generated by a KDP crystal have a duration of 3 ns and a bandwidth of 0.5 cm-1, as reported previously13.
The laser beam crossed the supersonic jet, synchronized with the laser with a repetition rate of 20 Hz, at 22 mm downstream from the nozzle. The fluorescence was viewed at right angles to the direction of propagation both of the laser beam and of the jet beam. The total fluorescence was monitored with a photomultiplier (Hamamatsu Photonics R106) to obtain the fluorescence excitation spectra and fluorescence decays. The detector system was the same as described in previous papers13--16'36. The laser wavelength was tuned to a given position within the absorption spectrum in the following way: the laser is scanned with a 0.02cm -1 step and the fluorescence-excitation spectrum is recorded until the top of a rovibronic absorption line or the bottom between two neighboring lines is reached. Since, in the latter case, the fluorescence was very weak, the intensity of the scattered light, which can be evaluated by trapping the sample using liquid nitrogen, was reduced to a reasonably low level by using UV filters (Toshiba UV35 and UV37).

SIMULATION
The absorption and fluorescence-excitation spectra and the average of the rotational quantum number J' for the excited state $1, ]', as a function of excitation frequency v were simulated by using, unless otherwise stated, an asymmetric rotor program17. Here J' is defined as: j, is the probability that a molecule is excited into a rotational level with rotational quantum numbers J', K, and K at an excitation frequency of v and at a temperature of T; the sum is taken over all the appropriate values of J', K and K. Detailed procedures for simulation are described below.
First, the frequency and intensity are calculated for each of the rovibronic absorption transitions by the use of the following rotational constants reported by Innes et al. 37" A"'-0.21285, B"= 0.19767 and C"= 0.10249cm -1 for the zero point vibrational level in So; A' 0.21122, B' 0.19678 and C' 0.10113 cm -1 for the same level in S 1. Then, a certain number of points are taken which are uniformly spaced along the v axis between -5 and 5 cm -1 (or between -30 and 30 cm-'X), with 0 taken at the band origin. At each point, i.e. at each frequency v, the intensities of rovibronic absorption transitions whose energies lie in the excitation bandwidth with its center at that point are summed up on the assumption that the exciting light has a triangular band shape; a simulated absorption spectrum is thus obtained.
Since the quantum yield of the fast component of fluorescence is known to be independent of the rotational level excited3, the excitation spectrum of the fast fluorescence can be regarded as identical to the absorption spectrum. On the other hand, the quantum yield of the slow component of fluorescence depends on the rotational level excited, and is proportional to (2J'+ 1) -1 13,17,34. In addition, the fluorescence of pyrazine is dominated by the slow component at low temperatures34, e.g. <30K. Accordingly, the excitation spectra of pyrazine at temperatures below 10 K were simulated by calculating the corresponding absorption spectra after each of the intensities of the rovibronic transitions concerned was multiplied by (2J' + 1) -1.
The average quantum number ]' as a ,function of v, which may be called a ]' spectrum, was simulated in a manner similar to those in which the absorption and excitation spectra were calculated.
When the pyrazine molecule was treated as an approximately symmetric top, a computer program was used which is similar to the asymmetric rotor program described above17. In such a case, mean rotational constants B" (A" + B")/2 and B' (A' + B')/2 were used.

RESULTS
All the results given below are concerned with the fluorescence generated by excitation within the 0-0 absorption band of jet-cooled pyrazine. For the results shown in Figures 1-3, the excitation bandwidth is 0.1 cm -1 and the rotational temperature of pyrazine is estimated to be 3 K (see below); for the results shown in Figures 4--6, the bandwidth is 0.5 cm-1.  Figure 2. For each of the observed decay curves, the integrated fluorescence intensities were evaluated which are to be assigned to the fast and slow fluorescence components, and the ratio between the resulting integrated intensities was regarded as the fluorescence quantum yield ratio, @1/@2. The value of @1/@2 was then multiplied by the lifetime ratio 2/1 to give N according to Eqn (13).  As is seen in Figure 1, the values of N vary markedly according to whether the excitation position is tuned to the top or to the bottom of the absorption lines belonging to ,both the P and the R branch.
Absorption and fluorescence-excitation spectra were simulated by the use of the asymmetric rotor program described in the preceding section. The spectral bandwidth was taken as 0.1 cm -1, while the temperature was changed from 2 to 10 K. The shapes of both spectra are sensitive to the temperature. It was found that the observed and calculated excitation spectra agree reasonably well with each other at 3 K. Figure 3 shows calculated absorption and excitation spectra for a bandwidth of 0.1 cm -1 and a temperature of 3 K. Under the same conditions, the average value of J', i.e. J', was calculated as a function of excitation wave number, yielding a J' spectrum. The results are also shown in Figure 3. In order to facilitate comparison with previously reported values of N (Table 1)13, additional N values for jet-cooled pyrazine were determined from decay curves that were measured with a greater excitation bandwidth of about 0.5 cm-1, using the nitrogen laser as a pumping light source. The procedure for determining N is based on Eqn (!3), and is the same as that described in the case of the smaller bandwidth of 0.1 cm- (Figure 1). The N values thus determined are shown in Figure   4 with open circles; in this case, the rotational temperature is estimated to be somewhat lower than 10 K. In connection with the experimental results given in Figure 4, calculations of jr, at different temperatures were performed as a function of excitation wave number, with the bandwidth fixed at 0.5 cm-1, using the asymmetric and symmetric rotor programs. The results are shown in Figures 5 and 6, respectively.

DISCUSSION
In the present experiments, the values of N were determined on the basis of Eqn (13). It is to be recalled, however, that the fundamental equations such as Eqns (8) AsT-+ 7s. Furthermore, Eqn (12) is valid only if the ratio C1/C2 is obtained from the fluorescence decay which is measured by means of a detector system with a sufficiently fast response. The value of N which is determined either from Eqn (12) or from Eqn (13) using the data obtained under the ideal instrumental conditions mentioned above, can be regarded as "intrinsic" in the sense that it represents the number Nwhich is inherent to the molecular level IS) concerned and is given by Eqns (6) or (7).
Here we are interested in the intrinsic number N and also in the is also shown for reference. Excitation bandwidth is 0.5 cm -1 in every case.
intrinsic lifetime of the fast fluorescence, i.e. :1 given by Eqn (8). In general, however, it is very difficult to determine directly and precisely these intrinsic quantities under perfect coherent excitation and perfect response. Thus, for pyrazine, if the pulse duration :pd is of the order of 1 ns, i.e. if the coherence bandwidth of the exciting light is smaller than Asr+ 7s, then the apparently observed :1 value will become equal to the value of :pa which is evidently larger than the intrinsic value (-100 ps). Also, the observed ratio C/C2 will become correspondingly small compared with the intrinsic value of C/C2. These arguments apply to the present experiments as well as to the experiments by some other authors (see Table I).
In our previous paper3, we pointed out the following: when the coherence bandwidth of the exciting light is (Asr + 7s), with g" being smaller than unity (narrow coherence bandwidth), IF(t) in Eqn (1) is changed to If'(t) which is expressed approximately in the form: Ie'(t) ffC1 exp (--fit/J1) "+" C2 exp (-t/r2) where C1, "t'l, C2 and :2 are the same as those given in Eqn (1). Thus, for the fast component of fluorescence the pre-exponential factor is reduced to gC1 and the lifetime is lengthened to :l/g, but for the slow component both quantities remain unchanged. As a result, in the case of narrow coherence bandwidth excitation, the number of effectively coupled triplet states, N', is given by N' C1/C2--N (16) On the other hand it follows from Eqn (15) that, on narrowing the coherence bandwidth of the exciting light, both and 2 remain unchangeda3. Accordingly, if 1/2 is evaluated from data on the fluorescence spectrum or decay obtained by narrow coherence bandwidth excitation, and if the values of intrinsic lifetime 1 and 2 are known, the intrinsic number N can be found from Eqn (13).
The data for N shown in Figure 1, along with the decay data given in Figure 2, clearly indicate that there is a marked tendency for N to be particularly large when the excitation is made at the bottom between two neighboring absorption lines. This observation is the same as that reported by Kommandeur et al.2, except that their N values, which were obtained by a different method, are smaller than ours by a factor of about 10.
The variation of the observed N value with excitation energy ( Figure   1) appears to be closely related to the variation of the ' value calculated by means of computer simulation (Figure 3). In fact, J' shows minima at the tops of absorption lines and maxima at the bottoms between successive lines.
For the 0 vibronic state of pyrazine, rl is nearly independent of the rotational level excited. It then follows from Eqn (8) that Asr is also independent of the rotational level, since Asr >> Ys. Therefore, substituting Eqn (14) into Eqn (6) yields: N(2J'+ 1) or N(J'+ 1/2) Here PTv is assumed to be a constant for a given vibronic state. Thus, except for the constant term of 1/2, N is proportional to the quantum number J', which may be replaced by J'. Evidently, this linear (or approximately proportional) relation between N and J' favors the fact that N and J' vary in similar ways across the 0--0 vibronic band (Figures   1 and 3).
It should be emphasized here that, if the pyrazine molecule is treated as a symmetric top, J' will increase simply as the excitation wave number increases in the R branch (decreases in the P branch), Since the pyrazine molecule is actually an asymmetric top, mixing must occur among rotational levels which the molecule would have if it were a symmetric top. As a result, the vibronic band concerned may have a complicated rotational structure in which a large number of weak, irregular transitions to rotational levels of high J' are superimposed on the regular transitions associated with the "parent" symmetric top. This is. the reason why the calculated j' spectrum shows the complex pattern seen in Figure 3.
In this way the observed variation of N across the vibronic band can be understood in terms of Eqn (17), which is based on the S-T mixed state model, without resorting to such a new theory as Kommandeur proposed. Closer inspection of Figures 1 and 3, however, will reveal that quantitatively a deviation occurs from the linear relation between N and j'mfor excitation at the tops of the absorption lines, an approximately linear relation is found to exist between N and J', but the N values at the bottoms are evidently larger than those inferred, using Eqn (17), from the N values at the tops. One of the reasons for this deviation is probably that our simulation is not satisfactory enough to produce quantitatively good results.
We now proceed to the discussion of the number of effectively coupled triplet states, N. In Table I  The values of N in Table I are confined, for the sake of simplicity, to those obtained by excitation in the R branch region. The values in columns I and II were taken from the experimental data shown in Figures 1 and 4, respectively. The values of N are found to be widely different, as has been pointed out.
The N values in column V for the bulk gas of pyrazine at room temperature (298 K) 13 were obtained by us under the same instrumental conditions as those in column Ilmnevertheless, it is seen that those in column II are significantly smaller than those in column V. The question will then be raised as to whether or not the difference between the N values is caused solely by the difference between the temperatures of the samples.
Let the low temperature of the jet sample be denoted by T1, and the high temperature of the bulk gas sample by T2. If it is assumed that Eqn (17) holds, then for a given excitation wave number the number N at T1 is related to that at T2 as follows" 2,]'(T1) + 1 N(T2) (18) N(T1) ;(T2) + 1 with T2 fixed at 298 K, the values of N(T1) were calculated for T1 10 and 1 K, using the values of]' as given in Figure 5 and also the values of N(T2) given in column V of Table I; for the details of the N(T2) values, see Figure 8 in Baba et a113. The results shown in Figure 4 as well as in columns III and IV of Table I Figure 4 and column II of Table I) fall roughly between N(T 10 K) and N(T 1 K). This means that the difference in N between the jet and bulk gas samples is largely attributable to the difference in temperature between the two samples.
As is seen from Figure 6, the jr,_9 curves (with , denoting excitation wave number) at different temperatures are practically the same in the R branch region, except for the positions very near the band origin, and J' increases monotonously with increasing ,. If, therefore, the pyrazine molecule is regarded as a symmetric top, Eqn (18) will predict that N(T1) is practically equal to N(T2); in other words, N does not depend on temperature. On the other hand, in the case of the asymmetric top ( Figure 5), J' for < 5 cm -1 in the R branch region increases with increasing temperature, and at higher temperatures the j'-9 curves varies in a complicated manner, giving two minima (at , 0 and 2 cmfor 298 K). Such behavior ofJ' as a function of , and T accounts for our experimental observation 13 that, at high temperatures, N has relatively large values and varies in a somewhat complicated manner even in the region of the R branch which is isolated from the Q and P branches. The N data in the remaining columns, VI-XII, of Table I were all obtained for jet-cooled pyrazine. The values of N in column VI were calculated by the use of an empirical relation 34 between N and J': Amirav and Jortner 34 derived this equation by combining an empirical relationship between the absolute fluorescence quantum yield of pyrazine and J' with the theoretical relationships given by Eqns (10) and (11) of this paper. These authors measured the fluorescence quantum yields using a chaotic light source for excitation. They assumed that Eqn (19) holds for J' [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The values in parentheses in column VI result from application of Eqn (19) to cases in which J' is smaller than 5. The N values in column VI are found to agree roughly with the corresponding values obtained in the present study (columns I and II).
In contrast to this, the N values in columns VII-XI, which were all obtained by evaluating the ratios C1/C:z directly from crude fluorescence decay curves, are one to three orders of magnitude smaller than the values obtained by the present authors and by Amirav and Jortner, the latter values being considered to represent (approximately) the intrinsic N values. Owing to the slow response of the detector systems employed, the crude decay curves mentioned above led to C values smaller than the true ones. Furthermore, although the N data in columns IX and XI were obtained using picosecond laser pulses for excitation, the data in columns VII, VIII and X were obtained using nanosecond laser pulses. Evidently, therefore, in the latter three cases the crude decay curves cannot give the intrinsic values of C1/C2 (=N).
These arguments account for the fact that the N values in columns VII-XI are much smaller than the intrinsic values. We now turn our attention to the N values in column XII, which were derived from the spectra of the molecular eigenstates (ME) of $1 pyrazine. The ME spectra were measured by Kommandeur and colleagues 21'22 under high resolution conditions (10-3cm-1). The values in column XII are the numbers of rovibronic states counted in their ME spectra. Taking account of possible AK 0 transitions, Kommandeur and colleagues 22 divided the above numbers by 2J'-i (in the case of the R branch) to obtain the N values with which we are concerned in Table I. However, with the resolution and sensitivity in their spectral measurements, some of the eigenstates may possibly have been missed from the ME spectra. In addition, if the symmetric top approximation is employed, the energy separation between successive AK 0 transitions in pyrazine is estimated to be less than 10 -3 cm -a for R(1)-R(3) a3. It is then conceivable that the AK =0 transitions were not resolved under their experimental conditions. In view of these circumstances, the values given in column XII have not been divided by 2J'-l. It is seen that these N values in column XII are significantly large compared with those in columns VII-XI. Lastly, mention should be made of the polarization of the fluorescence from azabenzenes including pyrazine. It has been found recently that the fluorescence of these molecules exhibits polarization, the characteristics of which depend on the initially excited rotational level33. In general, therefore, in such experiments as were designed in the present study, the polarization effect must be taken into account. We have examined this effect by measuring the decays of the parallel and perpendicularly polarized components of fluorescence from jetcooled pyrazine. The results indicate that, so far as the excitation within the 0-0 absorption band is concerned, there is no significant difference between, the two decay curves observed. This means that the fluorescence polarization has practically no effect on the experimental results obtained in the present study and hence on the conclusions derived from these results.

CONCLUSION
Analyses of the results of the present experiments on pyrazine as a typical representative of intermediate case molecules have revealed that the two problems concerned in this paper, i.e. the extraordinarily great variation of N with excitation energy and unreasonably small values of N hitherto reported in the literature, can be understood at least qualitatively within the framework of the conventional theory based on the S-T mixed state model.
It should be emphasized that, in order to investigate the effects of molecular rotation on electronic relaxation phenomena, one must treat the pyrazine molecule exactly as an asymmetric top, without assuming it to be an approximately symmetric rotor. This observation is important especially when the position of the exciting light is close to the band origin.