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Lifetime of NO C2Π(υ′ = 0)
Volume 56, number 1
CHEMICAL PHYSICS LETTERS
1.5 May 1978
LIFETIME OF NO C 21-l(u’ = 0) Shigeru YAGI, Takumi HIKIDA and Yuji MORI Depnrtment of Chemìstry, Tokyo Instïtute of Technology, Ohokayama, Meguroku, Tokyo, Japan
Receïved 3 November 1977 Revised manuscript receïved 27 January 1978
The lifetime of NO C*n(u’ = 0) was measured by a single photon counting technique usïng a nanosecond light pulser. After deconvolution, the decay rate constant of the predissociating rotational levels, (0.7 + 0.1) X 10’ s-l, and that of the non-predissociating rotational leveis. (7.2 + 2.0) X 10’ s-l, were obtained. The self-quenching rate constant for the nonpredissociating levek of NO C*H(u = 0) was found to be 4.5 X 10” M-’ s-l_
NO C 211(u’ = 0) bas been extensively
studied
from
absorption [ 1-31 and fluorescente spectra 14-91. Some interesting features have been reported with respect to the relaxation of NO CzIl(u’ = 0) by Callear and Pilling [7,8]. They have determïned the rate constants of various relaxation processes of this state from the fluorescente intensity measurements. NO C 211(u’ = 0) involves interestïng problems such as the leve1mïxing with NO B 2113,2(~’ = 7) [9,10], predissociation mechanism, partial quenching [SI, and cascade transition leadlng to the infrared lasïng action [l 11. It is als0 important that predissociation of the C211 states is responsible for the population inversion in the NO laser [12,13]. The lifetime of NO C21T(u’= 0) has been measured usïng synchrotron radiation by Benoist d’Azy et al. [ 14]_ They reported the lifetimes of predissociating rotational levels and non-predissociating levels, which were 3 + 0.3 and 20 f 2.0 r?s, respectively. In thïs letter we report measurements of the lifetime of NO C 211(~’ = 0) excited by a nanosecond flash lamp. Fluorescente decay was measured by a technique of single photon counting. The light source was a coaxial self-triggered light pulser which operated in relaxation mode. Fig. 1 shows a schematic diagram of this pulser. The lamp consists of a resistor (1 MQ), coaxial capacitor (about 200 pF) and two electrodes. The capacitor is composed of a brass rod 10 cm in length and 12 mm in diameter wrapped by a polyester
sT.cRT PULSE N
-
sTAI?u5s
STEL
‘-
__ W)D
8
hasINLEl
&ENCE CEL,.
Fig. 1. Construction of the nanosecond light pulser.
film in thickness of zbout 0.5 mm. The Iight source was ffled with 1.5-2.0 atm nitrogen and operated at 10 kV. It emitted light pulses of 4-7 ns (fwhm) at a repetition rate, 1-2 kHz. The spectral profde of the output pulses was a continuum _md was rather strong at shorter wavelengths down to 180 nm. The light pulses were dispersed through a vacuum ultraviolet monochromator and the monochromatic lïght pulses at 191 .O nm excited NO to NO C 211(u’= 0) with a band width about 2.0 nm. The fluorescente cel1 was directly connected to a VUV monochromator by a fused silica window. The fluorescente from the cell was detected by a photomultiplier (HTV-R106) directly and single photoelectron pulses were used as stop pulses for a time-to-amplitude converter (TAC). Start pulses for the TAC were obtained by monitoring the light source by a combmation of a photomultiplier (HTV-R300) and a fast dïscrîmïnator. All the resuits were deconvoluted using the time 113
1 0
1
1
1
100
200cao
sart% 1
Fig. 2. TypicaI decay curve obtained by 191 nm excitation. Observeddecay curve (a). deconvoluted decay curve @), and convoluted decay cuwe (c) from the decay curve (b). [NO]
=
0.15 torr. profile of the excitation light pulse according to the least squares method reported by Ware et al. [15]. A rypical observed fluorescente decay curve obtained by the 19 1.O nm excitation at [NO] = 0.15 torr, and the result of deconvolution, are shown in fig. 2. The deconvoluted decay curve conslsts of several componen&. These components probably correspond to decay processes such as predissociation of rotational levels exceeding the dissociation limit, radiative transiiion to lower states from NO C 211(u’ = 0), and the 7 band emission resulted from cascade transition. The fastest component is most pronounced and its lifetime is estimated to be about 2 ns by computer simulation. Judging from the lifetime, the fastest component may be attributed to the predissociating rotarional levels of NO C%(u’ = 0). The slowest component is assigned to A%+ resulting from the cascade transition from NO Czll(u = 0) as discussed in the following. The S emission is the most intense in the wavelength region between 190 and 220 nm, while the 7 emission extends to Ionger wavelength than 220 nm. Light filters were used to separate the 7 bands from the 6 band emission. A light filter, Coming 9863 (Fl), partly transmits the light between 240 and 420 nm, and a combination of Corning 9863 and a r-ray irradiated LlF plate [ 161 (F2) removes the light shorter than 260 mn, and Corning 5850 (F3) eliminates below 280 nm. Fig. 3 shows a deconvoiuted decay curve obtained by plating fdters between the cell and the photomultiplier. The curves have a lifetime of about 200 ns, which is in good agreement with the reported lifetime of NO A2Z+ [ 171. The fast rise of the 7 band fhrores114
15 May 1978
CHEMICALPHYSICSLEXTERS
Volume 56, number 1
Fïï_ 3. Deconvoluted decay curve obtaîned by 191.0 runex& tation with light fdters. [NO) = 0.5 torr_ cence indicates that the y bands are induced by the cascade transition of NO C 21T(u’= 0). However, the decay curve in fig. 2 involving the fast rise of the 7 band emission is unsuitable for abstraction of further information. When NO is excited by a light source of contïnuous spectrum, many emission bands of NO appear in the ultraviolet, but the 6(0,1) emission band is contaminated only slightly by the other emission bands. The time profile of the emission intens@ observed at the wavelength of the 6(0,1) band excited directly by the light puker, therefore, is expected to correspond to the decay of NO(C2fI, u’ = 0). FastestCorrponent
, 0
50
i
,
dlF2zcl( OmsEi,
Fig. 4. Typiwl decay curve of the S(O.1) band. [NO]= 0.7 torr. (a) Decay function obtained after deconvolution. Solid lïne shows the decay function of the slow (thïrd) component. (b) Decay function obtaiaed by deduchg the decay functïon of the thïrd component from Ca). Sotid line shows the decay functïon of the fast (second) component (c) Decay function obtaïned by deducing the decay function of the second component from (b).
Volume 56, number 1
CHEMICAL
200 n
1.0 -
0
0
0
0
0
0
08~
o
I
0.5
I
10 NO Prssure
I
15
O
t
20 torr
J
Fig. 5. The dependence of the lifetïme of the fust component on the NO pressure- The average lïfetime is 1.4 + 0.2 ns_
NO was irradïated directly by the light pulser and its fluorescente decay curve was measured through a monochromator with 0.6 nm band-pass (fwhm) at 198.0 nm whïch corresponds to the 6(0,1) emïssion band. Fig. 4 shows a deconvoluted decay curve of the 6(0,1) band at [NO] = 0.7 torr. It consists of three decay components and each rate constant of the three components can be calculated by extrapolation. The lïfetìmes of the first and second components at various NO pressures are shown in fìgs. 5 and 6. The rate constant of the first (fastest) component is independent of the NO pressure while that of the second component is dependent on the pressure. The average lifetime of the first component is 1.4 f 0.2 ns (TI)_ In fig. 6, a least squares treatment on tbe assumption that the plot is a linear function of NO pressure,
0
0
as
4
10
NO Pressure
I
I
15
20
torr
Fig. 6. The varîation of the decay rate of the second component witb the NO presmre. The solïd line was obtained by the least sq~ares method. The slape is 2.4 X 10’ torr-’ s-l and the.intercept is 7.2 X 10’ sW1witb a standard deviation of 2x la’s-‘.
PHYSICS LETTERS
15 May 1978
gives 15.2 + 5.3 ns for the radiative Iifetime of the second component (Ti) and 4.5 X lol1 MW1 .s-t for tbe seif-quenching rate constant of the non-predissociating levels of NO C2lT(u’ = 0). This self-quenchïQg rate constant is in good agreement wíth those by Benoist d’Azy et al., (4.8 + 0.6) X 10” MW1s-l 1’41. The values of 7l (1.4 ns) and 72 (15.2 ns) are also in reasonable agreement (Ti = 3 and ~~ = 20 ns) 1141, although they have detected the fiuorescence decay for whole integrated spectrum 1900-6000 A and ignored the fast rise of the -y bands by cascade transition of NO C211(u’ = 0). C&lear and Pillmg [S] have reported similar results (rl = 0.6 and r2 = 11.6 ns) from the fluorescente ïntensity measurements. The self-quenchïng rate constant for non-predissociating levels of c 2rr(u’ = 0) could be less relïable and subjected to a correction by a factor about 2, though the value is in good agreement with that obtaìned by Benoist d’Azy et ai. [ 141, in view of the large scatter of the data (fig. 6). Callear and Pillïng have reported a value much faster than the present study for the self-quenchïng of C2Il(u’ = 0) 171. Their value, however, has been obtained in a system with argon at very high pressure where the collisional perturbations on rotational levels are signifïctmt and therefore cannot be compared directly wíth the value in the present study. Fig. 7 shows a fraction of the first component obtained from the intercept of the solid lines in fig. 4. The initial population of the first component amounts to 90 f 3% of NO Czn(u’ = 0) _Thïs value is in good agreement with the population of predissociating rotational levels of NO C 211, (u’ = 0) calcualted by asurning a thermal Boltzmann distrïbution in the ground
I 0
(15
15 10 NO Presrure
20
torr
Fig. 7. The dependence of the ratio of the first component in the S(0, 1)band decay on the NO pressure. Thïs shows the ratio of populations of the hier and lower levels than the dissociation limit excited by light absorption.
115
Volume 56, number 1
CHEMICAL PHYSICS LETTERS
state (300 K) and Do = 52400 + 10 cm-l
reported by Callear and Pilling [8]_ In thïa calculation the rotational levels of the ground state are obtrdned by using spectroscopic constants reported by Gillette and Eyster [ 181, on the assumption of Hund’s case (a). The rotational levels of NO C*fI(u = 0) are obtained from the _ absorption spectrum reported by Lagerqvist and Miescher [l ] ignoring the perturbation by B *l&,(u’ = 7) [9]. Relative amplitudes of the Fr + F, or F, + Ft to F, + F, or F2 + F2 transitions were varied from 0.3 to í.0. The variation of this amplitude factor did not affect the results of the calculation, ranging from 88-4 to 88.9%, and from 91.6 to 92% in the case that the dissociation limit was placed between F&5/2) and Ft(7/2), and between F1(7/2) and F2(7/2), respectively. The lifetime of the third (slowest) component is about 35 ns. Since several weak bands appear in the vicinity of the E[O, 1) band and also the contribution of the ihird component to the decay is only about 2%, this component could not be identified.
References [l]
116
A_ Lagerqvïst and E h&scher, Helv. Phys. Acts 32 (1958) 221.
15 May 1978
[2] G.W. Bethke, J. Chem. Phys. 31(1959) 662. 13 ] M. Mandehnan and T. Canïngton, J. Quant_ Spectry. Radiative Transfer 14 (1974) 509. [4] R.A. Young and R.L. SharpIess, Discussions Faraday Sec. 33 (1962) 228. [S ] A.B. CalIear and LW_M. Smith, D-rxussions Faraday Sec. 37 (1964) 96. [6] R.W.F. Gross and N. Cohen, 3. Chem. Phys 48 (1968) 2582. [ 7] A.B. Callear and MJ. PIU@, Trans. Faraday Sec. 66 (1960) 1886. [ 8] A.B. Callear and Ml PiEng, T~~Ix Faraday Sec. 66 (1970) 1618. [9] F. Ackermann and E. Miescher, J. MOL Spectry. 31 (1969) 400. [ 101 E. Miescher, J. MOL Spectry. 53 (1974) 302. 111] M.C. Lm, IEEE J. Quantum Electron. 10 (1974) 5 16. [ 121 H. Huber, Phys. Letters 12 (1964) 102. [13] E. Miescher, J. Mot Spectry. 53 (1974) 302. [ 141 0. Benoist d’Azy, R. López-Delgado and k Tramer, Chem. Phys. 9 (1975) 327. [15] W.R. Ware, L.J. Doemeny andT.L. Nemzek, J. Phys. Chem 77 (1973) 2038. [ 16 ] P. E’ringsheimand P. Yuster, Phys Rev. 78 (1950) 293. [ 171 H. Zacharias, J.B. Halpem and K.H. Welge, Chem. Phys. Letters 43 (1976) 41. [18] R.H. Gillette and E.H. Ëyster, Phys. Rev. 56 (1939) 1113.
CHEMICAL PHYSICS LETTERS
1.5 May 1978
LIFETIME OF NO C 21-l(u’ = 0) Shigeru YAGI, Takumi HIKIDA and Yuji MORI Depnrtment of Chemìstry, Tokyo Instïtute of Technology, Ohokayama, Meguroku, Tokyo, Japan
Receïved 3 November 1977 Revised manuscript receïved 27 January 1978
The lifetime of NO C*n(u’ = 0) was measured by a single photon counting technique usïng a nanosecond light pulser. After deconvolution, the decay rate constant of the predissociating rotational levels, (0.7 + 0.1) X 10’ s-l, and that of the non-predissociating rotational leveis. (7.2 + 2.0) X 10’ s-l, were obtained. The self-quenching rate constant for the nonpredissociating levek of NO C*H(u = 0) was found to be 4.5 X 10” M-’ s-l_
NO C 211(u’ = 0) bas been extensively
studied
from
absorption [ 1-31 and fluorescente spectra 14-91. Some interesting features have been reported with respect to the relaxation of NO CzIl(u’ = 0) by Callear and Pilling [7,8]. They have determïned the rate constants of various relaxation processes of this state from the fluorescente intensity measurements. NO C 211(u’ = 0) involves interestïng problems such as the leve1mïxing with NO B 2113,2(~’ = 7) [9,10], predissociation mechanism, partial quenching [SI, and cascade transition leadlng to the infrared lasïng action [l 11. It is als0 important that predissociation of the C211 states is responsible for the population inversion in the NO laser [12,13]. The lifetime of NO C21T(u’= 0) has been measured usïng synchrotron radiation by Benoist d’Azy et al. [ 14]_ They reported the lifetimes of predissociating rotational levels and non-predissociating levels, which were 3 + 0.3 and 20 f 2.0 r?s, respectively. In thïs letter we report measurements of the lifetime of NO C 211(~’ = 0) excited by a nanosecond flash lamp. Fluorescente decay was measured by a technique of single photon counting. The light source was a coaxial self-triggered light pulser which operated in relaxation mode. Fig. 1 shows a schematic diagram of this pulser. The lamp consists of a resistor (1 MQ), coaxial capacitor (about 200 pF) and two electrodes. The capacitor is composed of a brass rod 10 cm in length and 12 mm in diameter wrapped by a polyester
sT.cRT PULSE N
-
sTAI?u5s
STEL
‘-
__ W)D
8
hasINLEl
&ENCE CEL,.
Fig. 1. Construction of the nanosecond light pulser.
film in thickness of zbout 0.5 mm. The Iight source was ffled with 1.5-2.0 atm nitrogen and operated at 10 kV. It emitted light pulses of 4-7 ns (fwhm) at a repetition rate, 1-2 kHz. The spectral profde of the output pulses was a continuum _md was rather strong at shorter wavelengths down to 180 nm. The light pulses were dispersed through a vacuum ultraviolet monochromator and the monochromatic lïght pulses at 191 .O nm excited NO to NO C 211(u’= 0) with a band width about 2.0 nm. The fluorescente cel1 was directly connected to a VUV monochromator by a fused silica window. The fluorescente from the cell was detected by a photomultiplier (HTV-R106) directly and single photoelectron pulses were used as stop pulses for a time-to-amplitude converter (TAC). Start pulses for the TAC were obtained by monitoring the light source by a combmation of a photomultiplier (HTV-R300) and a fast dïscrîmïnator. All the resuits were deconvoluted using the time 113
1 0
1
1
1
100
200cao
sart% 1
Fig. 2. TypicaI decay curve obtained by 191 nm excitation. Observeddecay curve (a). deconvoluted decay curve @), and convoluted decay cuwe (c) from the decay curve (b). [NO]
=
0.15 torr. profile of the excitation light pulse according to the least squares method reported by Ware et al. [15]. A rypical observed fluorescente decay curve obtained by the 19 1.O nm excitation at [NO] = 0.15 torr, and the result of deconvolution, are shown in fig. 2. The deconvoluted decay curve conslsts of several componen&. These components probably correspond to decay processes such as predissociation of rotational levels exceeding the dissociation limit, radiative transiiion to lower states from NO C 211(u’ = 0), and the 7 band emission resulted from cascade transition. The fastest component is most pronounced and its lifetime is estimated to be about 2 ns by computer simulation. Judging from the lifetime, the fastest component may be attributed to the predissociating rotarional levels of NO C%(u’ = 0). The slowest component is assigned to A%+ resulting from the cascade transition from NO Czll(u = 0) as discussed in the following. The S emission is the most intense in the wavelength region between 190 and 220 nm, while the 7 emission extends to Ionger wavelength than 220 nm. Light filters were used to separate the 7 bands from the 6 band emission. A light filter, Coming 9863 (Fl), partly transmits the light between 240 and 420 nm, and a combination of Corning 9863 and a r-ray irradiated LlF plate [ 161 (F2) removes the light shorter than 260 mn, and Corning 5850 (F3) eliminates below 280 nm. Fig. 3 shows a deconvoiuted decay curve obtained by plating fdters between the cell and the photomultiplier. The curves have a lifetime of about 200 ns, which is in good agreement with the reported lifetime of NO A2Z+ [ 171. The fast rise of the 7 band fhrores114
15 May 1978
CHEMICALPHYSICSLEXTERS
Volume 56, number 1
Fïï_ 3. Deconvoluted decay curve obtaîned by 191.0 runex& tation with light fdters. [NO) = 0.5 torr_ cence indicates that the y bands are induced by the cascade transition of NO C 21T(u’= 0). However, the decay curve in fig. 2 involving the fast rise of the 7 band emission is unsuitable for abstraction of further information. When NO is excited by a light source of contïnuous spectrum, many emission bands of NO appear in the ultraviolet, but the 6(0,1) emission band is contaminated only slightly by the other emission bands. The time profile of the emission intens@ observed at the wavelength of the 6(0,1) band excited directly by the light puker, therefore, is expected to correspond to the decay of NO(C2fI, u’ = 0). FastestCorrponent
, 0
50
i
,
dlF2zcl( OmsEi,
Fig. 4. Typiwl decay curve of the S(O.1) band. [NO]= 0.7 torr. (a) Decay function obtained after deconvolution. Solid lïne shows the decay function of the slow (thïrd) component. (b) Decay function obtaiaed by deduchg the decay functïon of the thïrd component from Ca). Sotid line shows the decay functïon of the fast (second) component (c) Decay function obtaïned by deducing the decay function of the second component from (b).
Volume 56, number 1
CHEMICAL
200 n
1.0 -
0
0
0
0
0
0
08~
o
I
0.5
I
10 NO Prssure
I
15
O
t
20 torr
J
Fig. 5. The dependence of the lifetïme of the fust component on the NO pressure- The average lïfetime is 1.4 + 0.2 ns_
NO was irradïated directly by the light pulser and its fluorescente decay curve was measured through a monochromator with 0.6 nm band-pass (fwhm) at 198.0 nm whïch corresponds to the 6(0,1) emïssion band. Fig. 4 shows a deconvoluted decay curve of the 6(0,1) band at [NO] = 0.7 torr. It consists of three decay components and each rate constant of the three components can be calculated by extrapolation. The lïfetìmes of the first and second components at various NO pressures are shown in fìgs. 5 and 6. The rate constant of the first (fastest) component is independent of the NO pressure while that of the second component is dependent on the pressure. The average lifetime of the first component is 1.4 f 0.2 ns (TI)_ In fig. 6, a least squares treatment on tbe assumption that the plot is a linear function of NO pressure,
0
0
as
4
10
NO Pressure
I
I
15
20
torr
Fig. 6. The varîation of the decay rate of the second component witb the NO presmre. The solïd line was obtained by the least sq~ares method. The slape is 2.4 X 10’ torr-’ s-l and the.intercept is 7.2 X 10’ sW1witb a standard deviation of 2x la’s-‘.
PHYSICS LETTERS
15 May 1978
gives 15.2 + 5.3 ns for the radiative Iifetime of the second component (Ti) and 4.5 X lol1 MW1 .s-t for tbe seif-quenching rate constant of the non-predissociating levels of NO C2lT(u’ = 0). This self-quenchïQg rate constant is in good agreement wíth those by Benoist d’Azy et al., (4.8 + 0.6) X 10” MW1s-l 1’41. The values of 7l (1.4 ns) and 72 (15.2 ns) are also in reasonable agreement (Ti = 3 and ~~ = 20 ns) 1141, although they have detected the fiuorescence decay for whole integrated spectrum 1900-6000 A and ignored the fast rise of the -y bands by cascade transition of NO C211(u’ = 0). C&lear and Pillmg [S] have reported similar results (rl = 0.6 and r2 = 11.6 ns) from the fluorescente ïntensity measurements. The self-quenchïng rate constant for non-predissociating levels of c 2rr(u’ = 0) could be less relïable and subjected to a correction by a factor about 2, though the value is in good agreement with that obtaìned by Benoist d’Azy et ai. [ 141, in view of the large scatter of the data (fig. 6). Callear and Pillïng have reported a value much faster than the present study for the self-quenchïng of C2Il(u’ = 0) 171. Their value, however, has been obtained in a system with argon at very high pressure where the collisional perturbations on rotational levels are signifïctmt and therefore cannot be compared directly wíth the value in the present study. Fig. 7 shows a fraction of the first component obtained from the intercept of the solid lines in fig. 4. The initial population of the first component amounts to 90 f 3% of NO Czn(u’ = 0) _Thïs value is in good agreement with the population of predissociating rotational levels of NO C 211, (u’ = 0) calcualted by asurning a thermal Boltzmann distrïbution in the ground
I 0
(15
15 10 NO Presrure
20
torr
Fig. 7. The dependence of the ratio of the first component in the S(0, 1)band decay on the NO pressure. Thïs shows the ratio of populations of the hier and lower levels than the dissociation limit excited by light absorption.
115
Volume 56, number 1
CHEMICAL PHYSICS LETTERS
state (300 K) and Do = 52400 + 10 cm-l
reported by Callear and Pilling [8]_ In thïa calculation the rotational levels of the ground state are obtrdned by using spectroscopic constants reported by Gillette and Eyster [ 181, on the assumption of Hund’s case (a). The rotational levels of NO C*fI(u = 0) are obtained from the _ absorption spectrum reported by Lagerqvist and Miescher [l ] ignoring the perturbation by B *l&,(u’ = 7) [9]. Relative amplitudes of the Fr + F, or F, + Ft to F, + F, or F2 + F2 transitions were varied from 0.3 to í.0. The variation of this amplitude factor did not affect the results of the calculation, ranging from 88-4 to 88.9%, and from 91.6 to 92% in the case that the dissociation limit was placed between F&5/2) and Ft(7/2), and between F1(7/2) and F2(7/2), respectively. The lifetime of the third (slowest) component is about 35 ns. Since several weak bands appear in the vicinity of the E[O, 1) band and also the contribution of the ihird component to the decay is only about 2%, this component could not be identified.
References [l]
116
A_ Lagerqvïst and E h&scher, Helv. Phys. Acts 32 (1958) 221.
15 May 1978
[2] G.W. Bethke, J. Chem. Phys. 31(1959) 662. 13 ] M. Mandehnan and T. Canïngton, J. Quant_ Spectry. Radiative Transfer 14 (1974) 509. [4] R.A. Young and R.L. SharpIess, Discussions Faraday Sec. 33 (1962) 228. [S ] A.B. CalIear and LW_M. Smith, D-rxussions Faraday Sec. 37 (1964) 96. [6] R.W.F. Gross and N. Cohen, 3. Chem. Phys 48 (1968) 2582. [ 7] A.B. Callear and MJ. PIU@, Trans. Faraday Sec. 66 (1960) 1886. [ 8] A.B. Callear and Ml PiEng, T~~Ix Faraday Sec. 66 (1970) 1618. [9] F. Ackermann and E. Miescher, J. MOL Spectry. 31 (1969) 400. [ 101 E. Miescher, J. MOL Spectry. 53 (1974) 302. 111] M.C. Lm, IEEE J. Quantum Electron. 10 (1974) 5 16. [ 121 H. Huber, Phys. Letters 12 (1964) 102. [13] E. Miescher, J. Mot Spectry. 53 (1974) 302. [ 141 0. Benoist d’Azy, R. López-Delgado and k Tramer, Chem. Phys. 9 (1975) 327. [15] W.R. Ware, L.J. Doemeny andT.L. Nemzek, J. Phys. Chem 77 (1973) 2038. [ 16 ] P. E’ringsheimand P. Yuster, Phys Rev. 78 (1950) 293. [ 171 H. Zacharias, J.B. Halpem and K.H. Welge, Chem. Phys. Letters 43 (1976) 41. [18] R.H. Gillette and E.H. Ëyster, Phys. Rev. 56 (1939) 1113.