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Formation of NH(A 3Πi) in the flash photolysis of HN3 at 121.6 nm. Role of N2 triplet states
Vohxne
116, number 5
CHEMICAL
PHYSICS
FORMATION OF NH(A311i) IN THEt FLASH AT 121.6 sun. ROLE OF N2 TRIPLET STATES Y. MARUYAMA, Deptifmenl
of
T. HIKIDA
Chemislty,
Tokyo InsMule
LETTERS
17 May 1985
PHOTOLYSIS
OF I-IN,
and Y. MORI of Technology,Megurokq
Ohokqvnm4
Tokyo, Japan
Received 4 February 1985: in final form 27 February 1985
Formation of NH(A311,) has been studied in the photolysis of HN3 at 121.6 nm. hieasurements of time-resolved fluorescence intensity show that NH(A3nI,) is largely formed by secondary reactions involving two energetic intermedxates 0’) and N2(B’3X;), which have hfetimes of 2.7 and 18 ps. These intermediates are tentatively assigned to N,(B3n,, respectively_
1_ Introduction
The vacuum ultraviolet photolysis of HN, below 160 nm has been reported to induce the fluorescence originating from NH(A 311i) accompanied by the NH(c ‘II) fluorescence [1,2]. However, the direct formation of NH(A 3Hi> + N2(X ‘Za is a spin-forbidden process. A spin-allowed decomposition into NH(A 3ili) + Nz(A 3Zz) is not possible when the incident excitation wavelength is longer than 120-6 nm
PI -
Welge [l] has suggested that the excited triplet NH may be formed by secondary reactions involving Nz(A 3Zz), or still higher excited triplet states of N2, when HNg is irradiated by the Kr or Xe resonance line_ Later, Okabe 121 reinvestigated the reaction mechanism, ana concluded that NH(A 3Ui) may be formed largely by the reaction of electTonically excited N, with HN3. The effect of pressure on the intensity ratio NH(A 311i)/NH(c IlI) indicates that the reaction dynamics involves a microsecond time scale. The moHt probable candidate has been consider& to be Nz(B ?I$,>._ Lifetimes of both NH(c In) and NH(A 311f) are known [3] to be much shorter, 480 ns. The e$ent of direct formation bf NH(A 3H& the spin:forbidden pr’&essj is estimated to be Iess than . 5% of--the spii@owed NH(c Ill) formation.N2(B ?JIg), fhe u&r-&ate df thZ: f=E positive s$stern, has lifetimes of 2-8 ~LS[4], which fit Gery well to the obser&&on made_.__ by ‘Okabe--i2], while r&ch_ 0 OOP-2614/85/S 0330 (N+th-Holland Ph+ics
0 EIsevier Science Publishers B.V. Publish&g Division)
longer lifetimes of l-2 s for N2(A 3Za [5] do not. N2(B’ 3ZJ is not discussed by Okabe, but it may also contribute to the formation of NH(A 311i) if its population is not negligible. The lifetime of N2(B’ 3Z;) is expected to be of the same order of magnitude as that of N2(B 31$,) [6]_ Recently, Haak and Stuhl 133 studied the photodecomposition of HN3 by the 193 nm ArF laser pulse. They observed emissions from NJ!I(c ‘II) and NH(A 311 $ induced by two-photon excitation_ Singleexponential decays were observed for the singlet emission, but were not observed for the triplet one_ They did not attempt to analyze the decay curves. In this paper we report an analysis of NH(A 3Hi + X 3ZZ-) emission time profiles observed when I-IN, was photolyzed by the pulsed light at 12 1.6 run _Results show that NH(A 311J is mostly formed by the sensitized reaction of I-IN, with triplet N,, confhming Okabe’s report, but the reaction seems to involve two different triplet states of Nz, most probably B 31-1g and B’3Z- il2. Experimental Experimental details are reported elsewhere 171. The light pulser was a co-axial self-triggered one. The discharge lvnp containing about 1 Torr of pure H2 emitted the 121.6 nm Lyman-a line as well as Hz molecular b&ds.around 160 MI. An 02 optical filter (1 371
Volume 116, number 5
CHEMICAL PHYSICS LETTERS
atm, 1 cm) was inserted using two MgF, windows between the discharge lamp and the reaction cell, to transmit only the 121.6 run resonance line [S 3_ The pulse repetition rate was 4-8 kHz with a pulse duration of =lO ns. The emission intensity was measured through a fused silica window at right angIes to the incident excitation beam with a combination of a OS m monochromator and a photomultiplier. HN3 was prepared by heating a mixture of NaN, and stearic acid under vacuum [2]. The gas evolved was passed through a column of P205 powder on glass wool and then it was trapped at liquid N2 temperature to remove non-condensable impurities_ The HN, gas was stored in an opaque vessel at a pressure less than 50 Torr.
17 May 1985
Fig. l- In&en&y time profiles of NH fluorescence observed when HN3 was photodecomposed by the 121.6 nm light pulse. The spectral resolution is 2.0 nm (fwhm). (a) at 326 nm, @) at 336 nm. [HNa] = 0.1 Toss, [As] = 8.0 Ton. Dots representobserved data and the calculated best-fit curvesare drawn by solid lines.
by a single-exponential decay with a lifetime of 75 ns, I,(t) =A exp(--t/75 ns); (b) slower rise (340 ns) followed by a slow decay (940 ns), Ib(t) = B [-exp(-t/
3_ Results and discussion
340 ns) + exp(-f/940 ns)] ; and (c) slower rise (340 ns) and very slow decay (3.5 I.CS), I,(t) = B’ [-exp(-t/
Emission spectra were recorded in a wavelength range from 250 to 600 run, where only the transitions NH(A 3~j + X 32-) and NH(c 'II--fa ‘a) were observed at 336 and 326 nm, respectively_ NH(e ITI) appears to be rotationally excited [2] and the O-O emission band extends to wavelengths greater than 326 run, where it overlaps the fluorescence from NH( 4 %Ii)_ An addition of Ar quenched a substantial amount of the rotational excitation and isolation of emission bands A”IIi from c ‘II WZIS partly achievedFig_ 1 shows time profiles of the NH emission intensity observed when 0.1 Torr HN3 was photolyzed by the 12: .6 nm pulse in the presence of 8.0 Torr Ar. Fig. la is a decay profile of NH(c III) observed at 326 run. NH(c llT) is formed by the direct photodissociation of HN3 within the excitation pulse duration of ~10 ns, and disappears in accordance with a first-order decay law. The zero-pressure lifetime of-NH(c ’ Ii) at 326 nm (bandhead) is estimated to be 440 2 40 ns in agreement with published data [3] _ The time profiles observed at 336 run are more complex, as shown in fig. lb. Initial quick rise and decay of emission intensities, similar to the NH(c ITI) fluorescence observed at 326 nm, are superimposed on a slow rise. Final slow decay of the emission intensity cannot be represented by a single exponential decay function. An analysis of the time profde shows that there may be three different components in it_ Those calculated by leastsquares fitting to reproduce the observed curve are: (a)
340 ns) + exp(-r/3 5 D)] _ The reproduced time profiIe represented by a solid line in fig. lb is given by a linear combination Of I,(t). r,(t) and I&). Of which coefficients were determined by least-squares fit_ Each time profile is shown in fig. 2. The frost component (a) decays more quickly than the emission intensity observed at 326 run. This component is assigned to high rotational levels (N = 14) of NH(c In> which is quenched by Ar and gives the decay with a lifetime of 75 ns. The second (b) and the third (c) components are assigned to the NH(A 3fli, u’ = 0) band_ The slower rises of the second and the third com-
372
Z-
,”
-I
l-
Fig. 2. Tie profIles-of three components which reproduced the observed curveshown in fig. 1 b. Curves(a), (b) and (c) are givenby la(f) =A exp(--t/75 as),&(t) = B [ --exp(-f/340 ns) iexp(-t/940 ns)], and I&) = B’[ -exp(--t/340 ns) + exp(-t/ 3500 ns)], respectively. The best fitted intensity profile to the curveshown in fig. lb is obtained by a linear combination of these functions when the relativevahtesof A LB, B' are l-0, 0.80,031, respectively.
Volume
116, number 5
CHEMICAL
PHYSICS
ponents have similar time constants, about 506 ns at zero pressure by extrapolation, and may be attributed to the finite life of NH(A 311i), 480 ns. This indicates that the same NH(A 311i) is formed by secondary reactions of at least two different intermediate species which have lifetimes of in the microsecond range. The absence of a fast rise of the NH(A 311j) fluorescence suggests that the direct formation of NH(A 31?i) is a very minor process. Decay Iifetimes of the second and the third components were obtained for various pressures of HN3 as shown in fig. 3. The plots fit straight lines of which intercepts give zero-pressure decay lifetimes of 2.7 f 0.2 and 18 + 4 ps. Quenching rate constants are obtained as 2.6 f 0.7 and 0.5 10.1 X lo-lo cm3 molecuIe-’ s-l, respectively. The shorter component with a zero-pressure lifetime of 2.7 p cannot be due to the vibrational relaxation of the vibrationally excited intermediate that has the longer lifetime of 18 ti in its low vibrational levels. Variation of the HN, pressure, or the addition of Ar or N, did not change the intensity ratio of the short (2.7 D) and long (18 p) components so much. Possible intermediates, triplet states of nitrogen which may be formed in the 121.6 nm photolysis of HN3, are N&4 3Ei>, Nz@ 3&), Nz(W 3A,,), and N2(B’%,-). Lif et’nnes of N2(A 3Zi), and N,(W 3A,) are very long, 2.0 s [9] and 0.49 ms (u = 2) [lo], respectively. Lifetimes of the various vibrational levels of N# 311g) have been reported frequently, agreeing within a factor of 2 or Iess [4], and which range from 2 2 TO8 .O w depending on vibrational levels. As general trends, shorter lifetimes have been observed for higher vibrational levels_ Lifetimes of N,(B’ 3x;) are not known at present, but their radiative Lifetimes are expected to be similar to N2(B 31J,) since both states undergo the same transition, 1~~2~+ ffg2p for N (B 311g + A 3Et) and og2p + 7ru2p for Nz(B’ 3E; + I35 l$). An estimated value for N2(B’ 32,-) has been reported to be 24-27 p [6]. Although it is not very conclusive, our data together with reported lifetimes suggest that the shorter component with a lifetime of 2.7 ,USis NZ(B 311g) &d the longer one with its lifetime of 18 /.s is NZ(B’ 32J. N,(B 311g) is probably in higher vibrational levels which has a shorter lifetime. In 121.6 nm photolysis of HN+ it could be as high as u’ = 12. In the active nitrogen system, the population of N2(B’ 35;;, II) has been reported to follow closely that
LETTERS
‘;,
17 May 1985
40 /
m-g 32 B d
2P 1
,opfl _*-*,O-@ 01
*
A0 _.----•-
Pressure
02
03
04
of HN3(Torr)
Fig. 3. Decay rates of the second (0) and the third (0) components against pressure of HN3 _
of N,(B 3llg, u + 4) by collision-induced cross energy transfer [6]. The rate of this energy transfer, however, is estimated to be much smaller than the decay rate of Nz(B’ 3Z;) under the present experimental conditions. In the photolysis of HN, at 121-6 nm, three different dissociation channels have been discussed: (a) NH(c III) + N2(X lx;), (b) NH(X 32-) + N,(B %-ig), and (c) NH(X 3Z-) + N,(E’ 3Z_;)_ The first and the second channels have been reported previously [3] D but the third one is new. Both triplet states of N2 probably sensitize the decomposition of I-IN, to form NH(A 311i) + Nz(X lIZi)_ These processes have similar orders of mngnitude. Fmther studies including emission intensity time profdes of the N, First Positive system are now under investigation in the 2 11.6 MI photolysis of m3_ Results are expected to clarify details of the I-IN, photolysis. References [l] [2] [3] [4] [S] (61 [7] [8] [9] [lo]
K.H. Welge, J. Chem. Phys. 45 (1966) 4673. H. Okabe, 3. Chem. Phys. 49 (1968) 2726. HX. Haak and F. Stuhl, J. Phys. Chem. 88 (1984) 3627. EE. Eyler and F-M. Pipkin, J. Chem. Phys. 79 (1983) 3654. B.H. Bromer and F. Spieweck, Planet. Space Sci. 15 (1967) 689. EM. Gartner and B.A_ Thrush, Proc. Roy. Sot. A346 (1975) 103. Y. Saito, T. Hikida, T. Ichimtrra and I’. Mori, J. Chem. Phys. 80 (1984) 31. T. Hikida, J-A. Eyre and LM Dorfman, J. Chem. Phys. 54 (1971) 3422. hf. Jeunehormne and A.B_F. Duncan. J. Chem. Phys_ 4i (1964) 1692. R. Covey, K-4. Saum and W_ Benesch. J. Opt. Sot. Am. 63 (1973) 592.
373
116, number 5
CHEMICAL
PHYSICS
FORMATION OF NH(A311i) IN THEt FLASH AT 121.6 sun. ROLE OF N2 TRIPLET STATES Y. MARUYAMA, Deptifmenl
of
T. HIKIDA
Chemislty,
Tokyo InsMule
LETTERS
17 May 1985
PHOTOLYSIS
OF I-IN,
and Y. MORI of Technology,Megurokq
Ohokqvnm4
Tokyo, Japan
Received 4 February 1985: in final form 27 February 1985
Formation of NH(A311,) has been studied in the photolysis of HN3 at 121.6 nm. hieasurements of time-resolved fluorescence intensity show that NH(A3nI,) is largely formed by secondary reactions involving two energetic intermedxates 0’) and N2(B’3X;), which have hfetimes of 2.7 and 18 ps. These intermediates are tentatively assigned to N,(B3n,, respectively_
1_ Introduction
The vacuum ultraviolet photolysis of HN, below 160 nm has been reported to induce the fluorescence originating from NH(A 311i) accompanied by the NH(c ‘II) fluorescence [1,2]. However, the direct formation of NH(A 3Hi> + N2(X ‘Za is a spin-forbidden process. A spin-allowed decomposition into NH(A 3ili) + Nz(A 3Zz) is not possible when the incident excitation wavelength is longer than 120-6 nm
PI -
Welge [l] has suggested that the excited triplet NH may be formed by secondary reactions involving Nz(A 3Zz), or still higher excited triplet states of N2, when HNg is irradiated by the Kr or Xe resonance line_ Later, Okabe 121 reinvestigated the reaction mechanism, ana concluded that NH(A 3Ui) may be formed largely by the reaction of electTonically excited N, with HN3. The effect of pressure on the intensity ratio NH(A 311i)/NH(c IlI) indicates that the reaction dynamics involves a microsecond time scale. The moHt probable candidate has been consider& to be Nz(B ?I$,>._ Lifetimes of both NH(c In) and NH(A 311f) are known [3] to be much shorter, 480 ns. The e$ent of direct formation bf NH(A 3H& the spin:forbidden pr’&essj is estimated to be Iess than . 5% of--the spii@owed NH(c Ill) formation.N2(B ?JIg), fhe u&r-&ate df thZ: f=E positive s$stern, has lifetimes of 2-8 ~LS[4], which fit Gery well to the obser&&on made_.__ by ‘Okabe--i2], while r&ch_ 0 OOP-2614/85/S 0330 (N+th-Holland Ph+ics
0 EIsevier Science Publishers B.V. Publish&g Division)
longer lifetimes of l-2 s for N2(A 3Za [5] do not. N2(B’ 3ZJ is not discussed by Okabe, but it may also contribute to the formation of NH(A 311i) if its population is not negligible. The lifetime of N2(B’ 3Z;) is expected to be of the same order of magnitude as that of N2(B 31$,) [6]_ Recently, Haak and Stuhl 133 studied the photodecomposition of HN3 by the 193 nm ArF laser pulse. They observed emissions from NJ!I(c ‘II) and NH(A 311 $ induced by two-photon excitation_ Singleexponential decays were observed for the singlet emission, but were not observed for the triplet one_ They did not attempt to analyze the decay curves. In this paper we report an analysis of NH(A 3Hi + X 3ZZ-) emission time profiles observed when I-IN, was photolyzed by the pulsed light at 12 1.6 run _Results show that NH(A 311J is mostly formed by the sensitized reaction of I-IN, with triplet N,, confhming Okabe’s report, but the reaction seems to involve two different triplet states of Nz, most probably B 31-1g and B’3Z- il2. Experimental Experimental details are reported elsewhere 171. The light pulser was a co-axial self-triggered one. The discharge lvnp containing about 1 Torr of pure H2 emitted the 121.6 nm Lyman-a line as well as Hz molecular b&ds.around 160 MI. An 02 optical filter (1 371
Volume 116, number 5
CHEMICAL PHYSICS LETTERS
atm, 1 cm) was inserted using two MgF, windows between the discharge lamp and the reaction cell, to transmit only the 121.6 run resonance line [S 3_ The pulse repetition rate was 4-8 kHz with a pulse duration of =lO ns. The emission intensity was measured through a fused silica window at right angIes to the incident excitation beam with a combination of a OS m monochromator and a photomultiplier. HN3 was prepared by heating a mixture of NaN, and stearic acid under vacuum [2]. The gas evolved was passed through a column of P205 powder on glass wool and then it was trapped at liquid N2 temperature to remove non-condensable impurities_ The HN, gas was stored in an opaque vessel at a pressure less than 50 Torr.
17 May 1985
Fig. l- In&en&y time profiles of NH fluorescence observed when HN3 was photodecomposed by the 121.6 nm light pulse. The spectral resolution is 2.0 nm (fwhm). (a) at 326 nm, @) at 336 nm. [HNa] = 0.1 Toss, [As] = 8.0 Ton. Dots representobserved data and the calculated best-fit curvesare drawn by solid lines.
by a single-exponential decay with a lifetime of 75 ns, I,(t) =A exp(--t/75 ns); (b) slower rise (340 ns) followed by a slow decay (940 ns), Ib(t) = B [-exp(-t/
3_ Results and discussion
340 ns) + exp(-f/940 ns)] ; and (c) slower rise (340 ns) and very slow decay (3.5 I.CS), I,(t) = B’ [-exp(-t/
Emission spectra were recorded in a wavelength range from 250 to 600 run, where only the transitions NH(A 3~j + X 32-) and NH(c 'II--fa ‘a) were observed at 336 and 326 nm, respectively_ NH(e ITI) appears to be rotationally excited [2] and the O-O emission band extends to wavelengths greater than 326 run, where it overlaps the fluorescence from NH( 4 %Ii)_ An addition of Ar quenched a substantial amount of the rotational excitation and isolation of emission bands A”IIi from c ‘II WZIS partly achievedFig_ 1 shows time profiles of the NH emission intensity observed when 0.1 Torr HN3 was photolyzed by the 12: .6 nm pulse in the presence of 8.0 Torr Ar. Fig. la is a decay profile of NH(c III) observed at 326 run. NH(c llT) is formed by the direct photodissociation of HN3 within the excitation pulse duration of ~10 ns, and disappears in accordance with a first-order decay law. The zero-pressure lifetime of-NH(c ’ Ii) at 326 nm (bandhead) is estimated to be 440 2 40 ns in agreement with published data [3] _ The time profiles observed at 336 run are more complex, as shown in fig. lb. Initial quick rise and decay of emission intensities, similar to the NH(c ITI) fluorescence observed at 326 nm, are superimposed on a slow rise. Final slow decay of the emission intensity cannot be represented by a single exponential decay function. An analysis of the time profde shows that there may be three different components in it_ Those calculated by leastsquares fitting to reproduce the observed curve are: (a)
340 ns) + exp(-r/3 5 D)] _ The reproduced time profiIe represented by a solid line in fig. lb is given by a linear combination Of I,(t). r,(t) and I&). Of which coefficients were determined by least-squares fit_ Each time profile is shown in fig. 2. The frost component (a) decays more quickly than the emission intensity observed at 326 run. This component is assigned to high rotational levels (N = 14) of NH(c In> which is quenched by Ar and gives the decay with a lifetime of 75 ns. The second (b) and the third (c) components are assigned to the NH(A 3fli, u’ = 0) band_ The slower rises of the second and the third com-
372
Z-
,”
-I
l-
Fig. 2. Tie profIles-of three components which reproduced the observed curveshown in fig. 1 b. Curves(a), (b) and (c) are givenby la(f) =A exp(--t/75 as),&(t) = B [ --exp(-f/340 ns) iexp(-t/940 ns)], and I&) = B’[ -exp(--t/340 ns) + exp(-t/ 3500 ns)], respectively. The best fitted intensity profile to the curveshown in fig. lb is obtained by a linear combination of these functions when the relativevahtesof A LB, B' are l-0, 0.80,031, respectively.
Volume
116, number 5
CHEMICAL
PHYSICS
ponents have similar time constants, about 506 ns at zero pressure by extrapolation, and may be attributed to the finite life of NH(A 311i), 480 ns. This indicates that the same NH(A 311i) is formed by secondary reactions of at least two different intermediate species which have lifetimes of in the microsecond range. The absence of a fast rise of the NH(A 311j) fluorescence suggests that the direct formation of NH(A 31?i) is a very minor process. Decay Iifetimes of the second and the third components were obtained for various pressures of HN3 as shown in fig. 3. The plots fit straight lines of which intercepts give zero-pressure decay lifetimes of 2.7 f 0.2 and 18 + 4 ps. Quenching rate constants are obtained as 2.6 f 0.7 and 0.5 10.1 X lo-lo cm3 molecuIe-’ s-l, respectively. The shorter component with a zero-pressure lifetime of 2.7 p cannot be due to the vibrational relaxation of the vibrationally excited intermediate that has the longer lifetime of 18 ti in its low vibrational levels. Variation of the HN, pressure, or the addition of Ar or N, did not change the intensity ratio of the short (2.7 D) and long (18 p) components so much. Possible intermediates, triplet states of nitrogen which may be formed in the 121.6 nm photolysis of HN3, are N&4 3Ei>, Nz@ 3&), Nz(W 3A,,), and N2(B’%,-). Lif et’nnes of N2(A 3Zi), and N,(W 3A,) are very long, 2.0 s [9] and 0.49 ms (u = 2) [lo], respectively. Lifetimes of the various vibrational levels of N# 311g) have been reported frequently, agreeing within a factor of 2 or Iess [4], and which range from 2 2 TO8 .O w depending on vibrational levels. As general trends, shorter lifetimes have been observed for higher vibrational levels_ Lifetimes of N,(B’ 3x;) are not known at present, but their radiative Lifetimes are expected to be similar to N2(B 31J,) since both states undergo the same transition, 1~~2~+ ffg2p for N (B 311g + A 3Et) and og2p + 7ru2p for Nz(B’ 3E; + I35 l$). An estimated value for N2(B’ 32,-) has been reported to be 24-27 p [6]. Although it is not very conclusive, our data together with reported lifetimes suggest that the shorter component with a lifetime of 2.7 ,USis NZ(B 311g) &d the longer one with its lifetime of 18 /.s is NZ(B’ 32J. N,(B 311g) is probably in higher vibrational levels which has a shorter lifetime. In 121.6 nm photolysis of HN+ it could be as high as u’ = 12. In the active nitrogen system, the population of N2(B’ 35;;, II) has been reported to follow closely that
LETTERS
‘;,
17 May 1985
40 /
m-g 32 B d
2P 1
,opfl _*-*,O-@ 01
*
A0 _.----•-
Pressure
02
03
04
of HN3(Torr)
Fig. 3. Decay rates of the second (0) and the third (0) components against pressure of HN3 _
of N,(B 3llg, u + 4) by collision-induced cross energy transfer [6]. The rate of this energy transfer, however, is estimated to be much smaller than the decay rate of Nz(B’ 3Z;) under the present experimental conditions. In the photolysis of HN, at 121-6 nm, three different dissociation channels have been discussed: (a) NH(c III) + N2(X lx;), (b) NH(X 32-) + N,(B %-ig), and (c) NH(X 3Z-) + N,(E’ 3Z_;)_ The first and the second channels have been reported previously [3] D but the third one is new. Both triplet states of N2 probably sensitize the decomposition of I-IN, to form NH(A 311i) + Nz(X lIZi)_ These processes have similar orders of mngnitude. Fmther studies including emission intensity time profdes of the N, First Positive system are now under investigation in the 2 11.6 MI photolysis of m3_ Results are expected to clarify details of the I-IN, photolysis. References [l] [2] [3] [4] [S] (61 [7] [8] [9] [lo]
K.H. Welge, J. Chem. Phys. 45 (1966) 4673. H. Okabe, 3. Chem. Phys. 49 (1968) 2726. HX. Haak and F. Stuhl, J. Phys. Chem. 88 (1984) 3627. EE. Eyler and F-M. Pipkin, J. Chem. Phys. 79 (1983) 3654. B.H. Bromer and F. Spieweck, Planet. Space Sci. 15 (1967) 689. EM. Gartner and B.A_ Thrush, Proc. Roy. Sot. A346 (1975) 103. Y. Saito, T. Hikida, T. Ichimtrra and I’. Mori, J. Chem. Phys. 80 (1984) 31. T. Hikida, J-A. Eyre and LM Dorfman, J. Chem. Phys. 54 (1971) 3422. hf. Jeunehormne and A.B_F. Duncan. J. Chem. Phys_ 4i (1964) 1692. R. Covey, K-4. Saum and W_ Benesch. J. Opt. Sot. Am. 63 (1973) 592.
373