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Rotational and vibrational relaxation rate constants for N2+(B2Σ, ν' = 0, N') colliding with He
Volume 135, number 1,2
27 March 1987
CHEMICAL PHYSICS LETTERS
ROTATIONAL AND VIBRATIONAL RELAXATION RATE CONSTANTS FOR N;( B *Z , Y’= 0, N’ ) COLLIDING WITH He
A. PLAIN and J. JOLLY Laboratolre de Physique des Gaz et des Plasmas ‘, Universitk Paris&d,
91405 Orsay Cedex, France
Received 1 December 1986
A tunable dye laser was used to populate selectively a single rotational-vibrational state of N 2 ( B ‘E , u’ = 0, N’ = O-l 5 ) . The population changes induced by collisions with He were determined using time-resolved spectroscopy in a flowing afterglow experiment. Total rotational transfer rates form the pumped level were found to vary with N’ between 1.6 and 2.5 x lo-“’ cm3 s-l. The vibrational quenching of N: (B, v’ =O) by He was also determined and found to be as low as 8.0X lo-l2 cm3 s-l.
1. Introduction
In previous studies we determined the vibrational quenching of N$ (B, v’ = 0, 1 and 2) by Nz and Ne [ 1,2 1. Nitrogen ions were formed in a dc discharge in pure Nz or in a mixture of Ne and N2. Due to the strong background emission of the plasma and to the variation of the gas temperature with pressure, it was very difficult, using such a method, to measure the weak quenching rate of N$ by He. To deal with these problems N: ions were created, in the present study, in a flowing afterglow experiment using the Penning reaction between metastable He atoms and N, molecules. The unknown vibrational and rotational deexcitation rates with He were then measurable with reasonable precision. PUiP
2. Experimental A schematic of the experimental apparatus used in this study is shown in fig. 1. Metastable atoms were created in a small armside dc discharge (10 cm long, 7 mm inner diameter). The intensity of the discharge current was 10 mA. He metastable atoms (2 ‘S, 2 3S), extracted from the discharge by the gas flow, reacted in the main part of the tube (50 cm long, 3 cm inner diameter) with nitrogen molecules
according to the efficient Penning ionisation process
’ Associated with the CNRS.
Molecular ions N: (B) are rapidly deactivated by
46
Fig. 1. Schematic diagram of the experimental apparatus.
N2(X ‘C) +He(2 ‘S, 2 3S) +N$(B
‘Z) +He+e.
(1)
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 135, number
CHEMICAL
1,2
PHYSICS
photon emission N:(B ‘Z)+N,+(X
*C)+hv.
(2)
3. Results and discussion For a rotational level N’ of the state NT (B, v’ = 0) the deactivation kinetics may be described by the following reactions:
v’=O,N’)+M
TR” -
N;(B,
v’=O, N’+2n),
(3a)
e
N:(B,u’=O,N’)+M-
1987
A0
Rotational levels N,+ (B, ZJ’= 0, N’) were selectively populated from the N: (X, U”= 0, N” =N’ ? 1) fundamental by means of a tunable dye laser pumped by a N2 laser, using BBQ in a mixture of toluene and ethanol. The dye laser produced 15-20 pJ pulses of 3 ns duration at ten pulses per second in the 380-400 nm range. The laser-induced fluorescence was observed (a) for rotational analysis, with a high-resolution monochromator on the (B, v’=O, ZV’)+(X, u” = 1, N”) transitions with N’ -N” = 1 (R branch) or N’ -N” = - 1 (P branch) and (b) for vibrational quenching studies, with a low-resolution monochromator to record the decay of all rotational levels of the state v’ = 0 on the P branch. Time-resolved measurements were obtained using a photomultiplier tube, working in the photoncounting mode, connected to a fast multichannel event counter (MEC) with a time resolution of 3.5 ns per channel [ 31. The double-triggering of the MEC (twice the laser frequency) allowed for subtraction of the photons emitted continuously by reaction (2). Decay frequencies of the vibrational or rotational levels were determined as functions of the total pressure in the flowing tube. The composition of the gas mixture was kept constant and controlled by mass flow meters (0.3Ohof N2 in He). Total pressures were determined using an MKS Baratron absolute pressure gauge; and gas concentrations were calculated from experimental parameters (gas flow and pressure) at 300 K.
N:(B,
27 March
LETTERS
products ,
(3b)
N: (B, v’ =O, N’) -
N:(X,
v”,N”)fhv, (3c)
where M is the collision partner (either a N2 molecule or a He atom), TF is the total rotational transfer rate out of the N’ level and ky is the vibrational quenching rate; A,,= l/r where T is the radiative lifetime. The total rotational transfer out of a level N populates the rotational levels N’ + 2n, where n is an integer, as the change in the rotational number obeys the selection rules for nuclear spin in homonuclear molecules. Reaction (3a), which expresses the energy transfer following rotational perturbation, results in a rearrangement inside the U’ vibrational level, whereas reactions (3b) and (3~) lead to a decrease in the vibrational level population. In this study two kinds of spectroscopic observation, following rotational laser perturbation, were performed in order to analyse separately the vibrational quenching mechanisms and the total rotational relaxation. (1) The spectroscopic observation, at low resolution, of the P branch of the (B, v’ = 0) - (X, v” = 1) transition of N: exhibited time-resolved decays with a single slope, in a semi-log plot, over the pressure range used in this study (1 to 5 Torr). Typical linear fits of the observed fluorescences are given by broken lines in fig. 2. In such measurements only vibrational quenching and radiative emission were observable and the decay rate can be expressed as A(v’)=Ao+k~[He]+k~2[N2],
(4)
where the square brackets denote atomic or molecular concentrations. Decay rates were independent of the rotational transition used to pump the (B, U’= 0) level. The slope of the straight line obtained in a Stem-Volmer plot gives both He and N, vibrational quenching. Since the quenching of N: (B, v’ = 0) by N2 has been measured previously [ 1] it was possible to determine the vibrational quenching by He: k,H’=(8+3)~10-~* cm3 s-‘. The low accuracy in the value ( z 35%) is the result of compromises in the experimental conditions. (i) The large difference between k? and k? (two orders of magnitude) leads us to use a gas mixture with a low percentage of N2 in He which produced a 47
CHEMICAL PHYSICS LETTERS
Volume 135, number 1,2
27 March 1987
as a function of time, during the induced fluorescence, can be considered in three different parts: (i) In the first part of the fluorescence the decay frequency is independent of time, which means that the back-transfer collision term may to a good approximation be neglected. Then decay frequencies may be simply expressed from reactions (3a), ( 3b) and (3~) as A(~‘=O,N’)=A(V’)+T,H”[H~]+T~~[N~].
10
20
30 Chonnr
40
50
60
I
Fig. 2. Fluorescence decays following laser perturbation of the B *E, v’ = 0, N = 5 level of N$ for different values of the total pressure (0.3% N2 in He), (A) 1.25 Ton; (B) 3 Torr, (C) 5 Torr. The broken lines are linear fits of the vibrational decays. Experimental points correspond to rotational decays of the pumped level and the full lines are linear fits of the total rotational transfer rates. The curves have been vertically translated for clarity.
weak light signal at low pressure. (ii) The production of metastable He atoms in the dc discharge decreases sharply for pressures in the reaction tube greater than S Torr, which limits the usable pressure range. Under such conditions, collisional relaxation rates remain lower than 11% of the total decay rate producing a large uncertainty in the result. Nevertheless this He vibrational quenching rate is, to our knowledge, the first experimental result published and the value is consistent with the maximum possible rate reported by Tellinghuisen et al. of k,H”<3x lo-” cm3 s-i [4]. (2) High-resolution observation of the initially pumped rotational level exhibited quite different decay behaviour (experimental points in fig. 2) that can be understood by including with the previously described vibrational deactivation mechanisms the rotational relaxation term. However the interpretation of the decays in fig. 2 which exhibit, at least at the higher pressures, multi-time rate constants, requires a consideration of multiple collision effects not expressed in reaction (3a). The decay freqency 48
(5)
While it is well established that the lifetime in the state V’= 0 varies with the rotational level, such variation is only slight over the range of levels studied here [ 51 and is ignored in the analysis. (ii) In the second part the decay frequency decreases with time, which indicates that back-transfer collisions become important. The delay between the laser pulse and the time at which back-transfer collisions play a role determines statistically the time between two collisions leading to a probability that the molecule will return in its initial state. For a He pressure of 1 Torr we achieved a “single collision time” of about 75 ns. Duncan et al. [6] reported a time of 100 ns determined from the Langevin collisional cross section for N: with He. These multi-collisional processes lead to a quasi-equilibrium for the populations of rotational levels having the same parity. (iii) At the end of the fluorescence, the decay frequency is again observed to be independent of time since the rotational populations have reached “quasiequilibrium” and the deactivation is governed by reactions (3b) and (3~). The measured decay rates are then identical to those observed using the low resolution spectroscopy reported in part (1). This third part of the decay is not observed at low pressure when the collisional frequency is not sufficient to produce the equilibrium before the fluorescence vanishes. In order to determine the relative efficiency of He and N2 in the total rotational transfer, experiments were performed to measure decay frequencies for increasing concentrations of N2 and fixed He pressure. Results are presented in fig. 3. The ordinate decay frequencies involve only the rotational relaxation (i.e. vibrational quenching has been subtracted from the total decay rate). Within experimental error the rotational relaxation rate isfound to be constant
Volume 135, number 1,2
CHEMICAL PHYSICS LETTERS
27 March 1987
10
0
2
4
6
8
10
12
14
16
18
I
20
N 2 CONCENTRATION < 10’ ’ an-3 )
Fig. 3. Rotational decay frequencies of the pumped level (B %, v’ = 0, N’ = 7) plotted against nitrogen density for a fixed helium pressure (0: 0.8 Torr He, 0: 2. I Torr He). The vibrational quenching by N2 and He has been subtracted from the total decay rate.
which indicates that only rotational transfer induced by He is important under the present experimental conditions. Actually the total rotational transfer rate with N, could not be measured and only an upper limit was determined TE* <2x lo-lo cm3 s-l. On the other hand, the total rotational transfer rate with He was determined for the levels N’ = 0 to 15. Rate coefficients and cross sections are presented in table 1. The errors are estimated to be f 10%. The cross sections were calculated using the relation Table 1 Total rotational transfer rate T L’ (lo-“cm3s-‘)andcrosssections (A *) of N2+(B ?E, u’ =O, N’) by He N
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T::
u
25.3 19.7 20.2 16.4 16.6 16.1 17.4 17.6 18.3 17.2 18.6 16.0 17.2 16.5 16.3 16.0
18.8 14.6 15.0 12.2 12.3 12.0 12.9 13.1 13.6 12.8 13.8 11.9 12.8 12.3 12.1 11.9
where ( v) is the mean relative velocity of the colliding particles calculated at 300 K. Considerations based solely on the magnitude of the energy defect in the rotational energy exchanges are not sufficient to quantitatively interpret the set of measured rate constants. One has to take into account that in a ‘C + electronic configuration all rotational levels, except N’ = 0, are doublet due to the spin-rotation interaction. Then collisions which induce a change in the parity of the molecular wavefunction but do not modify the rotational angular momentum of the nuclei (i.e. collisions which are elastic in Nbut inelastic in J) may have to be considered in order to explain the pre-eminence of the total transfer rate of the N’ = 0 rotational level. A complete analysis of the results will be presented in a forthcoming paper in which we will show that it is possible to deduce, from the values of the total rotational transfer rates, the state-to-state transfer rates k,, between rotational levels using relations developed by Alexander [ 71 in the infinite ordersudden approximation for rotationally inelastic collisions in a ?Z + electronic state. In conclusion we would like to not that if, as expected, helium is a poor vibrational quencher for N: B it is nevertheless a good partner for collisionally thermalizing the rotational distribution.
49
Volume 135, number 1,2
CHEMICAL PHYSICS LETTERS
References [ 1J J. Jolly and A. Plain, Chem. Phys. Letters 100 (1983) 425. [Z] A. Plain and J. Jolly, Chem. Phys. Letters 111 (1984) 135. [ 31 T. Maurin and F. Devos, Rev. Sci. Instr. 52 (198 I) 1765.
50
27 March 1987
[4] J.B. Tellinghuisen, C.A. Winkler, CC. Freeman, M.J. McEvan and L.F. Phillips, J. Chem. Sot. Faraday Trans. II 68 (1972) 833. [ 5] B.H. Mahan and A. G’Keefe, J. Chem. Phys. 76 ( 1981) 5606. [ 61 M.A. Duncan, V.M. Bierbaum, G.B. Ellison and S.R. Leone, J. Chem. Phys. 79 (1983) 5448. [ 7 1M.H. Alexander, J. Chem. Phys. 76 (1982) 3637.
27 March 1987
CHEMICAL PHYSICS LETTERS
ROTATIONAL AND VIBRATIONAL RELAXATION RATE CONSTANTS FOR N;( B *Z , Y’= 0, N’ ) COLLIDING WITH He
A. PLAIN and J. JOLLY Laboratolre de Physique des Gaz et des Plasmas ‘, Universitk Paris&d,
91405 Orsay Cedex, France
Received 1 December 1986
A tunable dye laser was used to populate selectively a single rotational-vibrational state of N 2 ( B ‘E , u’ = 0, N’ = O-l 5 ) . The population changes induced by collisions with He were determined using time-resolved spectroscopy in a flowing afterglow experiment. Total rotational transfer rates form the pumped level were found to vary with N’ between 1.6 and 2.5 x lo-“’ cm3 s-l. The vibrational quenching of N: (B, v’ =O) by He was also determined and found to be as low as 8.0X lo-l2 cm3 s-l.
1. Introduction
In previous studies we determined the vibrational quenching of N$ (B, v’ = 0, 1 and 2) by Nz and Ne [ 1,2 1. Nitrogen ions were formed in a dc discharge in pure Nz or in a mixture of Ne and N2. Due to the strong background emission of the plasma and to the variation of the gas temperature with pressure, it was very difficult, using such a method, to measure the weak quenching rate of N$ by He. To deal with these problems N: ions were created, in the present study, in a flowing afterglow experiment using the Penning reaction between metastable He atoms and N, molecules. The unknown vibrational and rotational deexcitation rates with He were then measurable with reasonable precision. PUiP
2. Experimental A schematic of the experimental apparatus used in this study is shown in fig. 1. Metastable atoms were created in a small armside dc discharge (10 cm long, 7 mm inner diameter). The intensity of the discharge current was 10 mA. He metastable atoms (2 ‘S, 2 3S), extracted from the discharge by the gas flow, reacted in the main part of the tube (50 cm long, 3 cm inner diameter) with nitrogen molecules
according to the efficient Penning ionisation process
’ Associated with the CNRS.
Molecular ions N: (B) are rapidly deactivated by
46
Fig. 1. Schematic diagram of the experimental apparatus.
N2(X ‘C) +He(2 ‘S, 2 3S) +N$(B
‘Z) +He+e.
(1)
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 135, number
CHEMICAL
1,2
PHYSICS
photon emission N:(B ‘Z)+N,+(X
*C)+hv.
(2)
3. Results and discussion For a rotational level N’ of the state NT (B, v’ = 0) the deactivation kinetics may be described by the following reactions:
v’=O,N’)+M
TR” -
N;(B,
v’=O, N’+2n),
(3a)
e
N:(B,u’=O,N’)+M-
1987
A0
Rotational levels N,+ (B, ZJ’= 0, N’) were selectively populated from the N: (X, U”= 0, N” =N’ ? 1) fundamental by means of a tunable dye laser pumped by a N2 laser, using BBQ in a mixture of toluene and ethanol. The dye laser produced 15-20 pJ pulses of 3 ns duration at ten pulses per second in the 380-400 nm range. The laser-induced fluorescence was observed (a) for rotational analysis, with a high-resolution monochromator on the (B, v’=O, ZV’)+(X, u” = 1, N”) transitions with N’ -N” = 1 (R branch) or N’ -N” = - 1 (P branch) and (b) for vibrational quenching studies, with a low-resolution monochromator to record the decay of all rotational levels of the state v’ = 0 on the P branch. Time-resolved measurements were obtained using a photomultiplier tube, working in the photoncounting mode, connected to a fast multichannel event counter (MEC) with a time resolution of 3.5 ns per channel [ 31. The double-triggering of the MEC (twice the laser frequency) allowed for subtraction of the photons emitted continuously by reaction (2). Decay frequencies of the vibrational or rotational levels were determined as functions of the total pressure in the flowing tube. The composition of the gas mixture was kept constant and controlled by mass flow meters (0.3Ohof N2 in He). Total pressures were determined using an MKS Baratron absolute pressure gauge; and gas concentrations were calculated from experimental parameters (gas flow and pressure) at 300 K.
N:(B,
27 March
LETTERS
products ,
(3b)
N: (B, v’ =O, N’) -
N:(X,
v”,N”)fhv, (3c)
where M is the collision partner (either a N2 molecule or a He atom), TF is the total rotational transfer rate out of the N’ level and ky is the vibrational quenching rate; A,,= l/r where T is the radiative lifetime. The total rotational transfer out of a level N populates the rotational levels N’ + 2n, where n is an integer, as the change in the rotational number obeys the selection rules for nuclear spin in homonuclear molecules. Reaction (3a), which expresses the energy transfer following rotational perturbation, results in a rearrangement inside the U’ vibrational level, whereas reactions (3b) and (3~) lead to a decrease in the vibrational level population. In this study two kinds of spectroscopic observation, following rotational laser perturbation, were performed in order to analyse separately the vibrational quenching mechanisms and the total rotational relaxation. (1) The spectroscopic observation, at low resolution, of the P branch of the (B, v’ = 0) - (X, v” = 1) transition of N: exhibited time-resolved decays with a single slope, in a semi-log plot, over the pressure range used in this study (1 to 5 Torr). Typical linear fits of the observed fluorescences are given by broken lines in fig. 2. In such measurements only vibrational quenching and radiative emission were observable and the decay rate can be expressed as A(v’)=Ao+k~[He]+k~2[N2],
(4)
where the square brackets denote atomic or molecular concentrations. Decay rates were independent of the rotational transition used to pump the (B, U’= 0) level. The slope of the straight line obtained in a Stem-Volmer plot gives both He and N, vibrational quenching. Since the quenching of N: (B, v’ = 0) by N2 has been measured previously [ 1] it was possible to determine the vibrational quenching by He: k,H’=(8+3)~10-~* cm3 s-‘. The low accuracy in the value ( z 35%) is the result of compromises in the experimental conditions. (i) The large difference between k? and k? (two orders of magnitude) leads us to use a gas mixture with a low percentage of N2 in He which produced a 47
CHEMICAL PHYSICS LETTERS
Volume 135, number 1,2
27 March 1987
as a function of time, during the induced fluorescence, can be considered in three different parts: (i) In the first part of the fluorescence the decay frequency is independent of time, which means that the back-transfer collision term may to a good approximation be neglected. Then decay frequencies may be simply expressed from reactions (3a), ( 3b) and (3~) as A(~‘=O,N’)=A(V’)+T,H”[H~]+T~~[N~].
10
20
30 Chonnr
40
50
60
I
Fig. 2. Fluorescence decays following laser perturbation of the B *E, v’ = 0, N = 5 level of N$ for different values of the total pressure (0.3% N2 in He), (A) 1.25 Ton; (B) 3 Torr, (C) 5 Torr. The broken lines are linear fits of the vibrational decays. Experimental points correspond to rotational decays of the pumped level and the full lines are linear fits of the total rotational transfer rates. The curves have been vertically translated for clarity.
weak light signal at low pressure. (ii) The production of metastable He atoms in the dc discharge decreases sharply for pressures in the reaction tube greater than S Torr, which limits the usable pressure range. Under such conditions, collisional relaxation rates remain lower than 11% of the total decay rate producing a large uncertainty in the result. Nevertheless this He vibrational quenching rate is, to our knowledge, the first experimental result published and the value is consistent with the maximum possible rate reported by Tellinghuisen et al. of k,H”<3x lo-” cm3 s-i [4]. (2) High-resolution observation of the initially pumped rotational level exhibited quite different decay behaviour (experimental points in fig. 2) that can be understood by including with the previously described vibrational deactivation mechanisms the rotational relaxation term. However the interpretation of the decays in fig. 2 which exhibit, at least at the higher pressures, multi-time rate constants, requires a consideration of multiple collision effects not expressed in reaction (3a). The decay freqency 48
(5)
While it is well established that the lifetime in the state V’= 0 varies with the rotational level, such variation is only slight over the range of levels studied here [ 51 and is ignored in the analysis. (ii) In the second part the decay frequency decreases with time, which indicates that back-transfer collisions become important. The delay between the laser pulse and the time at which back-transfer collisions play a role determines statistically the time between two collisions leading to a probability that the molecule will return in its initial state. For a He pressure of 1 Torr we achieved a “single collision time” of about 75 ns. Duncan et al. [6] reported a time of 100 ns determined from the Langevin collisional cross section for N: with He. These multi-collisional processes lead to a quasi-equilibrium for the populations of rotational levels having the same parity. (iii) At the end of the fluorescence, the decay frequency is again observed to be independent of time since the rotational populations have reached “quasiequilibrium” and the deactivation is governed by reactions (3b) and (3~). The measured decay rates are then identical to those observed using the low resolution spectroscopy reported in part (1). This third part of the decay is not observed at low pressure when the collisional frequency is not sufficient to produce the equilibrium before the fluorescence vanishes. In order to determine the relative efficiency of He and N2 in the total rotational transfer, experiments were performed to measure decay frequencies for increasing concentrations of N2 and fixed He pressure. Results are presented in fig. 3. The ordinate decay frequencies involve only the rotational relaxation (i.e. vibrational quenching has been subtracted from the total decay rate). Within experimental error the rotational relaxation rate isfound to be constant
Volume 135, number 1,2
CHEMICAL PHYSICS LETTERS
27 March 1987
10
0
2
4
6
8
10
12
14
16
18
I
20
N 2 CONCENTRATION < 10’ ’ an-3 )
Fig. 3. Rotational decay frequencies of the pumped level (B %, v’ = 0, N’ = 7) plotted against nitrogen density for a fixed helium pressure (0: 0.8 Torr He, 0: 2. I Torr He). The vibrational quenching by N2 and He has been subtracted from the total decay rate.
which indicates that only rotational transfer induced by He is important under the present experimental conditions. Actually the total rotational transfer rate with N, could not be measured and only an upper limit was determined TE* <2x lo-lo cm3 s-l. On the other hand, the total rotational transfer rate with He was determined for the levels N’ = 0 to 15. Rate coefficients and cross sections are presented in table 1. The errors are estimated to be f 10%. The cross sections were calculated using the relation Table 1 Total rotational transfer rate T L’ (lo-“cm3s-‘)andcrosssections (A *) of N2+(B ?E, u’ =O, N’) by He N
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T::
u
25.3 19.7 20.2 16.4 16.6 16.1 17.4 17.6 18.3 17.2 18.6 16.0 17.2 16.5 16.3 16.0
18.8 14.6 15.0 12.2 12.3 12.0 12.9 13.1 13.6 12.8 13.8 11.9 12.8 12.3 12.1 11.9
where ( v) is the mean relative velocity of the colliding particles calculated at 300 K. Considerations based solely on the magnitude of the energy defect in the rotational energy exchanges are not sufficient to quantitatively interpret the set of measured rate constants. One has to take into account that in a ‘C + electronic configuration all rotational levels, except N’ = 0, are doublet due to the spin-rotation interaction. Then collisions which induce a change in the parity of the molecular wavefunction but do not modify the rotational angular momentum of the nuclei (i.e. collisions which are elastic in Nbut inelastic in J) may have to be considered in order to explain the pre-eminence of the total transfer rate of the N’ = 0 rotational level. A complete analysis of the results will be presented in a forthcoming paper in which we will show that it is possible to deduce, from the values of the total rotational transfer rates, the state-to-state transfer rates k,, between rotational levels using relations developed by Alexander [ 71 in the infinite ordersudden approximation for rotationally inelastic collisions in a ?Z + electronic state. In conclusion we would like to not that if, as expected, helium is a poor vibrational quencher for N: B it is nevertheless a good partner for collisionally thermalizing the rotational distribution.
49
Volume 135, number 1,2
CHEMICAL PHYSICS LETTERS
References [ 1J J. Jolly and A. Plain, Chem. Phys. Letters 100 (1983) 425. [Z] A. Plain and J. Jolly, Chem. Phys. Letters 111 (1984) 135. [ 31 T. Maurin and F. Devos, Rev. Sci. Instr. 52 (198 I) 1765.
50
27 March 1987
[4] J.B. Tellinghuisen, C.A. Winkler, CC. Freeman, M.J. McEvan and L.F. Phillips, J. Chem. Sot. Faraday Trans. II 68 (1972) 833. [ 5] B.H. Mahan and A. G’Keefe, J. Chem. Phys. 76 ( 1981) 5606. [ 61 M.A. Duncan, V.M. Bierbaum, G.B. Ellison and S.R. Leone, J. Chem. Phys. 79 (1983) 5448. [ 7 1M.H. Alexander, J. Chem. Phys. 76 (1982) 3637.