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Lifetime and quenching rates for the H2 continuum
J. Quanr. Specfrosc. Radiat.
Transfer. Vol. 12. pp. 117421.
Pergamon
Press
1972. Printed
in Great
Britain
NOTE LIFETIME AND QUENCHING RATES FOR THE Hz CONTINUUM R. T. THOMPWN and R. G. FOWLER Departmentof Physics and Astronomy, University of Oklahoma, Norman, Okla., 73069, U.S.A. (Received 22 March 1971)
Abstract-When measured down to low pressures, the radiation processes of the H, continuum have proved to be unexpectedly complex, involving at least two states. The lifetime of the 3Zr state is found to be 26 nsec, with a resonance exchange cross-section of 2 x lo-l4 cm’ to some side state and a quenching cross section of 4.8 x IO-l6 cm’. INTRODUCTION
the invertion developed by HOLZBERLEIN(~)and the delayed coincidence technique described by JOHIWN and FOWLER(‘) the previous measurements of Holzberlein on the continuum in H, have been revised. The process of emission of the continuum is found to be more complex than previously envisioned. There are evidently two states in close resonance, and the apparent lifetime at pressures above 1 torr is not the true lifetime of the ‘xg state. Results of the new experimental data yield a low-pressure exchange crosssection of 2.0 x lo-l4 cm2 between the states and a high-pressure quenching cross-section of 4.8 x lo-l6 cm2 for both states. Application of a magnetic field applied axially to the invertron yielded no change of lifetime for fields up to about 18 gauss (calculated) which was sufficient to disperse the highly visible axial concentration of excited molecules. Linear asymptotic extrapolation of the high-pressure data to zero pressure yields a lifetime of 2.6 f 0.3 nsec for the side state, whereas linear extrapolation of the low pressure lifetimes indicates a true lifetime for the 0’ = 03cB+ state of 26 f 2 nsec at zero pressure. The new data were obtained by observing emitted light at 2750 and 2950 A ‘which should be due to transitions occurring between the stable lsa2sa 3xg and the unstable lsa2pa “c, vibrational levels. The results were corrected for a small pressure-dependent cascade component. UTILIZING
EXPERIMENTAL
OBSERVATIONS
The new observations of lifetimes z in molecular hydrogen were obtained at pressures torr using a 4 m Jarrell Ash monochromator and were combined with higher pressure data obtained earlier by Holzberlein to form the plot of l/z vs. pressure shown in Fig. 1. The significance of the l/z plot is that it reveals the dominant processes of a simple exponential state decay linearly according to the relation 0.0344800
1 -=A+crNo~=L+avp T
z.
kT’
where N, z population density of neutrals, IJ E quenching cross section, A E transition probability out of the excited state, 5 = mean molecular speed. 117
R. T. THOMPWNand R. G. FOWLER
118
The lifetimes at low pressure at the two wavelengths measured (2750 and 2950A) where found to be in the proportion X3, showing, as is expected, that the continuum in different spectral localities originates from different u per vibrational states. At 2950 A the transition is predominantly from U’= 0 of the 3f : state, while at 2750 A it comes predominantly from U’= 1. At high pressures, there was no such distinction between wavelengths. Data at the lowest pressures have therefore been reduced, by application of the wavelength factor, to equivalent u’ = 0 values. 280
1
I ?:
0
I
I
I
EXPLODE0
0 NO FILTER A 7-60 CORNING FILTER o MONOCHROMATOR (NEW DATA) ANALYTICAL APPROXIMATION
VIEW
I
0
4
8
12
16 20 PRESSURE
24 (TORR.)
FIG. 1. Inverse lifetime to pressure results for H,(lag2S30:
28
to la,lo~~:
I
32
36
I
40
transition). Inset shows
detail at ongin.
The lifetimes plotted in Fig. 1 correspond to the shortest decay observed. In each case, our least-squares computer program enables us to resolve any complex decays into a sum of exponentials and to identify the two or three fastest decays with reasonable accuracy. In the case of the H, continuum, only a very weak cascade component was present. Consequently, the behavior of the l/z plot is strikingly anomalous, having two linear regions, the high-pressure data extrapolating to a faster lifetime at zero pressure than the low-pressure data, a situation which cannot be explained by a cascade, even if there were a possibility that one had been overlooked. THEORETICAL
DISCUSSION
The observations plotted in Fig. 1 are characteristic of close-coupled systems. Let us consider the expected decay to be observed from two states a and b which decay at rates A, and A, from states having the same energy above the ground state so as to allow a collisional resonance, i.e. I$ = -u,N,+u,,N,+P,,
(2)
Nj, = - abNb + a,bNrr+ Pb,
(3)
119
Lifetime and quenching rates for the H, continuum
where P,, and Pa are the state production
rates in the active period, and
a, = A,+o,JN+a,fiN, ab = A,+a@N +a,UN, =
aab
o,,tiN.
The basic solutions are N, = De-&‘,
N, = Ce-&‘,
(4)
with 1
=
(ab+a~)+J(a2--aba,+a~+4a,bab3
,
2
(5)
and the general solutions after cutoff (i.e. P, = Pb = 0) are N
=
a
Cl
e-“~*+C,
eeA2’
(6)
and (7) where a’ = J(a,’ -&,a,
+ ai + 4tl,b&) ;
(8)
I, and 1, are the positively and negatively signed radicals, respectively. Under the experimental conditions used, the on-period will have resulted in exciting the states involved to saturation. Therefore, the initial populations at cutoff will be
Noo =
ab&
+
aaab-
abJb
(9)
aabah
and
This leads to an evaluation of the constants C, and C2 as Cl = GN,,,
c2
=
a’+ab ---N,, Za’
-
$N,, ,
(11)
+
$Nb,.
(12)
We are interested only in the 6nal form of equation (6) since it represents the state observed in radiation whereas the state represented by equation (7) is postulated to be a
120
R.T. THOMPSON and R. G. FOWLER
radiation of another frequency. Equation (6) becomes N
=
La
)_
tabzPa
+“baabpb
2GI’ 1 kbpo+
ab,pb)
f2 k%zab -
k”baPb
+ (a,olb
-
(e
_
+
%babapa)(e-
I2f _ e- I,r
1
%bC(ba)
(13) a1t+e-A21).
&baba)
Now 1, >>&, and the sum of the coefficients of the exponential in which it occurs is negative also, so that it is an unobservably rapid buildup adjustment of the states involved. The solid line in Fig. 1 is a plot of the decay constant & of equation (13) where, from equation (5),
(‘% +
Ab) + (0, + ob + @ab + ob,)uN
- ,,{
[A, - A, + (0, - ob + flab - ob,)fiN]2
+4e,b0b,ij2N2)
2 (14) Values chosen for the parameters to obtain the curve are A, = 39 x lo6 set- ‘, A, = 384 x lo6 set- ‘, (T, = fib = 4.8 x lo-l6 cm*, cab = 2.0 x lo- l4 cm*, cbo = 2.4 x lo-r4 cm*, 0 = 3.8 x lo5 cm/set (T = lZOO”K),N = 8.05 x 10” P (torr). It is not possible to determine from the decay constant whether the auxiliary state is the la+,, ‘I:, the 10~2s ‘I:, the lcr,2p7r 311U,the la,Zpn ‘II”, or all of them put together. Presumably there is enough rotational overlap for a close resonance with any of these levels. Certainly the potential curves all lie so close together on the small molecular separation side that easy transfer is to be expected. Because of the short lifetime measured for this side state, we would be inclined to identify the la,2pz ‘II,, which radiates as an allowed transition to the ground state, as the one whose lifetime was being observed at high pressure. We can say with certainty that there is a substantial amount of electron excitation directly into the “c, state, because the intensity at low pressures is linearly proportional to the pressure, but it is not possible for us to determine whether there is direct excitation to the side state. We may take the further hint that the side state has a large ‘allowed’ excitation cross section from the feeling of RICHARDSON U) that the continuum is enhanced at high pressure, and speculate that the 2.6 nsec lifetime is an unresolved mixture of two closely similar lifetimes for the ‘c, and ‘II, states. The quenching cross section of 6.0 x lo- l6 cm* obtained by CENTER(~)from data taken at pressures above one torr compares favorably with the results reported here, and we would not debate the point in favor of our value. The linear relationship of p/Z vs. p observed by CENTER@) is also compatible with the system described here. This can be shown by setting Nje = I\i, = 0 in equations (2) and (3), solving for N, and using our parameters plotting PINB,
vs. P-
An additional measurement by IMHOF and READ (')of 11.0 nsec fails to agree with either result reported here, however no pressure dependence is indicated in their report. Such information might show reason for the discrepancy. Probably they have made an extrapolation from some limited intermediate segment of the true curve.
Lifetime and quenching rates for the H, continuum
121
REFERENCES
1. T. M. HOLZBERLEIN, Rev. Scient. Znstr. X,1041 (1964). 2. A. WAYNE JOHNSONand R. G. FOWLER, J. them. Phys. 53,65 (1970). 3. R. G. FOWLERand T. M. HOLZBERLEIN, J. them. Phys. 45, 1123 (1966). 4. A. J. MERER and R. S. MULLIKEN. Laboratorv of Molecular Structure and Spectra, Department of Physics, University of Chicago, Tech. Report, P200 (1968). 5. 0. W. RICHARDSON, Molecular Hydrogen and Its Spectrum, p. 293. Yale University Press, New Haven (1934). 6. R. E. CENTER,Private communication. 7. R. E. IMHOF and F. H. READ, Lifetime measurements by an electron photon coincidence method, Second Znt. Conf. on Beam-Foil Spectroscopy. Lysekil, Sweden, June (1970).
Transfer. Vol. 12. pp. 117421.
Pergamon
Press
1972. Printed
in Great
Britain
NOTE LIFETIME AND QUENCHING RATES FOR THE Hz CONTINUUM R. T. THOMPWN and R. G. FOWLER Departmentof Physics and Astronomy, University of Oklahoma, Norman, Okla., 73069, U.S.A. (Received 22 March 1971)
Abstract-When measured down to low pressures, the radiation processes of the H, continuum have proved to be unexpectedly complex, involving at least two states. The lifetime of the 3Zr state is found to be 26 nsec, with a resonance exchange cross-section of 2 x lo-l4 cm’ to some side state and a quenching cross section of 4.8 x IO-l6 cm’. INTRODUCTION
the invertion developed by HOLZBERLEIN(~)and the delayed coincidence technique described by JOHIWN and FOWLER(‘) the previous measurements of Holzberlein on the continuum in H, have been revised. The process of emission of the continuum is found to be more complex than previously envisioned. There are evidently two states in close resonance, and the apparent lifetime at pressures above 1 torr is not the true lifetime of the ‘xg state. Results of the new experimental data yield a low-pressure exchange crosssection of 2.0 x lo-l4 cm2 between the states and a high-pressure quenching cross-section of 4.8 x lo-l6 cm2 for both states. Application of a magnetic field applied axially to the invertron yielded no change of lifetime for fields up to about 18 gauss (calculated) which was sufficient to disperse the highly visible axial concentration of excited molecules. Linear asymptotic extrapolation of the high-pressure data to zero pressure yields a lifetime of 2.6 f 0.3 nsec for the side state, whereas linear extrapolation of the low pressure lifetimes indicates a true lifetime for the 0’ = 03cB+ state of 26 f 2 nsec at zero pressure. The new data were obtained by observing emitted light at 2750 and 2950 A ‘which should be due to transitions occurring between the stable lsa2sa 3xg and the unstable lsa2pa “c, vibrational levels. The results were corrected for a small pressure-dependent cascade component. UTILIZING
EXPERIMENTAL
OBSERVATIONS
The new observations of lifetimes z in molecular hydrogen were obtained at pressures torr using a 4 m Jarrell Ash monochromator and were combined with higher pressure data obtained earlier by Holzberlein to form the plot of l/z vs. pressure shown in Fig. 1. The significance of the l/z plot is that it reveals the dominant processes of a simple exponential state decay linearly according to the relation 0.0344800
1 -=A+crNo~=L+avp T
z.
kT’
where N, z population density of neutrals, IJ E quenching cross section, A E transition probability out of the excited state, 5 = mean molecular speed. 117
R. T. THOMPWNand R. G. FOWLER
118
The lifetimes at low pressure at the two wavelengths measured (2750 and 2950A) where found to be in the proportion X3, showing, as is expected, that the continuum in different spectral localities originates from different u per vibrational states. At 2950 A the transition is predominantly from U’= 0 of the 3f : state, while at 2750 A it comes predominantly from U’= 1. At high pressures, there was no such distinction between wavelengths. Data at the lowest pressures have therefore been reduced, by application of the wavelength factor, to equivalent u’ = 0 values. 280
1
I ?:
0
I
I
I
EXPLODE0
0 NO FILTER A 7-60 CORNING FILTER o MONOCHROMATOR (NEW DATA) ANALYTICAL APPROXIMATION
VIEW
I
0
4
8
12
16 20 PRESSURE
24 (TORR.)
FIG. 1. Inverse lifetime to pressure results for H,(lag2S30:
28
to la,lo~~:
I
32
36
I
40
transition). Inset shows
detail at ongin.
The lifetimes plotted in Fig. 1 correspond to the shortest decay observed. In each case, our least-squares computer program enables us to resolve any complex decays into a sum of exponentials and to identify the two or three fastest decays with reasonable accuracy. In the case of the H, continuum, only a very weak cascade component was present. Consequently, the behavior of the l/z plot is strikingly anomalous, having two linear regions, the high-pressure data extrapolating to a faster lifetime at zero pressure than the low-pressure data, a situation which cannot be explained by a cascade, even if there were a possibility that one had been overlooked. THEORETICAL
DISCUSSION
The observations plotted in Fig. 1 are characteristic of close-coupled systems. Let us consider the expected decay to be observed from two states a and b which decay at rates A, and A, from states having the same energy above the ground state so as to allow a collisional resonance, i.e. I$ = -u,N,+u,,N,+P,,
(2)
Nj, = - abNb + a,bNrr+ Pb,
(3)
119
Lifetime and quenching rates for the H, continuum
where P,, and Pa are the state production
rates in the active period, and
a, = A,+o,JN+a,fiN, ab = A,+a@N +a,UN, =
aab
o,,tiN.
The basic solutions are N, = De-&‘,
N, = Ce-&‘,
(4)
with 1
=
(ab+a~)+J(a2--aba,+a~+4a,bab3
,
2
(5)
and the general solutions after cutoff (i.e. P, = Pb = 0) are N
=
a
Cl
e-“~*+C,
eeA2’
(6)
and (7) where a’ = J(a,’ -&,a,
+ ai + 4tl,b&) ;
(8)
I, and 1, are the positively and negatively signed radicals, respectively. Under the experimental conditions used, the on-period will have resulted in exciting the states involved to saturation. Therefore, the initial populations at cutoff will be
Noo =
ab&
+
aaab-
abJb
(9)
aabah
and
This leads to an evaluation of the constants C, and C2 as Cl = GN,,,
c2
=
a’+ab ---N,, Za’
-
$N,, ,
(11)
+
$Nb,.
(12)
We are interested only in the 6nal form of equation (6) since it represents the state observed in radiation whereas the state represented by equation (7) is postulated to be a
120
R.T. THOMPSON and R. G. FOWLER
radiation of another frequency. Equation (6) becomes N
=
La
)_
tabzPa
+“baabpb
2GI’ 1 kbpo+
ab,pb)
f2 k%zab -
k”baPb
+ (a,olb
-
(e
_
+
%babapa)(e-
I2f _ e- I,r
1
%bC(ba)
(13) a1t+e-A21).
&baba)
Now 1, >>&, and the sum of the coefficients of the exponential in which it occurs is negative also, so that it is an unobservably rapid buildup adjustment of the states involved. The solid line in Fig. 1 is a plot of the decay constant & of equation (13) where, from equation (5),
(‘% +
Ab) + (0, + ob + @ab + ob,)uN
- ,,{
[A, - A, + (0, - ob + flab - ob,)fiN]2
+4e,b0b,ij2N2)
2 (14) Values chosen for the parameters to obtain the curve are A, = 39 x lo6 set- ‘, A, = 384 x lo6 set- ‘, (T, = fib = 4.8 x lo-l6 cm*, cab = 2.0 x lo- l4 cm*, cbo = 2.4 x lo-r4 cm*, 0 = 3.8 x lo5 cm/set (T = lZOO”K),N = 8.05 x 10” P (torr). It is not possible to determine from the decay constant whether the auxiliary state is the la+,, ‘I:, the 10~2s ‘I:, the lcr,2p7r 311U,the la,Zpn ‘II”, or all of them put together. Presumably there is enough rotational overlap for a close resonance with any of these levels. Certainly the potential curves all lie so close together on the small molecular separation side that easy transfer is to be expected. Because of the short lifetime measured for this side state, we would be inclined to identify the la,2pz ‘II,, which radiates as an allowed transition to the ground state, as the one whose lifetime was being observed at high pressure. We can say with certainty that there is a substantial amount of electron excitation directly into the “c, state, because the intensity at low pressures is linearly proportional to the pressure, but it is not possible for us to determine whether there is direct excitation to the side state. We may take the further hint that the side state has a large ‘allowed’ excitation cross section from the feeling of RICHARDSON U) that the continuum is enhanced at high pressure, and speculate that the 2.6 nsec lifetime is an unresolved mixture of two closely similar lifetimes for the ‘c, and ‘II, states. The quenching cross section of 6.0 x lo- l6 cm* obtained by CENTER(~)from data taken at pressures above one torr compares favorably with the results reported here, and we would not debate the point in favor of our value. The linear relationship of p/Z vs. p observed by CENTER@) is also compatible with the system described here. This can be shown by setting Nje = I\i, = 0 in equations (2) and (3), solving for N, and using our parameters plotting PINB,
vs. P-
An additional measurement by IMHOF and READ (')of 11.0 nsec fails to agree with either result reported here, however no pressure dependence is indicated in their report. Such information might show reason for the discrepancy. Probably they have made an extrapolation from some limited intermediate segment of the true curve.
Lifetime and quenching rates for the H, continuum
121
REFERENCES
1. T. M. HOLZBERLEIN, Rev. Scient. Znstr. X,1041 (1964). 2. A. WAYNE JOHNSONand R. G. FOWLER, J. them. Phys. 53,65 (1970). 3. R. G. FOWLERand T. M. HOLZBERLEIN, J. them. Phys. 45, 1123 (1966). 4. A. J. MERER and R. S. MULLIKEN. Laboratorv of Molecular Structure and Spectra, Department of Physics, University of Chicago, Tech. Report, P200 (1968). 5. 0. W. RICHARDSON, Molecular Hydrogen and Its Spectrum, p. 293. Yale University Press, New Haven (1934). 6. R. E. CENTER,Private communication. 7. R. E. IMHOF and F. H. READ, Lifetime measurements by an electron photon coincidence method, Second Znt. Conf. on Beam-Foil Spectroscopy. Lysekil, Sweden, June (1970).