- Email: [email protected]
dissociation of hydrogen molecules
Volume
125, number
1
CHEMICAL
PHYSICS
LETTERS
21 March 1986
INFLUENCE OF THE VIBRATIONAL QUANTUM NUMBER OF THE RESONANT STATE IN RESONANT MULTIPHOTON IONIZATION/DISSOCIATION OF HYDROGEN MOLECULES J.H.M. BONNIE, P.J. EENSHUISTRA,
J. LOS and H.J. HOPMAN
Association EURA TO&l- FOM, FOM Institute for Atomrc and Molecular Physrcs, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands Received
3 January
1986
We have studied the resonant multiphoton ionization of hydrogen in a three-photon excitation, one-photon ionization scheme. Superimposed on the ionization process we find a dissociation mechanism which manifests itself in a strong H+ signal. The ratio of H+ to Hi stgnals depends on the vibrational quantum number U’ of the intermediate state and on the laser intensity. We present a simple model which qualitatively reflects this dependence.
1. Introduction In hydrogen discharges, at gas pressures around 5 X 1O-3 mbar, an unexpectedly high H- ion density can be found [ 11. Under optimum conditions this density can amount to 30% of the electron density. Since these H- ions are easily destroyed in the discharge, there must be a very efficient production mechanism. It is suggested [2,3] that H- ions are produced by the reaction: H2(u’> t e- + H- t Ho .
0)
The cross section of this reaction is strongly dependent on the vibrational quantum number u” [4]. One way to test this hypothesis is to measure the vibrational distribution of hydrogen molecules in such a discharge and compare it with calculated distributions [2,3]. Pealat et al. [5] have tried to measure this distribution with CARS. Due to the low detection’sensitivity they were not able to measure beyond u” = 3. We have set up an experiment to measure this distribution with resonant multiphoton ionization (RMI), which is a new technique in this field. The possibility of detecting molecular hydrogen in a quantum-state-specific manner with RMI was first demonstrated by Mariner0 et al. [6], in a twophoton excitation, one-photon ionization scheme. 0 009-2614/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
We have chosen in favour of a three-photon excitation, one-photon ionization scheme, which has also been used by Pratt et al. [7,8]. If the resonance is one of the levels of the B 1 zi state we speak of the three-photon equivalence of the Lyman bands and if the resonance is one of the levels of the C 1II, state we speak of the three-photon equivalence of the Werner bands. The diagnostic, in our apparatus, consists of the time-of-flight analysis of ions formed in the RMI process. We expected to be able to solve the problems related with the detection of RMI ions despite the continuous flow of plasma towards the laser focus. Because of the plasma we did not attempt the more complicated detection of photoelectrons. On starting the measurements, initially without discharge so that all molecules were in u” = 0, we discovered an unexpected dissociation process leading to H+, superimposed on the ionization process. Although the appearance of ions always coincided with a resonance of the laser wavelength with one of the Lyman or Werner transitions, we found strong variations in the ratio of the number of H+ to the number of I$ ions with the vibrational quantum number u’ of the resonant level. Moreover, a laser intensity effect was observed. Pratt et al. [7,8] do not report any evidence of H+ production in the ion signal. When 27
Volume 125, number 1
CHEMICALPHYSICS LETTERS
looking at the photoelectron spectra, they found, in a Lyman transition, an unexpected electron peak which they tentatively assigned to the ionization of H*(n = 2) resulting from the multiphoton dissociation of H2 [7]. For the Werner bands they do not report any evidence for H+ production [8] which is in sharp contrast with our measurements. A recent publication by Comaggia et al. [9] proves the existence of an important dissociation mechanism in the RMI of hydrogen. In this experiment four photons are used to excite the molecule to the uE = 2 level of the inner well of the E,F 1Zg’state. Cornaggia et al. list and discuss several processes which could explain the high probability of the multiphoton dissociation of H2.
21 March 1986
atoms on the measured spectra. In fact there is no effect, except for the ionisation signal in the H+ channel at h * 29 1.8 nm, which corresponds to threephoton excitation, from the n = 1 to n = 4 level, onephoton ionization of hydrogen atoms.
3. Results
2. Experimental
The selection rules for the three-photon equivalence of the Lyman and Werner bands have been discussed by Pratt et al. [7,8]. In short, the Lyman bands have four rotational branches labeled N(Aj = -3), P(Aj = -l), R(Aj = tl) and T(Aj = t3) out of which we observe only P and R branches. The Werner bands have seven rotational branches out of which we observe only P(Aj = -l), Q(Aj = 0) and R(Aj = tl). All
A detailed description of the experiment will be given in a forthcoming paper. Tunable UV radiation between 285 and 305 nm is generated by frequency doubling the output of an excimer pumped dye laser. At the top of the dye tuning curve typically 1.5 mJ W laser pulse energy is focused by an 8 cm lens in front of an aperture in a discharge chamber. Pulse duration is about 15 ns. The pressure in the chamber is ~10~~ mbar and in the region outside the chamber, far from the aperture, the pressure is approximately 1000 times lower. The dimensions of the aperture are 2 X 4 mm2 and the laser beam is focused approximately 5 mm in front of it. It must be emphasized that for all measurements discussed in this article the discharge was turned off. The ions generated by the laser beam are accelerated by an electric field of 10 kV/ cm into a periodic focusing/defocusing lens system, which takes care of the transport of the ions to the detector. This transport system is in fact a time-offlight mass spectrometer which enables us to distinguish between H+ and I-$ ions. The detector is a Johnston particle multiplier which is employed in current mode. After amplification, the signal is fed into a gated, current-integrating analog-to-digital converter. Both H+ and H; signals and laser pulse energy are measured for every lasershot. The whole experiment is controlled by a microcomputer. When the filaments in the discharge box are turned on, a large number of H atoms are created. This offers the possibility of examining the effect of the presence of H
Fig. 1. RMI ion spectrum of hydrogen for part of the Werner (2-O) and the Lyman (11-O) band. The lower and middle curves represent the Hz and H* ionization signals respectively for which the scales are the same. The upper curve shows the variation of laser pulse energy with wavelength.
28
Volume 125, number 1
CHEMICAL PHYSICS LETTERS
these observations are consistent with the results of Pratt et al. [7,8]. The RMI ion spectrum of hydrogen for part of the Werner (u’ = 2-u” = 0) band and the Lyman (u’ = 11-Y” = 0) band is given in fig. 1. The assignment is performed with the aid of the single-photon absorption data of Dabrowski and Herzberg [lo]. The lower and middle curves represent the Hg and H+ ionization signals respectively, for which the scales are the same. The upper curve represents the variation of laser pulse energy. The rapid oscillations in this signal are caused by the tracking mechanism of the frequency doubler, whereas the slow overall decrease is due to the wavelength dependence of the dye gain. In fig. 1 the influence of the shot-to-shot variation in the laser intensity has been reduced by averaging over 30 shots for every wavelength point. The stepsize in fig. 1 is 16.8 pm. As can be seen in fig. 1, about 40% of the ionization signal of the Werner (2-O) band consists of H+. The Lyman (11-O) band however is seen purely as H+. Results for all bands investigated, are summarized in table 1, which gives the measured ratios of the H+ to the Hz signals, which we shall refer to as H+/Hz, for the R(1) transition of the Lyman bands and the Q(1) transition of the Werner bands. Also in this table
Table 1 Results for the measured ratio H+/Hl for the bands investigated . The measured ratio was deduced from the top of the resonance profile of the R(1) transition for the Lyman bands and the Q(1) transition for the Werner bands. The wavelength at which this transition occurs, and the pulse energy when the laser was at this wavelength are given. The estimated ratio is the value for the ratio H+/Hl that is calculated Rand
Measured Wavelength ratio (mn)
Pulse energy
Estimated ratio
(mJ) Lyman (13-O) (12-O) (11-O) (9-O) (8-O) (7-O) Werner (2 -0) (l-0) (O-0)
>lO >lO >lO 5 3 1 0.6 0.1 0.02
286.5 289.1 291.8 297.6 300.7 304.0
1 .o 1.3 1.1 0.9 1.1 0.8
large large large large large 0.9
298.8 296.0 302.9
1.4 0.5 1.0
0.6 0.0 0.0
i1
21 March 1986
I
10
04 !ASE9
08 PULSE
I 2 ENERGY
I .6
2
1m.J)
Fig. 2. Variation of the ratio H+/H: as a function of Laser pulse energy for the Q(1) transition of the Werner (2-O) band. The data points are measured values whereas the full curve is a calculation.
are the pulse energies used when measuring these peaks. Note the increase of H+/Hz with increasing u’! To gain some insight into the dependence of the ratio H+/Hz on the laser intensity, we measured the Q( 1) peak of the Werner (2-O) band at different pulse energies. Laser pulse energy was varied by detuning the frequency doubler in a reproducible manner. The ratio H+/H$ was derived from the top values of the resonance profiles. The results of these measurements are represented by the data points in fig. 2. The error bars in this figure account for statistical errors only and not for systematic errors like differences in detection efficiency for H+ and Hz or the fact that we varied laser pulse energy and not the true laser intensity in the focus.
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CHEMICAL PHYSICS LETTERS
4. Discussion In our experiment the measured ratio H+/Hz depends on three unrelated parameters which we discuss in succession. (I ) Detection efficiency of ZP and Z3$. The de tection efficiency for H+ is less than that for Hz. This is due to the lower secondary emission coefficient of copper-beryllium, for H+ ions in comparison to Hz ions with the same energy [l 11. With the observed decrease in H+/Hz under the same conditions over a few months, probably due to contamination effects in the particle multiplier, we assume that, in our experiment, H+ ions are detected less efficiently than I-$ ions by a factor of 3 at the most. If one wants to compare theoretically predicted ratios with the measured ratios, the predicted values must be multiplied by a factor y which should have a value between 1 and 0.3. (2) Type of electronic/vibronic transition. We never observed any H+ or Hl signal when the ionization process was not resonantly enhanced. This means that the differences in the processes leading to the formation of H+ and Hz must occur after the threephoton excitation step has taken place. Starting from either the B 1Zi or the C 1Il, state of H2 there are two possible ways leading to .H+ production by the absorption of two photons in succession: H;(u’)+hv+H*
(2)
H*2(u’) t hv -f I$@+) t efollowed by I-$(u+) t hu + H+ + Ilo ,
(3)
in which u+ is the vibrational quantum state in which the Hz ions are formed. From our point of view the hydrogen molecules do not necessarily absorb the fourth photon immediately after the three-photon excitation step. In fact they may ‘wait” for a time which corresponds to the lifetime of the excited state. Also the excited atom H* and the G ion may wait for a certain time before they absorb the fifth photon leading to H+ formation. Of course other H+ production mechanisms are also conceivable, but they would require the absorption of more than two photons after the excitation step. If reaction (2) were the only 30
H+ production mechanism, meaning that reaction (3) would stop after the first step, then it would be difficult to explain the observed lack of I$ ions in the Lyman (~‘-0) bands with u’> 10. It would imply that no I$ ions were produced, which is a onephoton process after the excitation step, whereas the complete reaction (2), which needs two photons after the excitation step, does happen. This seems unrealistic and we therefore infer that reaction (3)‘i.sthe explanation for the dependence of the dissociation probability on the vibrational quantum number u’ of the resonant level. Let nl (t) and n2(u+, t) be the number of H+ ions and Hz ions in a specific vibrational quantum state at time t respectively. Then the decrease 6n2(u+, t) in a short time interval 6t due to the dissociation of I-$, the second step in reaction (3), is given by: 6n2(u+, t) = -n2(u+, t)od(u+, A)Z6t,
(4)
where uc(u+, A) is the cross section for the dissociation of Hi by photons of wavelength X and Z is the laser intensity in photons/cm2. Integrating this formula over time gives the number of @ ions that are not yet dissociated at time t = T: n2(u+, T)= n2(u+, 0) exp[--oc(u+, X)17].
(5)
The number of H+ ions formed by dissociating I-I$(u+)is: nl(7) = n2(u+, 0) (1 - exp[-u&u+,
+I+’
followed by H* t hv + H+ t e- ,
21 March 1986
X)ZT]) .
(6)
In the experiment Hi ions are created in different vibrational quantum states. To calculate the total ratio H+/Hz one must add (5) and (6) separately for all u+ values and then divide the sum for (6) by the sum for (5). Because the H+ ions are detected less efficiently than the Hi ions by a factor 7, the expected result for the measured ratio H+/Hz is: II+ -_= Hz
Z g(u+) (1 - exp [-uc(u+, X)17]) y
Z g(u+) exp[-uc(u+, X)17]
’
(7)
The weight factors g(u+) determine which fraction of the formed I-$ ions is in a specific vibrational quantum state and have in fact been deduced by Pratt et al. [7,8] for some of the bands we have investigated. Because the $ ions are created in an electric field of 1 MV/m, they are extracted from the focal region in a time that is less than the laser pulse duration. We thus
Volume 125,
CHEMICAL PHYSICS L3Z’TERS
number 1
Table 2 Cross sections Ud(V+, h) in cm2 and weight factors g(u”, for the photodissociation For the Lyman bands with u* S 7 the weight factors are nat known Band
21 March 1986
of H,*(V> ions for the various bands investigated.
Relevant cross sections
Weight factors
fern21 Lyman
(X3-0)
ad{“+ = 8, h = 287.5 nm) = 3.7 x IO”8 Od(V+ = 7, h = 287.5 nm) = 2.9 X lo-l9 Od(V* = 6, h = 287.5 nm) = 4.0 X 10-t’
(12-O)
(11-O)
0d(“+=7,h=2YOmll)=5.4X
IO-l9
od(V+ = 6,h=290nm)=3.5x
10-‘g
Od(V+ = 5,h=290nm)=5.4X
10-t’
od(V+-6,h=292.5
X to-”
nm)=3,0
od(V’ = 5, h = 292.5 nm) = 6.2 x IO-“’ cd(V+ =4,h=292.5nm)=9.2k (9-O)
IO-”
Od(V+ = 5, h = 297.5 nm) = 7.6 X 10-t’ ad(“* = 4,h=297.5mn)=8.4X
IO-”
Od(“+ = 3,k = 297.5 nm) = 1.1 X IO-‘* (S-0)
od(V+=4&=300mn)=8.0~ ad(Vi=3,k=3~Nn)=9.6X a&J+ = 2,h=300nm)=2*5
(7 -0)
=
2,h=305nm)=1.7X
0d(VS=3,h=30511m)=7.4X (2-O)
(1-O)
(O-O)
10-t’ x lo--2o
ad(“+ = 1, A = 305 nm) = 8.3 x 1O-29 Od(V+
Werner
10-l*
Dd(V* = I,
g(v’=
1)=0.1
10m2’
g(V* = 2) = 0.3
IO-l9
g(v* = 3) = 0.6
A = 290 nm) = 4.0 X 1O*22
g(“+ = 1) = 0.07
ad(V+ =2,X=29fJmn)=5.3X od(V* - 3,X=2YQmn)=l.SX
iO-‘*
g(V+ = 2) = 0.72
IO-t8
g(V+ = 2) = 0.21
Od(V’ = t,A=295nm)=zAX
10-z2
g
Od(V’ = 2, h = 295 MI) = 3.7 X 1O-2o
g(V+ = 2) = 0.07
od(V’=
g(v+ = 0) = I,0
0, A = 302.5 nm) = 0
expect r to be determined by the residence time in the focus, At this point we must make an estimate both for I and 7 since we cannot measure the focal parameters in our experiment yet. We expect the diameter d of the laser focus to be 40 Mmat the most. This implies r = 1 ns. For a I mJ pulse the average intensity in this focus would be =S X lo9 W/cm2. In table Z?we give the values o&.8+, A) [K!] and g(u+) _17,8]for the various bands. For the Lyman (~‘-0) bands with u’ > 7 the g@*) values are not known from the literature but because of the large internuclear separation at the right turning point in the B 12$ state we expect that H$ ions will be form” ed predominantly with the energetically largest pas-
sible ui value, Therefore in table 2 we give the cross sections for the three highest possible us vahres in these bands which imply large values for H+& as is indeed observed in the experiment. If we assume a linear dependence between the laser pulse energy and the intensity in the focus and take y = 0.6 we can caIculate the ratio H*/Hs for the other bands. The results for these calculations are given in table 1 under *estimated ratio”. The fact that we see some Hi in the Werner (1-O) and (0-O) baud disagrees with the calculated ratio for these bands. ‘I% may be an indication that other H+ production mechanisms than the dissociation of H$ contribute to the total H+ signal. (3) Laser intensity. The observed dependence of 31
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CHEMICAL PHYSICS LETTERS
the ratio H+/I$ on the laser pulse energy can also be understood from eq. (7). If we again assume a linear dependence of the intensity in the laser focus with the total laser pulse energy and take 7 = 0.6, we can calculate the ratio H+/Hz for the Werner (2-O) band as a function of laser pulse energy. The result is the curve in fig. 2, which represents the measured behaviour. This intensity effect is most likely the reason why Pratt et al. [7,8], when they measured in the same wavelength region as we do, did not find any hard evidence for an H+ production mechanism: their intensity was probably too low. The assumption that they were working with a lower intensity than we are is confirmed by the fact that they observed the R(0) and R(1) peak of the Werner (2-O) band as two different peaks [ 83, whereas we see them as one peak due to the ac Stark broadening of the resonance profile caused by the laser field [ 131.
5. Conclusion
In resonant multiphoton ionization of hydrogen, via the three-photon equivalence of the Lyman and Werner bands, a strong dissociation process is superimposed on the ionization process. The degree of dissociation depends on the laser intensity and on the vibrational quantum number u’ of the resonant level. The u’ dependence can be explained in terms of the dependence of the cross section a,($, h), for photodissociation of I$ ions, on the vibrational quantum number v+. However the measurements do not exclude other dissociation mechanisms since it migh be possible that the cross section for the first part of reaction (2) also depends on u’, as, in a similar way, the dissociation cross section for I$ depends on u+. Ultimate proof can be obtained by looking at the photoelectron spectra under such conditions that the dissociation process occurs.
32
21 March 1986
Acknowledgement The authors wish to thank A.N.M. Bontekoe, P. Dljkstra and W. van Schelt for their assistance. This work is part of the research program of the association agreement of EURATOM and the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (ZWO) and EURATOM.
References PI M. Bacal, Physica Scripta T2/2 (1982) 467. I21 J.R. Hiskes and A.M. Karo, J. Appl. Phys. 56 (1984) 1927. I31 C. Gorse, M. Capitelli, J. Bretagne and M. Bacal, Chem. Phys. 93 (1985) 1. [41 M. Allan and SF. Wong, Phys. Rev. Letters 41 (1978) 1791. [51 M. Pealat, J.-P.E. Taran, M. Bacal and F. HiIlion, J. Chem. Phys. 82 (1985) 4943. [61 E.E. Marinero, C.T. Rettner and R.N. Zare, Phys. Rev. Letters 48 (1982) 1323. [71 S.T. Pratt, P.M. Dehmer and J.L. Dehmer, J. Chem. Phys. 78 (1983) 4315. [81 S.T. Pratt, P.M. Dehmer and J.L. Dehmer, Chem. Phys. Letters 105 (1984) 28. PI C. Cornaggla, J. Morellec and D. Normand, J. Phys. B18 (1985) WOl. 1101 I. Dabrowski and G. Herzberg, Can. J. Phys. 52 (1974) 1110. 1111 E.S. Chambers,Phys. Rev. 133 (1964) A1202. 1121 G.H. Dunn, Photodissociation of H2f and Dz, Theory and Tables, JILA Report No. 92 (January 30,1968). [13] L.A. Lompre, G. Mainfray, C. Manus and J.P. Marinier, J. Phys. B14 (1981) 4307.
125, number
1
CHEMICAL
PHYSICS
LETTERS
21 March 1986
INFLUENCE OF THE VIBRATIONAL QUANTUM NUMBER OF THE RESONANT STATE IN RESONANT MULTIPHOTON IONIZATION/DISSOCIATION OF HYDROGEN MOLECULES J.H.M. BONNIE, P.J. EENSHUISTRA,
J. LOS and H.J. HOPMAN
Association EURA TO&l- FOM, FOM Institute for Atomrc and Molecular Physrcs, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands Received
3 January
1986
We have studied the resonant multiphoton ionization of hydrogen in a three-photon excitation, one-photon ionization scheme. Superimposed on the ionization process we find a dissociation mechanism which manifests itself in a strong H+ signal. The ratio of H+ to Hi stgnals depends on the vibrational quantum number U’ of the intermediate state and on the laser intensity. We present a simple model which qualitatively reflects this dependence.
1. Introduction In hydrogen discharges, at gas pressures around 5 X 1O-3 mbar, an unexpectedly high H- ion density can be found [ 11. Under optimum conditions this density can amount to 30% of the electron density. Since these H- ions are easily destroyed in the discharge, there must be a very efficient production mechanism. It is suggested [2,3] that H- ions are produced by the reaction: H2(u’> t e- + H- t Ho .
0)
The cross section of this reaction is strongly dependent on the vibrational quantum number u” [4]. One way to test this hypothesis is to measure the vibrational distribution of hydrogen molecules in such a discharge and compare it with calculated distributions [2,3]. Pealat et al. [5] have tried to measure this distribution with CARS. Due to the low detection’sensitivity they were not able to measure beyond u” = 3. We have set up an experiment to measure this distribution with resonant multiphoton ionization (RMI), which is a new technique in this field. The possibility of detecting molecular hydrogen in a quantum-state-specific manner with RMI was first demonstrated by Mariner0 et al. [6], in a twophoton excitation, one-photon ionization scheme. 0 009-2614/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
We have chosen in favour of a three-photon excitation, one-photon ionization scheme, which has also been used by Pratt et al. [7,8]. If the resonance is one of the levels of the B 1 zi state we speak of the three-photon equivalence of the Lyman bands and if the resonance is one of the levels of the C 1II, state we speak of the three-photon equivalence of the Werner bands. The diagnostic, in our apparatus, consists of the time-of-flight analysis of ions formed in the RMI process. We expected to be able to solve the problems related with the detection of RMI ions despite the continuous flow of plasma towards the laser focus. Because of the plasma we did not attempt the more complicated detection of photoelectrons. On starting the measurements, initially without discharge so that all molecules were in u” = 0, we discovered an unexpected dissociation process leading to H+, superimposed on the ionization process. Although the appearance of ions always coincided with a resonance of the laser wavelength with one of the Lyman or Werner transitions, we found strong variations in the ratio of the number of H+ to the number of I$ ions with the vibrational quantum number u’ of the resonant level. Moreover, a laser intensity effect was observed. Pratt et al. [7,8] do not report any evidence of H+ production in the ion signal. When 27
Volume 125, number 1
CHEMICALPHYSICS LETTERS
looking at the photoelectron spectra, they found, in a Lyman transition, an unexpected electron peak which they tentatively assigned to the ionization of H*(n = 2) resulting from the multiphoton dissociation of H2 [7]. For the Werner bands they do not report any evidence for H+ production [8] which is in sharp contrast with our measurements. A recent publication by Comaggia et al. [9] proves the existence of an important dissociation mechanism in the RMI of hydrogen. In this experiment four photons are used to excite the molecule to the uE = 2 level of the inner well of the E,F 1Zg’state. Cornaggia et al. list and discuss several processes which could explain the high probability of the multiphoton dissociation of H2.
21 March 1986
atoms on the measured spectra. In fact there is no effect, except for the ionisation signal in the H+ channel at h * 29 1.8 nm, which corresponds to threephoton excitation, from the n = 1 to n = 4 level, onephoton ionization of hydrogen atoms.
3. Results
2. Experimental
The selection rules for the three-photon equivalence of the Lyman and Werner bands have been discussed by Pratt et al. [7,8]. In short, the Lyman bands have four rotational branches labeled N(Aj = -3), P(Aj = -l), R(Aj = tl) and T(Aj = t3) out of which we observe only P and R branches. The Werner bands have seven rotational branches out of which we observe only P(Aj = -l), Q(Aj = 0) and R(Aj = tl). All
A detailed description of the experiment will be given in a forthcoming paper. Tunable UV radiation between 285 and 305 nm is generated by frequency doubling the output of an excimer pumped dye laser. At the top of the dye tuning curve typically 1.5 mJ W laser pulse energy is focused by an 8 cm lens in front of an aperture in a discharge chamber. Pulse duration is about 15 ns. The pressure in the chamber is ~10~~ mbar and in the region outside the chamber, far from the aperture, the pressure is approximately 1000 times lower. The dimensions of the aperture are 2 X 4 mm2 and the laser beam is focused approximately 5 mm in front of it. It must be emphasized that for all measurements discussed in this article the discharge was turned off. The ions generated by the laser beam are accelerated by an electric field of 10 kV/ cm into a periodic focusing/defocusing lens system, which takes care of the transport of the ions to the detector. This transport system is in fact a time-offlight mass spectrometer which enables us to distinguish between H+ and I-$ ions. The detector is a Johnston particle multiplier which is employed in current mode. After amplification, the signal is fed into a gated, current-integrating analog-to-digital converter. Both H+ and H; signals and laser pulse energy are measured for every lasershot. The whole experiment is controlled by a microcomputer. When the filaments in the discharge box are turned on, a large number of H atoms are created. This offers the possibility of examining the effect of the presence of H
Fig. 1. RMI ion spectrum of hydrogen for part of the Werner (2-O) and the Lyman (11-O) band. The lower and middle curves represent the Hz and H* ionization signals respectively for which the scales are the same. The upper curve shows the variation of laser pulse energy with wavelength.
28
Volume 125, number 1
CHEMICAL PHYSICS LETTERS
these observations are consistent with the results of Pratt et al. [7,8]. The RMI ion spectrum of hydrogen for part of the Werner (u’ = 2-u” = 0) band and the Lyman (u’ = 11-Y” = 0) band is given in fig. 1. The assignment is performed with the aid of the single-photon absorption data of Dabrowski and Herzberg [lo]. The lower and middle curves represent the Hg and H+ ionization signals respectively, for which the scales are the same. The upper curve represents the variation of laser pulse energy. The rapid oscillations in this signal are caused by the tracking mechanism of the frequency doubler, whereas the slow overall decrease is due to the wavelength dependence of the dye gain. In fig. 1 the influence of the shot-to-shot variation in the laser intensity has been reduced by averaging over 30 shots for every wavelength point. The stepsize in fig. 1 is 16.8 pm. As can be seen in fig. 1, about 40% of the ionization signal of the Werner (2-O) band consists of H+. The Lyman (11-O) band however is seen purely as H+. Results for all bands investigated, are summarized in table 1, which gives the measured ratios of the H+ to the Hz signals, which we shall refer to as H+/Hz, for the R(1) transition of the Lyman bands and the Q(1) transition of the Werner bands. Also in this table
Table 1 Results for the measured ratio H+/Hl for the bands investigated . The measured ratio was deduced from the top of the resonance profile of the R(1) transition for the Lyman bands and the Q(1) transition for the Werner bands. The wavelength at which this transition occurs, and the pulse energy when the laser was at this wavelength are given. The estimated ratio is the value for the ratio H+/Hl that is calculated Rand
Measured Wavelength ratio (mn)
Pulse energy
Estimated ratio
(mJ) Lyman (13-O) (12-O) (11-O) (9-O) (8-O) (7-O) Werner (2 -0) (l-0) (O-0)
>lO >lO >lO 5 3 1 0.6 0.1 0.02
286.5 289.1 291.8 297.6 300.7 304.0
1 .o 1.3 1.1 0.9 1.1 0.8
large large large large large 0.9
298.8 296.0 302.9
1.4 0.5 1.0
0.6 0.0 0.0
i1
21 March 1986
I
10
04 !ASE9
08 PULSE
I 2 ENERGY
I .6
2
1m.J)
Fig. 2. Variation of the ratio H+/H: as a function of Laser pulse energy for the Q(1) transition of the Werner (2-O) band. The data points are measured values whereas the full curve is a calculation.
are the pulse energies used when measuring these peaks. Note the increase of H+/Hz with increasing u’! To gain some insight into the dependence of the ratio H+/Hz on the laser intensity, we measured the Q( 1) peak of the Werner (2-O) band at different pulse energies. Laser pulse energy was varied by detuning the frequency doubler in a reproducible manner. The ratio H+/H$ was derived from the top values of the resonance profiles. The results of these measurements are represented by the data points in fig. 2. The error bars in this figure account for statistical errors only and not for systematic errors like differences in detection efficiency for H+ and Hz or the fact that we varied laser pulse energy and not the true laser intensity in the focus.
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4. Discussion In our experiment the measured ratio H+/Hz depends on three unrelated parameters which we discuss in succession. (I ) Detection efficiency of ZP and Z3$. The de tection efficiency for H+ is less than that for Hz. This is due to the lower secondary emission coefficient of copper-beryllium, for H+ ions in comparison to Hz ions with the same energy [l 11. With the observed decrease in H+/Hz under the same conditions over a few months, probably due to contamination effects in the particle multiplier, we assume that, in our experiment, H+ ions are detected less efficiently than I-$ ions by a factor of 3 at the most. If one wants to compare theoretically predicted ratios with the measured ratios, the predicted values must be multiplied by a factor y which should have a value between 1 and 0.3. (2) Type of electronic/vibronic transition. We never observed any H+ or Hl signal when the ionization process was not resonantly enhanced. This means that the differences in the processes leading to the formation of H+ and Hz must occur after the threephoton excitation step has taken place. Starting from either the B 1Zi or the C 1Il, state of H2 there are two possible ways leading to .H+ production by the absorption of two photons in succession: H;(u’)+hv+H*
(2)
H*2(u’) t hv -f I$@+) t efollowed by I-$(u+) t hu + H+ + Ilo ,
(3)
in which u+ is the vibrational quantum state in which the Hz ions are formed. From our point of view the hydrogen molecules do not necessarily absorb the fourth photon immediately after the three-photon excitation step. In fact they may ‘wait” for a time which corresponds to the lifetime of the excited state. Also the excited atom H* and the G ion may wait for a certain time before they absorb the fifth photon leading to H+ formation. Of course other H+ production mechanisms are also conceivable, but they would require the absorption of more than two photons after the excitation step. If reaction (2) were the only 30
H+ production mechanism, meaning that reaction (3) would stop after the first step, then it would be difficult to explain the observed lack of I$ ions in the Lyman (~‘-0) bands with u’> 10. It would imply that no I$ ions were produced, which is a onephoton process after the excitation step, whereas the complete reaction (2), which needs two photons after the excitation step, does happen. This seems unrealistic and we therefore infer that reaction (3)‘i.sthe explanation for the dependence of the dissociation probability on the vibrational quantum number u’ of the resonant level. Let nl (t) and n2(u+, t) be the number of H+ ions and Hz ions in a specific vibrational quantum state at time t respectively. Then the decrease 6n2(u+, t) in a short time interval 6t due to the dissociation of I-$, the second step in reaction (3), is given by: 6n2(u+, t) = -n2(u+, t)od(u+, A)Z6t,
(4)
where uc(u+, A) is the cross section for the dissociation of Hi by photons of wavelength X and Z is the laser intensity in photons/cm2. Integrating this formula over time gives the number of @ ions that are not yet dissociated at time t = T: n2(u+, T)= n2(u+, 0) exp[--oc(u+, X)17].
(5)
The number of H+ ions formed by dissociating I-I$(u+)is: nl(7) = n2(u+, 0) (1 - exp[-u&u+,
+I+’
followed by H* t hv + H+ t e- ,
21 March 1986
X)ZT]) .
(6)
In the experiment Hi ions are created in different vibrational quantum states. To calculate the total ratio H+/Hz one must add (5) and (6) separately for all u+ values and then divide the sum for (6) by the sum for (5). Because the H+ ions are detected less efficiently than the Hi ions by a factor 7, the expected result for the measured ratio H+/Hz is: II+ -_= Hz
Z g(u+) (1 - exp [-uc(u+, X)17]) y
Z g(u+) exp[-uc(u+, X)17]
’
(7)
The weight factors g(u+) determine which fraction of the formed I-$ ions is in a specific vibrational quantum state and have in fact been deduced by Pratt et al. [7,8] for some of the bands we have investigated. Because the $ ions are created in an electric field of 1 MV/m, they are extracted from the focal region in a time that is less than the laser pulse duration. We thus
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Table 2 Cross sections Ud(V+, h) in cm2 and weight factors g(u”, for the photodissociation For the Lyman bands with u* S 7 the weight factors are nat known Band
21 March 1986
of H,*(V> ions for the various bands investigated.
Relevant cross sections
Weight factors
fern21 Lyman
(X3-0)
ad{“+ = 8, h = 287.5 nm) = 3.7 x IO”8 Od(V+ = 7, h = 287.5 nm) = 2.9 X lo-l9 Od(V* = 6, h = 287.5 nm) = 4.0 X 10-t’
(12-O)
(11-O)
0d(“+=7,h=2YOmll)=5.4X
IO-l9
od(V+ = 6,h=290nm)=3.5x
10-‘g
Od(V+ = 5,h=290nm)=5.4X
10-t’
od(V+-6,h=292.5
X to-”
nm)=3,0
od(V’ = 5, h = 292.5 nm) = 6.2 x IO-“’ cd(V+ =4,h=292.5nm)=9.2k (9-O)
IO-”
Od(V+ = 5, h = 297.5 nm) = 7.6 X 10-t’ ad(“* = 4,h=297.5mn)=8.4X
IO-”
Od(“+ = 3,k = 297.5 nm) = 1.1 X IO-‘* (S-0)
od(V+=4&=300mn)=8.0~ ad(Vi=3,k=3~Nn)=9.6X a&J+ = 2,h=300nm)=2*5
(7 -0)
=
2,h=305nm)=1.7X
0d(VS=3,h=30511m)=7.4X (2-O)
(1-O)
(O-O)
10-t’ x lo--2o
ad(“+ = 1, A = 305 nm) = 8.3 x 1O-29 Od(V+
Werner
10-l*
Dd(V* = I,
g(v’=
1)=0.1
10m2’
g(V* = 2) = 0.3
IO-l9
g(v* = 3) = 0.6
A = 290 nm) = 4.0 X 1O*22
g(“+ = 1) = 0.07
ad(V+ =2,X=29fJmn)=5.3X od(V* - 3,X=2YQmn)=l.SX
iO-‘*
g(V+ = 2) = 0.72
IO-t8
g(V+ = 2) = 0.21
Od(V’ = t,A=295nm)=zAX
10-z2
g
Od(V’ = 2, h = 295 MI) = 3.7 X 1O-2o
g(V+ = 2) = 0.07
od(V’=
g(v+ = 0) = I,0
0, A = 302.5 nm) = 0
expect r to be determined by the residence time in the focus, At this point we must make an estimate both for I and 7 since we cannot measure the focal parameters in our experiment yet. We expect the diameter d of the laser focus to be 40 Mmat the most. This implies r = 1 ns. For a I mJ pulse the average intensity in this focus would be =S X lo9 W/cm2. In table Z?we give the values o&.8+, A) [K!] and g(u+) _17,8]for the various bands. For the Lyman (~‘-0) bands with u’ > 7 the g@*) values are not known from the literature but because of the large internuclear separation at the right turning point in the B 12$ state we expect that H$ ions will be form” ed predominantly with the energetically largest pas-
sible ui value, Therefore in table 2 we give the cross sections for the three highest possible us vahres in these bands which imply large values for H+& as is indeed observed in the experiment. If we assume a linear dependence between the laser pulse energy and the intensity in the focus and take y = 0.6 we can caIculate the ratio H*/Hs for the other bands. The results for these calculations are given in table 1 under *estimated ratio”. The fact that we see some Hi in the Werner (1-O) and (0-O) baud disagrees with the calculated ratio for these bands. ‘I% may be an indication that other H+ production mechanisms than the dissociation of H$ contribute to the total H+ signal. (3) Laser intensity. The observed dependence of 31
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the ratio H+/I$ on the laser pulse energy can also be understood from eq. (7). If we again assume a linear dependence of the intensity in the laser focus with the total laser pulse energy and take 7 = 0.6, we can calculate the ratio H+/Hz for the Werner (2-O) band as a function of laser pulse energy. The result is the curve in fig. 2, which represents the measured behaviour. This intensity effect is most likely the reason why Pratt et al. [7,8], when they measured in the same wavelength region as we do, did not find any hard evidence for an H+ production mechanism: their intensity was probably too low. The assumption that they were working with a lower intensity than we are is confirmed by the fact that they observed the R(0) and R(1) peak of the Werner (2-O) band as two different peaks [ 83, whereas we see them as one peak due to the ac Stark broadening of the resonance profile caused by the laser field [ 131.
5. Conclusion
In resonant multiphoton ionization of hydrogen, via the three-photon equivalence of the Lyman and Werner bands, a strong dissociation process is superimposed on the ionization process. The degree of dissociation depends on the laser intensity and on the vibrational quantum number u’ of the resonant level. The u’ dependence can be explained in terms of the dependence of the cross section a,($, h), for photodissociation of I$ ions, on the vibrational quantum number v+. However the measurements do not exclude other dissociation mechanisms since it migh be possible that the cross section for the first part of reaction (2) also depends on u’, as, in a similar way, the dissociation cross section for I$ depends on u+. Ultimate proof can be obtained by looking at the photoelectron spectra under such conditions that the dissociation process occurs.
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Acknowledgement The authors wish to thank A.N.M. Bontekoe, P. Dljkstra and W. van Schelt for their assistance. This work is part of the research program of the association agreement of EURATOM and the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (ZWO) and EURATOM.
References PI M. Bacal, Physica Scripta T2/2 (1982) 467. I21 J.R. Hiskes and A.M. Karo, J. Appl. Phys. 56 (1984) 1927. I31 C. Gorse, M. Capitelli, J. Bretagne and M. Bacal, Chem. Phys. 93 (1985) 1. [41 M. Allan and SF. Wong, Phys. Rev. Letters 41 (1978) 1791. [51 M. Pealat, J.-P.E. Taran, M. Bacal and F. HiIlion, J. Chem. Phys. 82 (1985) 4943. [61 E.E. Marinero, C.T. Rettner and R.N. Zare, Phys. Rev. Letters 48 (1982) 1323. [71 S.T. Pratt, P.M. Dehmer and J.L. Dehmer, J. Chem. Phys. 78 (1983) 4315. [81 S.T. Pratt, P.M. Dehmer and J.L. Dehmer, Chem. Phys. Letters 105 (1984) 28. PI C. Cornaggla, J. Morellec and D. Normand, J. Phys. B18 (1985) WOl. 1101 I. Dabrowski and G. Herzberg, Can. J. Phys. 52 (1974) 1110. 1111 E.S. Chambers,Phys. Rev. 133 (1964) A1202. 1121 G.H. Dunn, Photodissociation of H2f and Dz, Theory and Tables, JILA Report No. 92 (January 30,1968). [13] L.A. Lompre, G. Mainfray, C. Manus and J.P. Marinier, J. Phys. B14 (1981) 4307.