J. Phys. Chem. 1995,99, 15335-15341
15335
Alignment Effects in the Dissociation of H2+ in Collisions with Laser-Excited Sodium Atoms H. Hulser, M. Braun, and G. Kubsch Fakultat fur Physik, Universitat Freiburg, Hemann-Herder-Strasse 3, 0-79104 Freiburg, Germany
E. E. B. Campbell and I. V. Hertel* Max Bom Institut fur Nichtlineare Optik und Kurzzeitspektroskopie, Postfach 1107, 0-12474 Berlin, Gemany Received: January 30, 1 9 9 9
Alignment effects are reported for the dissociation of H2+ in collisions with laser-excited sodium in the laboratory collision energy range 600-2400 eV. Measurement of coincidences between H+ and H for different laser polarizations enables a straightforward analysis of the experimental results and reduces the number of possible dissociation mechanisms when compared with measurements in which only protons are detected. A mechanism involving autoionization of high-lying Rydberg states of H2 is proposed as one possible mechanism for the production of protons with very low kinetic energies.
”* c
1. Introduction The investigation of atomic alignment has led to a much deeper understanding of the dynamics of valence electrons during inelastic and charge transfer processes in atom-atom and atom-ion collisions during the past 20 years (see e.g. refs 1 and 2). For many systems a simple, intuitive picture of the interaction mechanisms could be obtained over a large range of collision energies. In contrast, very little is known about the influence of the atomic alignment in collisions between an atom and a molecule. For first, pioneering experiments see refs 3 and 4. Such experiments could, at least in principle, provide model systems for the study of orbital selective elementary chemical reactions. Our aim in starting the experiments reported in this paper was to probe to what extent one could “switch on or off” chemical reactions by changing the alignment of the electronic charge cloud in the target atom via rotation of the polarization direction of the linearly polarized laser light used to excite the atom. We chose to study the collision-induced dissociation of H2+ since this is a relatively simple “reaction” with the simplest possible molecule. As target, we chose a quasi-one-electron atom, sodium, which can be efficiently excited to the first electronically excited state using a two-mode CW dye laser: H :
+ Na(3p)
-
H+
+ H + Na(3s,3p)
(1)
The collisional dissociation of H2+ has been extensively studied for many different (nonaligned) collision partners, mainly rare gases, over many years5-18 In spite of the effort that has gone into trying to understand the dissociation dynamics, there are still a number of puzzles which remain to be solved. In particular, the origin of very low kinetic energy protons which lead to a pronounced maximum in the center of the proton kinetic energy distributions has still to be fully understood and is probably different for different collision systems and collision energy regimes. Our results show clear, and in some cases very large, alignment effects which have a marked collisional energy dependence in the range 600-2400 eV and, in addition, vary with proton kinetic energy. A mechanism is proposed for the production of slow protons which is consistent with the @
Abstract published in Advance ACS Abstracts, October 1, 1995.
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alignment measurements; however, even for this “simple” model system, it is not possible to fully interpret the results until detailed NaH2+ potential surfaces are made available. 2. Apparatus A schematic diagram of the apparatus is shown in Figure 1. H2+ ions are produced in a Colutron ion source, accelerated by an electric field, momentum selected by an analyzing magnet, and focused by einzel lenses. The energy of the ion beam which can be used in the experiments ranges from 500 eV to 2.5 keV. The ion beam is collimated by a series of apertures, passes through the collision center, and is focused on to the entrance aperture of a double hemispherical electrostatic energy analyzer. The ion beam diameter at the energy analyzer is less than 1 mm. The energy analyzer can be rotated about the collision center in the angular range from -3” to +IOo in the collision plane as defined by the crossed projectile (H2+) and target (Na) beams. The energy resolution is (0.8 eV (measured fwhm of the parent projectile beam), and the angular resolution is 0.25”. The sodium target beam is produced from a recycling oven at a temperature of ca. 450 “C with a nozzle diameter of 0.3 mm. The sodium beam diameter at the collision center is 5 nun with a sodium atom density of ca. lotocm-3. Since we are mainly interested in observing effects of the alignment of the target atom on the collision process, our target has to be a low-density atomic beam (to avoid problems of radiation trapping”), and we thus have much smaller count rates than in previous
0022-3654/95/2099-15335$09.00/0 0 1995 American Chemical Society
Hulser et al.
15336 J. Phys. Chem., Vol. 99, No. 42, 1995 experiments in which collision cells were used. A liquid nitrogen cold trap near to the collision center serves to keep Torr the background pressure in the scattering chamber at during the measurements. The sodium beam is excited to the 3P3n(F=3) state by a linearly polarized two-mode continuous dye laser pumped by an Ar+ laser.20 This two-mode laser produces the two frequencies required to pump from both hyperfine levels of the sodium ground state and thus allows us to avoid the problem of losing atoms from the pump cycle due to spontaneous decay to the F = 1 ground state. (Because of the Doppler broadening in the beam and the closeness of the hyperfine levels, a significant number of atoms will always be excited to the F = 2 upper state, which can then decay to F = 1 in the ground state.) By this means, it is possible to obtain 30-40% of the sodium atoms in the excited 3P(F=3) state compared to ca. 10% using standard single-mode excitation. The polarization direction of the laser light can be rotated within the scattering plane, and the alignment of the excited sodium atoms is monitored by a photodiode looking onto the collision center at an angle of 45" to the scattering plane. The transmission energy of the hemispherical energy analyzer is scanned over a large range E = Ed2 f AE, where EO is the collision energy in the laboratory frame of reference, to ensure that all protons produced by the collision are detected. To obtain one proton spectrum, the.transmission energy is scanned on average 18 times with a collection time of 0.5 s per energy value on each scan, leading to a total collection time of about 20 min per proton spectrum. At each value of the transmission energy the proton intensity is measured for scattering from background gas, scattering from ground state sodium, and scattering from excited sodium with the atoms aligned parallel and perpendicular to the direction of the projectile beam. In a second mode of operation, experiments in which the protons are measured in coincidence with the fast neutral hydrogen atoms from the dissociated molecular ion were carried out by allowing the fast atoms to pass directly through the energy analyzer and detecting them with microchannel plates (see Figure 1) after residual ions were removed from the beam by an electrostatic deflection field.
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Figure 2. Some H2+ molecular potentials taken from data given by Sharp.*' The inelastic energy loss in the collision Q and the collisional excitation of the molecular ion above the dissociation limit 6 are illustrated for a Franck-Condon transition from a low-lying vibrational level in the ground electronic state.
Figure 3. Schematic of the scattering geometry. The position of the
molecular axis is described by the angles e,, and q c m . The projectile ion beam direction is given by the x axis, and the xy plane is the scattering plane. between the excited charge cloud of our sodium target atoms and the molecular axis. In a standard alignment collision experiment involving ionatom or atom-atom collisions with laser excited atoms, a polarization parameter PIcan be directly determined from the scattering intensities for laser light polarized parallel (0")and perpendicular (90") to the initial velocity vector:
3. Experimental Method The kinetic energy in the laboratory frame of reference of the protons produced from the collisional fragmentation of Hz+ is given by
where EOis the laboratory energy of the H2+, Q is the inelastic energy loss during the collision, E is the excitation of the molecular ion above the relevant dissociation limit, q c m is the angle the intermolecular axis makes with the scattering plane, and Ocm is the angle between the intermolecular axis and the initial velocity vector of the ion beam within the scattering plane. Q and E are illustrated in Figure 2, which shows some of the lowest-lying potential energy curves of H2+, taken from the data given by Sharp?' which are relevant to the following discussion. The experimental geometry is illustrated schematically in Figure 3. The finite acceptance angle of the detector provides a means to obtain information on the direction of the internuclear axis at the moment of dissociation even in experiments in which only the protons are detected (as reported in section 4.1) although the molecules are randomly oriented with respect to the initial velocity vector (see the discussion below). This makes it possible, in principle, to know the relative alignment
where Iex(0") and Iex(90") are the measured scattering intensities with the laser polarized parallel and perpendicular to the initial velocity vector, I, is the measured scattering intensity without laser excitation,&, is the proportion of excited target atoms, c;! is a depolarization parameter that accounts for the fine and hyperfine depolarization of the sodium atoms and has the value 317 for ideal optical pumping of Na(3p),' and PI is the reduced polarization parameter, i.e., the value that would have been measured if pure Na p orbitals could have been prepared. From this reduced polarization parameter, one can obtain a parameter e,,,, which gives the probability that the asymptotic preparation of a CJ state (i.e., parallel to the initial velocity vector) in the atomic target will lead to the observed collision event.
(4) This can in turn be related to the often used Fano-Macek alignment parameter, A20
The formalism described above for atom-atom or atom-atomic
Dissociation of H2+ in Collisions with Na Atoms ion collisions can be directly applied to the experiments reported here in section 4.2 in which coincidences between protons and neutral hydrogen atoms are measured: in this case the coincidence technique allows us to directly determine the position of the molecular axis on dissociation. For dissociative molecular ion collisions the relevant symmetry axis for describing the a or n nature of the prepared target is not the relative velocity vector of the collision partners but rather the direction of the H2+ molecular axis, which is not necessarily the same due to the random orientation of the molecular ions. This random orientation considerably complicates the interpretation of the data for experiments in which only the protons are detected. The fragments from those molecules whose axes lie along the direction between the collision center and the detector will always be detected. For every other axis position the detection probability depends on the primary ion beam energy as well as on the kinetic energy of the fragments in the center of mass reference frame and the experimental geometry. To help our interpretation of the measured proton energy spectra and to allow us to obtain the alignment parameter Quo from the data, we simulate the proton energy spectra by assuming direct, Franck-Condon transitions to repulsive, electronically excited states of H2+. It has been shown by, for example, Brenton et alS6and Guyon et aLZ2that such a simple picture can satisfactorily reproduce the form of the wings of the proton kinetic energy distribution for collisional dissociation of H2+ with a range of collision partners and energies on the order of kiloelectronvolts. The procedure which we use is similar to that described by Brenton et a1.6 with the additional inclusion of a polarization effect. For a given scattering angle and collision energy, we calculate the proton energy spectrum by multiplying the probability that a particular vibrational level in the ground electronic state is occupied (using the data of von Busch and D ~ n n * with ~ ) the Franck-Condon factors for transitions to the electronically excited state (for the present measurements 2pau, as discussed in section 4.1). We weight this probability with a factor exp(aAE,ib), where hE,,b is the dissociation energy of the particular vibrational level, to account for the increase in cross section with increasing vibrational quantum number. We then sum over all vibrational levels in the ground electronic state. The proton energy spectrum is obtained from the probability of transitions to the excited state as a function of the intemuclear distance ~H-H+.The weighting factors, a, are free parameters obtained by fitting the shape of the proton energy spectrum to the spectrum obtained from collisions with ground state (nonpolarized) targets and are dependent on the collision energy. As a validation of this procedure, we note that the factors which we obtain from fitting the spectrum from collisions with background gas (predominantly H2) are in good agreement with the relative collisional dissociation cross sections determined experimentally by Lindsay et al.I4 for 1 keV collisions between H2+ and H2 as a function of the vibrational quantum number. Calculations are carried out for all possible directions of the molecular ion axis before fragmentation, and the fragments which would be able to reach our detector are then recorded as a function of their laboratory kinetic energy. It is important to note at this point that the deflection of the H2+ system (center of mass) due to scattering can be completely neglected in comparison to the effect due to the transverse kinetic energy release in the dissociation. A rough estimate of the scattering angles to be expected in this collision system can be obtained from considering deflection functions calculated from Na(3s)-H+ and Na(3p)-H+ potentials given by Jitschin et aLZ4 From these results we do not expect to have any
J. Phys. Chem., Vol. 99, No. 42, 1995 15337 contribution from reduced scattering angles ELabeLab > 50 eVo, which is much less than the angular resolution of our experiment for the collision energies investigated here. Additional evidence for the very small scattering angles in this system is obtained from the coincidence experiments which show that the angular width-of the H+-H coincidence counts is the same as the angular width of the primary ion beam (f0.25"). The proton signals at larger OLab are therefore not due to scattering but are solely due to the detection of protons with a kinetic energy component perpendicular to the initial relative velocity direction, €1= EO&abZ. We use the above model to simulate a polarization effect in the sodium collisions by assuming that the dissociation probability depends on the angle between the molecular axis and the laser polarization direction (i.e., on the alignment of the Na(3p) orbital before the collision). We assume a dependence
x
x
.
well-known from photodissociation experiment^.^^ Here is the angle between the molecular axis and the electric vector of the linearly polarized light, PZ is the second-order Legendre polynomial, and p is the so-called asymmetry parameter. We want to point out here that eq 6 is a strict consequence of the single-photon excitation (i.e., the involvement of an atomic p state with a multipole moment of rank 2). The parameter /3 is, however, an average over all impact parameters and incident azimuthal angles of the trajectory. It is thus a measure of the so-called "integral alignment" similar to that detected in scattering angle averaged ion-atom collisions with polarization analysis of the reemitted radiation.26 The p parameter can be related to a correspondingly averaged alignment parameter (euu) as follows:
(7)
In this way we can simulate the proton energy spectra for sodium excitation with 0" and 90" polarized laser light. The value of
p used in the simulations is adjusted until (euu)reproduces the experimentally determined PI (eqs 3 and 4), thus enabling us
to extract the alignment parameter Quo from the experimental data. It should be emphasized here that we are making use of a simple Franck-Condon picture only to enable us to extract information from the energy spectra. This picture obviously does not take into account the interaction between the H2+ projectile ions and the sodium atoms. It is the details of these, unfortunately as yet unknown, molecular potentials as well as the atomic charge cloud dynamics with respect to the internuclear and molecular axes that are responsible for any observed alignment effects. In the high-energy limit where the atomic Na(3p) charge cloud can be considered space fixed during the collision, the process is somewhat simplified and could be described in the Franck-Condon picture. Even then, the polarization-dependent interaction potential has to be known where Fourier components, in this approach, induce the transitions. It is not obvious, however, that the H2+ velocities studied in the present work are high enough for this simplification.
4. Results and Discussion 4.1. Measurements of Proton Kinetic Energy Distributions. A typical proton energy spectrum is shown in Figure 4 for collisions with ground state sodium at a collision energy of 1600 eV and a detection angle of 0". The contribution from
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Figure 7. Alignment parameter (@uu) as a function of Eof3Lab2 = E L obtained from simulating the proton intensities in the tails of the kinetic energy distributions (see text) for (a) 600, (b) 1000, (c) 1200, (d) 1600 (squares), and 2400 eV (triangle). rl
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6. Proton kinetic energy spectra for the process H2+ Na(3p) H Na(3s,3p)for a collision energy of 600 eV and a detection of 0.5". Data are shown for excitation with 0" (squares) and 90" (dashed).polarized laser light: (a) experiment, (b) simulation.
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The black shading shows the difference spectra 1(90°) - Z(Oo) for these two laser polarizations. The data include a 70% contribution from scatteringfrom Na(3s); scatteringfrom background molecules has been extracted. aligned due to the depolarizing influence of the Na fine and hyperfine structure. In Figure 6a we show spectra obtained experimentally (EO = 600 eV, e b b = 0.5") for 0" and 90" polarized laser light. The total cross sections for collisional fragmentation from Na in the ground electronic state (3s) and the first excited state (3p) are very similar so that the integrated count rates are identical within the limits of experimental uncertainty. The data shown in Figure 6a include the contribution from ground state sodium. Note, however, that in the difference spectrum Z(90") - Z(0") also shown in Figure 6a the ground state contribution drops out. A significant polarization effect can be seen in the difference spectrum with a laser polarization parallel to the direction of the molecular ion beam, producing more ions in the "tails" of the energy distribution than for laser polarization perpendicular to the ion beam direction. The simulated difference spectrum in Figure 6b, with (euu)= 0.7, was obtained by adjusting the value of (euu)until the value of P1 (eq 2) obtained from the integrated intensities in the two "Franck-Condon" tails, multiplied by the depolarization parameter c2, matched the experimentally determined P I for the same proton energy range. As can be seen in Figure 6, the forms of the simulated spectra are also in excellent agreement with the experimental spectra. It can also be seen that even a relatively large alignment effect unfortunately only leads to a very small effect in the experimental data after the proportion of ground state atoms (70%), the depolarization of Na(3p) due to fine and hyperfine structure, and the experimental geometry are all taken into account. The experimental alignment parameters for the "fast" protons obtained from our fitting procedure described above are shown in Figure 7 for five different collision energies and a range of detection angles. The values plotted are the average of five different measurements, and the error bars are the standard deviation of each set of measurements. For the lowest collision
energy investigated, 600 eV, we find a very clear alignment effect of (euu) 0.7, which means that at this collision energy the molecular ion is most likely to dissociate when the target atom is aligned with its charge cloud parallel to the molecular axis, Le., in a u state. As the collision energy is increased, the preparation of a z state becomes more favorable for the dissociation, in particular for larger values of €1 with the crossover between u and n moving to smaller values of €1as the collision energy is increased. (The results at 1200 eV collision energy are the exception, for reasons which are not yet understood, and show exactly the opposite trend.) An increasing value of EoOLab2not only means a larger value of €1 but also, due to our fitting criteria (see above), means that the minimum proton kinetic energy E used in the data analysis increases with increasing EOebb2. The production of protons with small kinetic energies (0.015 to 10.3 eV for 600 eV, 0.09 to K0.2 eV for 1600 eV) is much more probable when a cr atomic target is prepared. If we believe our "Franck-Condon" picture, this would correspond to protons produced from dissociation of molecules in very high-lying vibrational states (see Figures 2 and Figure 6b); however, the protons may be produced by another mechanism. Protons with higher kinetic energies (lower-lying vibrational levels, possibly corresponding to collisions with smaller impact parameters) become increasingly important as the collision energy is increased and are more probable when a n atomic orbital is prepared. It is not possible to determine whether one dissociation mechanism involving the formation of a particular NaH2+ electronic state or a combination of two or more is responsible for the results reported in Figure 7 . The results cannot be satisfactorily explained by a simple "hand-waving'' model and will have to await the availability of the appropriate NaHZf potential surfaces before they can be properly interpreted. The large central peak corresponding to protons with very small kinetic energies in the center of mass frame of reference, E 0, has been reported many times for H2+ collisional fragmentation, and a number of mechanisms have been discussed in the literature: (i) direct electronic transitions to the repulsive 2p0, state (as discussed above) from very highly excited vibrational states in H2+,17 (ii) an excitation into the vibrational continuum of the ground state,27 (iii) an excitation of the nuclear or electron motion over the dissociation limit via van der Waals forces,28 (iv) charge transfer followed by predissociation to H+ H-,13 and (v) rotational predissociation
+
:
15340 J. Phys. Chem., Vol. 99, No. 42, 1995
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Hulser et al.
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Figure 8. Experimentally determined polarization effect PI for the central maximum as a function of collision energy for a detection angle of 0
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of highly excited quasi-bound H2+ states (with lifetimes > s ) . ~It could be shown that the form of this central peak is independent of target gas, collision energy, and intemal excitation of the molecular ion.9 The relative intensity, however, depends on the internal excitation of the H2+ and the polarizability of the target atom (for collisions with rare gases). Foumier et aL9 used these results to argue convincingly against mechanism i and also showed that the form of the central peak could be reproduced satisfactorily by assuming mechanism v. We have observed a very small alignment effect for this central peak which, however, shows a clear trend with increasi_ng collision energy. The experimentally determined values of P I , obtained by integrating over the proton intensities in the energy range omitted in the analysis of the spectra discussed above and applying eq 2, are shown in Figure 8 for a detection angle of 0”. We do not give the alignment parameter (euu)in this case since we are unable to unambiguously determine the position of the molecular axis on dissociation. If rotational predissociation (mechanism v) on the picosecond time scale was the only mechanism for the production of these very slow protons, the rotation of the molecule during the dissociation would rule out the observation of any alignment effect. Although rotational predissociation may still be a dominant mechanism in these collisions, the trend of the results in Figure 8 indicates that an additional mechanism may be contributing. 4.2. Coincidence Measurements. We can simplify the data analysis by detecting only those products which come from molecular ions oriented with their axis pointing in the direction of the detector with the help of coincidence measurements. For these experiments, the fast neutral hydrogen atoms produced from fragmentation of H2+ passed through the electrostatic energy analyzer and were detected by two channel plates mounted in the chevron configuration (see Figure 1). Any residual ions (positively or negatively charged) which may also have passed through the two apertures in the energy analyzer were deflected away from the detector by an electric field. These fast neutral atoms are used to trigger the coincidence electronics which register the corresponding protons if they are produced with the required kinetic energy release to be detected with the electron multiplier after traversing the double hemispherical energy analyzer. In Figure 9 we show the count rate for coincidences between protons and neutral hydrogen atoms as a function of the proton kinetic energy for a collision energy of 2400 eV. By this means we not only determine the geometry but can also immediately rule out any contributions from, for example, mechanism iv (H2+ Na H+ HNa+) and, for the central peak, mechanisms in which the molecule is rotationally excited in the collision. In contrast to the experiments in which only protons are detected, we see a large difference in the measurements with and without laser excitation. Given that we have 30% of the atoms in the excited state, we
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Figure 9. H+-H coincidence counts as a function of the proton kinetic energy in the lab system for a collision energy of 2400 eV: crosses, collisions with Na(3s); triangles, 90” laser polarization; diamonds, 0” laser polarization. The counts with laser excitation have a 70% contribution from Na(3s). can deduce the cross section for dissociation from laser excited Na(3p) to be approximately a factor of 2 larger than that for Na(3s). The intensity of the central maximum relative to the “tails” is noticeably smaller than for the noncoincidence proton measurements, presumably since some of the contributing mechanisms for the production of these very slow protons have now been removed. There is a clear preference for dissociation in collisions with cr prepared targets in the central maximum. We obtain an alignment parameter (eoo)= 0.63 f 0.2 (PI = 0.26 f 0.4) for E 0 eV (slightly less if we integrate over the full range of the central peak), which is in agreement with the trend seen in Figure 7 but significantly larger than the value obtained from the noncoincidence proton measurements. We also see in Figure 9 that for a proton kinetic energy of 2 eV in the center of mass frame, Le., lab kinetic energies of 1135 and 1265 eV, respectively, we have an almost complete n preparation with (euu)= 0.05 f 0.1. This result is in keeping with the result shown in Figure 7d for the noncoincidence proton measurements but indicates that the n preparation is important for only a relatively small proton kinetic energy range. Evidence for an additional maximum in the proton kinetic energy distribution at Ed2 f 40 eV, which shows no alignment effect at this collision energy, can also be seen in Figure 9. It is possible that the process leading to protons with kinetic energies in this range is responsible for the cr contribution seen in Figure 7 for lower collision energies. A possible interpretation for the alignment effect observed for the very low energy protons in the central maximum could be charge transfer to autoionizing Rydberg states in the H2 molecule. It is known from photoionization experiments on Hr+ carried out, for example, by Ito et that slow protons can be produced via autoionization of the H2 Q1’Cu+Rydberg states in the dissociative continuum of H2+. Charge transfer in general is certainly the dominant process in collisions between Na atoms and H2+.30 At the high collision energy investigated here (2400 eV), we could expect a “space-fixed” behavior such that charge transfer from a cr prepared Na orbital would preferentially populate high-lying C states in H2, which can then autoionize. As the collision energy is reduced, we could expect that a “locking effect” (see e.g. ref 3 1) would become important, whereby a n-prepared orbital rotates during the collision and also preferentially produces a molecular state on charge transfer. This very simplified picture would at least be in aggrement with the trend seen in Figure 8 where the noncoincidence, low kinetic energy release data appear to go from a
Dissociation of H2+ in Collisions with Na Atoms negative (ndominance) at low colhsion energies to a positive PI(a dominance) at high collision energies. An additional effect which may lead to an altemating PI could be competition with, for example, autoionization of H2(Q2IHg)Rydberg states, which should show the opposite polarization trend. More detailed results over a larger collision energy range are required to shed more light on this problem.
5. Conclusion We have shown that the collisional dissociation of H2+ can show a strong dependence on the alignment of the laser-prepared target atom in collisions with Na(3p). Measurements in which protons and hydrogen atoms are detected in coincidence help to define the relative orientation of the laser excited charge cloud and the internuclear axis of the molecular ion and, in addition, reduce the number of possible dissociation mechanisms that lead to detectable signals, thus simplifying the data analysis and interpretation. A satisfactory explanation of the dynamics involved in terms of the formation of molecular states of particular symmetry in the NaH2+ quasi-molecule formed during the collision is unfortunately not possible without detailed potential surfaces for this system. We hope that the very intriguing and promising experimental results presented here will encourage further theoretical and experimental developments in this challenging field.
Acknowledgment. Financial support from the Deutsche Forschungsgemeinschaft through SFB 276 “Korrelierte Dynamik hochangeregter atomarer und molekularer S ysteme” is gratefully acknowledged. References and Notes (1) Andersen, N.; Gallagher, J.; Hertel, I. V. Phys. Rep. 1988, 165, 1. (2) Campbell, E. E. B.; Schmidt, H.; Hertel, I. V. Adv. Chem. Phys. 1988, 72, 37.
J. Phys. Chem., Vol. 99, No. 42, 1995 15341 (3) Rettner, C. T.; Zare, R. N. J . Chem. Phys. 1982, 77, 2416. Hertel, I. V. Z. Phys. A (4) Reiland, W.; Jamieson, G.; Tittes, H.-U.; 1982, 307, 51. (5) Anderson, S. J.; Swan, J. B. Phys. Lett. 1974, 48A, 435. (6). Brenton, A. G . ; Foumier, P. G.; Govers, B. L.; Richard, E. G.; Beynon, J. H. Proc. R . SOC.London 1984, A395, 111. (7) Caudano, R.; Delfosse, J. M. J . Phys. B 1968, 1, 813. (8) Champion, R. L.; Doverspike, L. D.; Bailey, T. L. J . Chem. Phys. 1966, 45, 4317. (9) Foumier, P. G.; Brenton, A. G.;Jonathan, P.; Beynon, J. H. Int. J . Mass Specrrom. Ion Processes 1987, 79, 8 1. (10) Gibson, D. K.; Los, J.; Schopman, J. Physica 1968, 40, 385. (1 1) Govers, T. R.; Guyon, P. M. Chem. Phys. 1987, 113, 425. (12) Jaecks, D. H.; Yenen, 0.;Wiese, L.; Calabrese, D. Phys. Rev. 1990, A41 5934. (13) Jonathan, P.; Lee, A. R.; Brenton, A. G . ;Beynon, J. H. Inr. J . Mass Spectrom. Ion Processes 1987, 79, 101. (14) Lindsay, B. G.; Yousif, F. B.; Latimer, C. J. J . Phys. B 1988, 21, 2593. (15) McClure, G. W. Phys. Rev. 1965, Z04A, 769. (16) Moran, T. F.; Fullerton, D. C. Chem. Phys. Lerr. 1968, 2, 625. (17) Peek, J. M. Phys. Rev. 1965, 140A, 11. (18) Liao et al. J . Chem. Phys. 1990, 93, 4818. (19) Fischer, A.; Hertel, I. V. Z. Phys. A 1982, 304, 103. (20) Campbell, E. E. B.; Hiilser, H.; Witte, R.; Hertel, I. V. Z. Phys. D 1990, 16, 21. (21) Sharp, T. E. Ar. Dura 1971, 2, 119. (22) Guyon, P. M.; Baer, T.; Cole, S. K.; Govers, T. R. Chem. Phys. 1988, 119, 145. (23) von Busch; Dunn, G. H. Phys. Rev. 1972, A5, 1726. (24) Jitschin, W.; Osimitsch, S.; Mueller, D. W.; Reihl, H.; Allan, R. J.; Schbller, 0.;Lutz, H. 0. J . Phys. B 1986, 19, 2299. (25) Zare, R. N. Mol. Photochem. 1972, 45, 553. (26) Fano, U.; Macek, J. H. Mod. Phys. 1973, 45, 553. (27) Baudon, J. J. Phys. B 1973, 6, 850. (28) Russek, A. Physica 1970, 48, 165. (29) Ito, K.; Lablanquie, P.; Guyon, P. M.; Nenner, I. Chem. Phys. Lerr. 1988, 151, 121. (30) de Bruijn, D. P.; Neuteboom, J.; Sidis, V.; Los, J. Chem. Phys. 1984, 85, 215. (31) Hertel, I. V.; Schmidt, H.; Biihnng, A,; Meyer, E. Rep. Prog. Phys. 1985, 48, 375. ~
JP950298T
