J. Phys. Chem. A 2010, 114, 11175–11188
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Level Crossings in the Ionization of H2 Rydberg Molecules at a Metal Surface† E. A. McCormack, M. S. Ford, and T. P. Softley* Department of Chemistry, UniVersity of Oxford, Chemistry Research Laboratory, Mansfield Road, Oxford OX1 3TA, United Kingdom ReceiVed: March 29, 2010; ReVised Manuscript ReceiVed: June 1, 2010
The ionization of H2 Rydberg states at a metal surface is investigated using a molecular beam incident at grazing incidence on a gold surface. The H2 molecules, excited by stepwise two-color laser excitation, are selected in each of the accessible Stark eigenstates of the N+ ) 2, n ) 17 Rydberg manifold in turn and the ionization at the surface is characterized by applying a field to extract the ions formed. Profiles of extracted ion signal versus applied field show resonances that can be simulated by assuming an enhancement of surface ionization at fields corresponding to energy-level crossings between the populated N+ ) 2 manifold and the near-degenerate N+ ) 0 Stark manifolds. It is concluded that the slow (microsecond time scale) rotationelectronic energy transfer to N+ ) 0 states occurring at these crossings takes place in the time interval following application of the field ramp when the molecule is still distant from, and unperturbed by, the surface. However, the energy levels are strongly perturbed by image-dipole interactions as the molecule approaches close to the surface, leading to additional energy-level crossings. Adiabatic behavior at such crossings affects the intensity of the observed resonances in the surface ionization signal but not their field positions. Resonances are also observed in the surface ionization profiles at fields above the field-ionization threshold; some of these show asymmetric “Fano-type” line shapes due to quantum interference in the nonradiative coupling to degenerate bound and continuum states. 1. Introduction In two previous papers we reported on experimental studies of the ionization of a beam of very highly electronically excited, H2 Rydberg molecules interacting with a flat metal surface.1,2 In the present paper we present new experimental results and analysis that clarify the understanding of the detailed dynamics occurring in the H2 Rydberg molecules as they approach the surface. Ionization of Rydberg atoms and molecules at surfaces can be considered as a model type of system for studying charge transfer at interfaces. Such studies take advantage of the long lifetimes of the molecular Rydberg states and the ease with which the Rydberg electron distribution can be manipulated using state selection and applied fields (Stark or Zeeman effects). The Stark effect in Rydberg states is qualitatively very similar to that for the H atom, and therefore, the very high degeneracy of levels of high principal quantum number n is split by the field, the energies varying with field in an approximately linear fashion.3 The highly polarized electron distribution in these fieldshifted states gives rise to a very large dipole moment, which for some states is strongly aligned parallel or antiparallel to the field direction. High resolution laser spectroscopic methods enable the state selection of these Rydberg states with widely differing polarization characteristics, and thus one of the goals of our current research program is to explore how the Rydbergsurface processes vary with the electron distribution of the incoming Rydberg molecules. Previous studies of Rydberg-surface interactions using Rydberg atoms4-17 have established the basic physics of the ionization process at metal and semiconductor surfaces. It is found that as the atom approaches the surface, the Rydberg electron becomes subject to inhomogeneous electric fields caused by the generation of an image dipole in the metal, giving †
Part of the “Klaus Mu¨ller-Dethlefs Festschrift”.
rise initially to a splitting of the atomic energy levels.8,9,11 At a sufficiently close distance of approach (∼4 times the Rydberg radius ∼4 n2a0) the electronic potential barrier between the atom and the surface is lowered and narrowed, and tunneling ionization, or above-barrier ionization,18 of the Rydberg electron occurs into the degenerate conduction band of the metal. The main technique employed so far to study the surface ionization process is to detect the ions that are produced and to measure the field required to pull the ions away from collision with the surface: the closer the ionization occurs relative to the surface, the greater the extraction field (Emin) required to overcome the attractive image-charge force and the incoming kinetic energy, as given by the formula (in a.u.),5
Emin(Zi,T⊥) )
[ ] 1 + 2Zi
T⊥ Zi
2
(1)
where Zi is the distance of ionization from the surface and T⊥ ) 1/2mV⊥2 is the kinetic energy perpendicular to the surface of the atom at the point of ionization. This equation is based on an image-charge model for a perfect conductor which assumes that the total energy of an ion at a distance Z from the surface and in the presence of an applied electric field, E, is given in atomic units by
)-
1 - EZ + T⊥ 4Z
(2)
It is expected that the distance of ionization from the surface, Zi, would increase strongly with the principal quantum number n and would also depend on the orientation of the polarized electron distribution; i.e., a surface-oriented electron distribution
10.1021/jp102817c 2010 American Chemical Society Published on Web 07/01/2010
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would be more likely to ionize further from the surface than a vacuum-oriented distribution.19 Experiments with Xe Rydberg atoms scattering at an Au(111) surface have shown that the distance at which ionization occurs, as deduced by inversion of the threshold field in eq 1, varies in proportion to n2 as expected but, surprisingly, shows little dependence on the orientation of the Rydberg electron distribution.13,14 This has been explained by dipole reorientation effects as the system passes adiabatically through energy level crossings.17 The surface ionization probability at a given distance is also expected to be dependent on the detailed form of the long-range chargeinduced surface potential (which is specific to the material), the degree of surface roughness,6 the presence of adsorbates or thin films,7 and the presence of “patch charges”.15,16 The use of Rydberg molecules, rather than atoms, results in the introduction of additional degrees of complexity into the physical problem through the need to consider the vibrationrotation motion of the Rydberg molecule, and also the possibility of bond dissociation. A particularly interesting aspect of the previously reported results1,2 was the observation of resonance structures in the surface ionization profiles (plots of surface ionization probability versus applied field) that were attributed to level crossings between the dense manifolds of molecular Rydberg energy levels, as discussed in detail below. Another closely related matter of interest was the role of the interaction between rotation and electronic degrees of freedom in the incoming Rydberg molecules in the surface ionization process. To date, the possible competing processes to ionization have not been studied directly; these include not only surface-induced predissociation of the incoming molecules but also secondary chemical processes following ionization (especially where chemically active adlayers are present), secondary-electron ejection from the surface following ion impact, energy exchange between the Rydberg molecule and molecules on the surface leading bond to breaking at the surface, and inelastic scattering of the incoming molecules. There are also an almost infinite number of possible variations in the nature of the surface in these experiments, and the interaction of Rydberg species with surfaces is potentially a means to probe the nature of electronically excited states at surfaces;20 this field could be a rich area for studying thin films, nanostructures, bandgap effects, etc. in the future. Such studies are also of interest in relation to plasma-surface interactions, controlled deposition,21,22 desorption of Rydberg matter from a surface,23-26 and controlled chemistry. The interaction of Rydberg atoms with a metal surface has been used to make direct measurements of the van der Waals force and retardation effects,27 and the deflection of atoms as a result of this force is potentially important for guiding ultracold electronically excited atoms28 and in ultracold atom-chip experiments.29 In the present paper we present a more detailed and extensive analysis of the previously reported level crossing effects in H2, reporting new experimental measurements in which a wide range of different Stark levels are populated. A key question addressed in this paper is the extent to which the surface itself has an impact on the dynamics that contribute to the resonance effects that are observed in the surface ionization profiles. 2. Experimental Section The excitation scheme for H2 Rydberg states has been discussed in detail in ref 30. In brief, a population of H2 Rydberg states is produced in a pulsed, skimmed molecular beam using a VUV-UV doubly resonant excitation scheme. The VUV frequency (laser 1) is resonant with the R(0) B 1Σu+(V′ ) 0) -
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Figure 1. Schematic diagram of the interaction region of the experimental apparatus.
X 1Σg+(V′′ ) 0) one-photon transition of para-hydrogen at an excitation energy of 90 242.33 cm-1, populating only the J′ ) 1 level in the B 1Σu+(V′ ) 0) intermediate state. The UV frequency (laser 2) is resonant with the one-photon transitions from the intermediate state to the Rydberg series converging on the ionization thresholds associated with the para-H2+ vibration-rotation levels, principally V+ ) 0, N+ ) 0 and 2 of the X 2Σg+ ground ionic state at a total energy of approximately 124 000 cm-1 above the neutral ground state. The laser polarizations are mutually perpendicular, and as shown in ref 30, the main series accessible (and having a significant lifetime) in zero field from the J′ ) 1 intermediate state is the (nd2)1 series with MJ ) 0 (notated (nlN+)J, where n is the principal quantum number and l, N+, and J specify the orbital angular momentum of the Rydberg electron, the rotational angular momentum of the ion core, and the total angular momentum, respectively). A schematic overview of the interaction region of the experimental apparatus is shown in Figure 1. As in refs 1, 2, and 30, the VUV beam (λ ) 110.81 nm) is obtained by nonresonant frequency tripling of the frequency-doubled output (10 Hz, 6 ns, 6 mJ/pulse) of a Nd:YAG pumped dye laser (Quanta Ray PDL3) focused (f ) 150 mm) into a cell containing a Kr/Ar mixture (1080 mbar/200 mbar). The VUV is refocused into the H2 beam using a lithium fluoride lens (f ) 70 mm), and it intersects the molecular beam at an angle of 45°. The UV beam (λ ) 291-296 nm, 4 mJ/pulse) is provided by a second frequency-doubled dye laser (Quanta Ray PDL3) pumped by the same Nd:YAG laser (Spectra Physics GCR 290) and is focused in the plane of the surface using a cylindrical lens (f ) 285 mm); its direction is perpendicular to the VUV beam and at 135° to the molecular beam direction. The pulsed (10 Hz) molecular beam is formed by passing pure H2 gas at a backing pressure of 2 bar through a pulsedvalve orifice (General Valve Series 9) of diameter 0.5 mm, and then through a 1 mm diameter skimmer, located 3 cm from the valve orifice, into a differentially pumped chamber in which the pressure is ∼1 × 10-6 mbar during operation of the pulsed valve. The molecular beam is intersected by the laser beams at a distance of 170 mm from the skimmer face. As shown in
Ionization of H2 Rydberg Molecules at a Metal Surface
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11177 Ions formed by ionization at the surface appear at a different time-of-flight from those formed by field ionization in the gas phase.30 By selecting the excitation of a specific Stark state with laser 2 and then pulsing a variable positive repelling voltage to the surface, we can observe the surface ionization profiles as a function of the extraction field for this state. These profiles represent the probability that the surface ionization occurs and is detected at that field. The gold surface used in the experiments was produced by vapor deposition in the same manner as described in our previous paper.1
Figure 2. (a) Stark spectrum of the N+ ) 2, n ) 17 manifold at 300 V cm-1 with labels showing k assignments (-14 to +16) and “a” or “b” labels for subcomponents as described in text. (b) Simulated spectrum obtained by diagonalization of the Hamiltonian in a case (d) basis set.30
Figure 1, the excitation from the ground state to the Rydberg states occurs above the sample surface in a region of spatially homogeneous electric field between the metal surface and a mesh grid electrode (81% transmitting Ni mesh with 90 lines per inch). The molecular beam axis is oriented at an angle of 7° with respect to the surface and the surface/extraction grid separation is 12 mm. The time-of-flight of the Rydberg molecules between excitation and interaction with the surface is in the range 7-10 µs. This corresponds to a vertical distance of excitation above the surface of 2.5-3.0 mm. Excitation was performed in a 300-650 V cm-1 homogeneous field by applying a negative potential to the mesh electrode with the surface grounded. This field results in a splitting of the zero-field states into hydrogenic Stark manifolds.3,30 The (nd2)1 states, which are the “bright states” (i.e., the origin of the transition intensity) are admixed into the N+ ) 2 high-l states of the same principal quantum number n at this field, allowing excitation of levels across the full range of the Stark manifold.3,30-32 The Rydberg excitation spectrum (see Figure 2) can be recorded through pulsed-field ionization of the excited states after a delay of 1 µs by the application of a +3600 V potential to the metal surface (corresponding to an applied field of ∼3000 V cm-1). The field also serves to direct the ions through a field-free time-of-flight region to a multichannel plate (MCP) detector. To detect surface-induced ionization (as in previous papers1,2), a field must be applied that is sufficient to draw the ions away from the surface, i.e., sufficient to overcome both the attractive image-charge force between the ion and the surface and also the original kinetic energy of the incoming molecular beam (see eq 1). The field must be applied before the surface-induced ionization occurs, as the time scale between ionization and full collision of the ion with the surface is subnanosecond, but the field must be lower than the field-ionization threshold for the Rydberg states. In these experiments surface-induced ionization is detected by applying a positive pulse to the surface (to give a total field 33-3200 V cm-1) with a time delay of 1 µs with respect to the initial excitation, and hence several microseconds before interaction with the surface. As above, the ions are repelled and can subsequently be detected at the MCP detector.
3. Results 3.1. Populated Stark States of the H2 Rydberg Molecules. A Rydberg excitation spectrum, detected by pulsed-field ionization (extraction field 3000 V cm-1, 1 µs after excitation) with the excitation occurring in the presence of a Stark field of 300 V cm-1, is shown in Figure 2 for the N+ ) 2, n ) 17 Stark manifold. Each peak in the spectrum is labeled with an effective parabolic quantum number k, correlating with the labeling of the equivalent Stark states in the hydrogen atom. The l quantum number is substantially mixed at this field and thus is not specified. Strictly speaking, the parabolic quantum number (k ) n1 - n2 where n1 and n2 represent the number of nodes in the wave function in parabolic coordinates3) is only rigorously defined for the H atom system, but under conditions where the low-l states are strongly admixed, it is an approximately good quantum number for H2. It also gives a useful indication of the electronic distribution of the Rydberg molecule with respect to the field direction (and hence the surface); in particular, the blueshifted states with positive-k have a vacuum-oriented electron distribution and red-shifted states with negative-k are surface oriented with this field configuration. The simulation shown in Figure 2 is used to aid the assignment of the spectrum and was produced by diagonalization of the Stark Hamiltonian in a Hund’s case (d) basis set, as described in refs 1 and 30. In Figure 2 it is seen that some of the peaks corresponding to red-shifted states, labeled with negative-k values, are split into two components labeled a and b. In fact, as shown in Figure 3, the energy level calculation shows that there are five states for each k value divided into two groups of three and two nearly degenerate states for a and b, respectively. At low fields (or zero field), such splittings can be considered to arise from the coupling of the Rydberg electron orbital angular momentum l with the rotational angular momentum N+ of the H2+ core (N+ + l ) J), yielding five states for each l value (J ) l + 2, ..., l - 2). As shown in ref 30, the N+ ) 2 states with MJ ) 0 are divided into two noninteracting groups (even in the presence of a homogeneous field), one set with |J - l| ) odd and one with |J - l| ) even. The eVen set have nonzero matrix elements with the N+ ) 0 states whereas the odd states cannot mix with the N+ ) 0 manifold. At higher fields, where the angular momenta N+ and l are decoupled by the field and J is not a good quantum number, an analysis of the eigenfunctions shows that the five eigenstates for each k value are better considered to represent the five possible combinations of MN+ and ml, (the z-projections of N+ and l) that sum to give the total projection number MJ ) 0 (MN+ ) 0, (1, (2 and ml ) 0, -1, -2), as listed in Table 1. The division into two sets of noninteracting states is maintained at high field, and the table categorizes the states as odd or eVen according to whether the wave functions can be expressed as linear combinations of the l - N+ coupled states with |J - l| odd or even. The reason for the energetic splitting of these
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Figure 3. Calculated Stark map for N+ ) 2, n ) 17 illustrating the splitting into the various k levels (+16 to -16 labeled at the right-hand side) and the splitting of each of these (see inset) into five components labeled ka1,2,3 and kb1,2.
TABLE 1: Quantum Numbers for the Near-Degenerate Levels of a Given k Statea |J - l| odd/even
lmin
label
ml
M N+
odd even even odd even
1 0 1 2 2
a1 a2 a3 b1 b2
(1 0 (1 (2 (2
-1 0 -1 -2 -2
a The labels correspond to those shown in Figure 3. “odd/even ” refers to the two blocks of the Hamiltonian in which the zero-field basis functions in the l - N+ coupled basis set have |J - l| odd or even.
groups is connected with the amount of low-l character contributing to the wave functions. The two lower-energy states for each k value (labeled b) correspond to ml ) (2 (MN+ ) -2) in the high-field limit, and there can be no admixture of states with l < 2 (as l cannot be less than ml). The group of three higher-energy states (labeled a) correspond to the ml ) (1, 0 components, and the eigenfunctions of these states do have an admixture of N+ ) 2 np character. Strong admixture of the N+ ) 2, 17s state does not occur for any of these states in the field range of interest. Mixing with the (ns2)2 state is only possible in principle for the |J - l| ) even block, but in practice for the field range under consideration, the separation between the np and ns states is sufficiently large to inhibit any such mixing. It should be emphasized that in the Stark spectrum the admixture of the “bright” (nd2)1 state with the components of the high-l manifold does not lead to population of all the levels; the (nd2)1 basis function belongs to the |J - l| ) odd block of the Hamiltonian. Only the a1 and b1 states belong to this block and can borrow intensity from the (nd2)1 state, the other states remaining “dark”. A final significant point is that the (ns0)0 states are believed to be strongly predissociated in this region of the spectrum, and therefore, any states that contain a strong admixture of such character (these would be in the even block only) would not appear in the spectrum. 3.2. Gross Structure of the Surface Ionization Profiles. The surface ionization signal is shown in Figure 4 as a function of the ion-extraction field for a selection of the Stark states from
Figure 4. Observed surface ionization profiles as a function of probefield strength for a selection of N+ ) 2, n ) 17 Stark states populated at an initial field of 300 V cm-1 (see Figure 2a). The bold line shows the field at which the initially populated state crosses the field-lowered adiabatic (N+ ) 0) ionization threshold.
the N+ ) 2, n ) 17 manifold that are populated by laser excitation in the presence of an initial ∼300 V cm-1 field (as in the spectrum shown in Figure 2). The ion-extraction field is applied 1 µs after excitation. For each state populated, the high intensity part of the signal is observed within a “field window” (e.g., for the -6a state, the range is approximately 700-1300 V cm-1.) At the low-field end, the opening of the window is determined principally by the minimum field required to pull the ions away from the surface, given the characteristic ionization distance of the populated states (see eq 1); at the high-field end the closing of the window is determined by the field at which gas-phase field ionization (or field-induced rotational autoionization) will remove Rydberg molecules before interaction with the surface. We will show later that the low-
Ionization of H2 Rydberg Molecules at a Metal Surface
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Figure 5. Linear Stark map illustrating the Stark levels for N+ ) 2, n ) 17 and the N+ ) 0, n ) 22-25 manifolds: only the “a” type states are shown. The levels in bold correspond to those for which simulations of the surface ionization profiles are shown in Figure 6; crossings with these levels give rise to the observed resonances.
field onset is also limited by the lowest field at which a level crossing between Stark manifolds of different N+ occurs. 3.2.1. Threshold Detection Field. Regarding the low-field onset, for atomic Rydberg states, it would be expected that the threshold field, calculated using eq 1, would occur for n ) 17 at around 1900 V cm-1 for the given mean perpendicular kinetic energy (310 ms-1) and an expected ionization distance of 4 n2a0. But as explained in our previous work,1,2 the N+ ) 2 Rydberg states of H2 appear to behave in a manner identical to that expected for the near-degenerate N+ ) 0 states of higher principal quantum number. The N+ ) 0, n ) 23 manifold levels are almost degenerate with the N+ ) 2, n ) 17 manifold (see Figure 5), and for n ) 23 an ion extraction onset of around 700 V cm-1 would be predicted (again assuming an ionization distance of 4 n2a0); this is approximately in accordance with the behavior observed for the central levels of the N+ ) 2, n ) 17 manifold in Figure 4. Thus it is apparent that a nonradiative energy-transfer process is occurring between core-rotation and electronic excitation that facilitates the surface ionization of the levels at distances much greater than would be expected on the basis of the initially populated level alone. An important question to address is whether this energy transfer takes place in the delay time of several microseconds between excitation and interaction with the surface or only in the final nanosecond before collision as part of the interaction with the surface itself. It should be noted that the surface perturbation of the Rydberg state is likely to be negligible for distances greater than 10 n2a0; for n ) 17 this distance is 150 nm so that, for an incoming velocity of 310 ms-1, the time over which a significant interaction with the surface can occur is of order 500 ps. Thus, a fast energy-transfer process would be required if the rotation-electronic energy transfer were to be a purely surface-induced process, whereas if it takes place in the gas phase during the several microsecond time delay before surface interaction, the rate might be 4 orders of magnitude
lower and the effect would still be observed. We will return to a discussion of this point below. 3.2.2. Field Ionization Cutoff. It is found that at the highfield end, the surface-ionization profiles arising from population of the set of states labeled “b” extend to fields significantly higher than observed for the corresponding “a” states, demonstrating that the initial population and subsequent evolution of the b states results in states that are more stable with respect to gas-phase ionization at these high fields than the a states. As discussed previously,1 the gas-phase field ionization process occurring for all these N+ ) 2 states is actually field-induced rotational autoionization, and for the initially populated a states this process is observed to occur at, or just above, the field for which the N+ ) 2 energy levels cross the N+ ) 0 classical field-ionization threshold. This threshold field is indicated by the bold line in Figure 4. Once the levels cross this threshold, they are degenerate with the N+ ) 0 continuum, and coupling between the N+ ) 2 and N+ ) 0 channels should lead to autoionization. As noted above and previously,1 all the initially populated MJ ) 0 states (the odd-block a1 and b1 states) should be metastable with respect to autoionization into the N+ ) 0 continuum as there are no couplings in a homogeneous field to cause the N+ ) 2 to N+ ) 0 mixing, at least for the states with pure MJ ) 0 character; thus, an additional perturbation causing MJ-mixing is required to allow the autoionization to happen. However, the time scale of the experiment is long; there is a delay of several microseconds between the ramping up of the field and the interaction of the molecules with the surface. Thus even if the autoionization rate is very slow (e.g., a lifetime ∼1 µs), a cutoff for the surface signal at the N+ ) 0 threshold would still be observed and only a very minor MJ-mixing perturbation is actually required. Possible sources of the MJ-mixing include a small inhomogeneity of the applied field, effects of local inhomogeneous fields due to ions produced in the initial excitation volume,3 and a degree of imperfection of the laser
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polarizations (or, equivalently, a slight misalignment of the polarizations with respect to the field direction.) As discussed below, the most likely explanation is the last one. Given the appearance of the surface-ionization signal well above the N+ ) 0 field ionization threshold when the b states are initially populated, it would appear that these states are more resilient than the a states to the MJ-mixing external perturbations that are necessary to cause autoionization. If it is assumed that the MJ-mixing originates from a slight rotation of the laser polarization compared to the field direction, then this differentiation between a and b states can be explained as follows. A coherent superposition of nearly degenerate MJ ) 0 and MJ ) (1 states (predominantly MJ ) 0) would be formed at excitation as a consequence of this polarization rotation (defining the quantization axis with respect to the applied field direction). The principal MJ-mixing would tend to conserve ml, because states of given ml and different MN+ are almost degenerate at high field; hence the coherent superposition can be thought of as an MN+-mixed state. If it is further assumed that the fieldinduced rotational autoionization process conserves the MN+ quantum number (which would be a selection rule in the decoupled basis), then only those states with significant N+ ) 2, MN+ ) 0 contributions would be able to autoionize; only these can couple to the N+ ) 0 states, which have only MN+ ) 0 character. The a1 states will have superpositions of the form C0 | ml ) 1, MN+ ) -1〉 + C1 | ml ) 1, MN+ ) 0〉 and can therefore autoionize through this type of coupling, whereas the b1 states, having the form C0 | ml ) 2, MN+ ) -2〉 + C1 | ml ) 2, MN+ ) -1〉, cannot autoionize into the MN+ ) 0 continuum. It is also possible that the incorporation of l ) 1 character into the a states helps to enhance the autoionization rates. 3.3. Resonances in the Surface-Ionization Profiles. The profiles do not vary smoothly as the ion-extraction field increases but rather show a series of sharp resonant features, as has been seen in our earlier work with population of the zero-field nd states of principal quantum numbers n ) 17-21.1 Previously, we have suggested that such peaks in the profiles, which represent an enhancement in the surface ionization/detection probability, occur at fields for which there are energy level crossings between the populated N+ ) 2 states and the higher-n Stark manifolds belonging to the N+ ) 0 series (the N+ ) 0, n ) 22-46 states are near-degenerate with the N+ ) 2, n ) 17-21 states). If the field is ramped up, following excitation, to the value corresponding to one of the N+ ) 2/N+ ) 0 levelcrossings, and then held at that field while the molecule approaches the surface over a period of microseconds, there is time for energy transfer between the Rydberg electron and the rotating core to occur |N+ ) 2, n〉 f |N+ ) 0, n′〉 (where n′ > n), leading to an ionization behavior characteristic of the neardegenerate N+ ) 0 states of higher principal quantum number, as discussed above. Through its N+ ) 0 character (and hence higher-n character) the molecule ionizes further from the surface and the ion can be extracted by an applied field that would not be possible for the originally populated N+ ) 2 state. This gives rise to a peak at the level-crossing field in the surface ionization profile. Note that the time for which the field is held at the crossing point (several microseconds) is a crucial aspect of the model. As stated above, the coupling between the populated a1, b1, N+ ) 2, and N+ ) 0 states is very weak because it only arises from a small degree of MJ-mixing. It is therefore assumed that the N+ ) 2 to N+ ) 0 transition can only occur if the molecule is held for microseconds at the crossing field but otherwise does not occur at other crossing points that the system may pass through when the field is rising; for these crossings
McCormack et al. the subnanosecond time scale spent by the system at the crossing point is insufficient for the N+ ) 2 to 0 transition to occur. The width of the observed resonances, where these can be individually resolved, is of order 4-5 V cm-1: this magnitude is consistent with expected fluctuations and/or drift of the applied field. Once the system has transferred at a crossing to a level of the N+ ) 0 manifold (for the N+ ) 2, n ) 17 states the crossing N+ ) 0 manifolds are primarily n ) 22-25), the subsequent dynamics needs to be considered. The applied field is held constant until after surface interaction occurs, and so there are no more level crossings induced by the field. However, once the molecule comes close to the surface (
