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DISPERSED FLUORESCENCE AS A PROBE OF MOLECULAR PHOTOIONIZATION DYNAMICS

ERWIN D. POLIAKOFF

Department of Chemistry Louisiana State University

Baton Rouge, Louisiana 70803

CONTENTS

I. Introduction II. Method

III. Experimental IV. Background

A. Franck-Condon approximation applied to photoionization B. Shape resonances and Franck-Condon breakdown

V. Selected results A. N20: A vibrationally resolved polyatomic shape resonance B. Continuum channel coupling:

Valence-hole/valence-hole coupling C. Continuum channel coupling:

Core-hole/valence-hole coupling D. Rotationally resolved studies

VI. Future developments Acknowledgment References

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I. INTRODUCTION

Molecular photoionization provides a natural means of studying the correlation of electronic and nuclear motion, as the electron energy can be continuously adjusted and the nuclear motion can be probed sensitively using appropriate detection schemes. Moreover, photoionization exhibits characteristics of molecular scattering that are of central importance in chemical physics [1-11], yet is sufficiently simple to be theoretically tractable. This chapter describes studies of resonant molecular photoionization that employ dispersed fluorescence from photoions as an experimental tool. Several recently studied examples are presented to highlight current topics of interest, and also to demonstrate the utility of dispersed fluorescence for studies of molecular photoionization. These case studies show how fundamental resonant phenomena facilitate the conversion of electronic and nuclear motion. In so doing, they underscore a central and recurring theme in molecular ionization studies, namely, that a qualitative microscopic understanding of the scattering dynamics [11] requires probes that provide information on molecular aspects (e.g., vibration, rotation, alignment, etc.) of the ionization process. In retrospect, this is hardly surprising, as many of the processes of interest are molecular in origin. However, there are subtleties in obtaining the relevant experimental data, and useful experimental approaches are described in the following sections.

A central goal is to understand the response of the resonance complex to changes in the molecular geometry. Progress in fundamental studies — as well as the application of molecular photoionization as an analytical tool — requires insight into how the ionization dynamics are affected by changes in the molecular geometry. For this reason, it is essential that experiments selectively sample alternative vibrational levels of the photoion, as different vibrational levels probe alternative internuclear configurations. This requirement for vibrationally resolved data is a strong motivation for dispersed fluorescence measurements, as they can provide highly resolved (including rotationally resolved) data on the photoions over a wide range of incident photon energies.

Vibrationally resolved data obtained as a function of electron kinetic energy illuminate the correlation of electronic and nuclear motion. In particular, resonant ionization phenomena, such as shape resonant ionization, frequently induce coupling between nuclear and electronic motion [1-5]. However, variable photon energy is needed to tune to and through the resonant excitation, and this requirement can be a serious obstacle using traditional tools involving photoelectron spectroscopy. Typically, the necessity of a large range of photon energies dictates that synchrotron radiation be used as the source of ionizing radiation [12]. While synchrotron radiation sources are tunable, they do not simultaneously provide high resolving power and high flux, so traditional photoelectron measurements have been unable to probe the molecular motion (i.e., vibration and rotation) while varying the photoelectron energy continuously over a wide range [13]. Dispersed fluorescence measurements circumvent this difficulty because the detection bandwidth is uncoupled from, and therefore not limited by,

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the excitation bandwidth [14]. As a result, dispersed fluorescence measurements have been used to investigate a variety of resonant photoionization phenomena [14-27], including those noted below.

• Vibrationally resolved partial photoionization cross section data have illustrated the behavior of a polyatomic shape resonance (N2O) for the first time [21]. These results have important implications for surface and materials science, as well as for their intrinsic significance.

• Continuum channel coupling effects have been observed following shape resonant excitation [14,19,20,23,24]. When used for core-hole processes, these studies probe aspects of core electron excitation that depend of the internuclear separation via the channel coupling of the core-hole complex to valence-hole continua of the ion [19,20,23].

• Rotationally resolved fluorescence spectra have been generated for molecular photoions (N2 [17], HC1 [26], and 0 2 [27]) which reveal the partitioning of angular momentum between electronic and nuclear motion.

• An unusual species, CV+, has been produced following creation of a core-hole state of O2, and vibrationally resolved emission has been observed and characterized [22]. Such observations are unexpected because doubly-charged diatomic ions are usually unstable on the time scale of typical fluorescence decays.

• Competition between ionization and dissociation for Rydberg states near the ionization threshold has been investigated for HC1 [18].

In this chapter, some of these studies are described in order to demonstrate that discerning molecular vibration and rotation over a broad electron energy range provides a window into fundamental ionization processes. Sections II-IV discuss technical and scientific background material and Sec. V describes selected studies of current interest. Future developments are sketched briefly in Section VI, and these possible outgrowths illustrate that there are many enticing possibilities for future applications of dispersed fluorescence as a probe of resonant ionization processes.

H. METHOD

Dispersed fluorescence measurements are simple, in practice as well as concept. The idea is that the intensity of fluorescence from a particular quantum

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level of a photoion is proportional to the rate of production of that level, i.e., its partial photoionization cross section [14]. In this regard, the information content from dispersed fluorescence studies is similar (though not identical) to photoelectron spectroscopy. It is useful to describe the strategy of a dispersed fluorescence measurement as a means of highlighting the capabilities.

Figure 1. Potential curves for the example of photoionization of N2, also showing the ionization and subsequent fluorescence transitions from N2+(B2Xu*,v' "4 X2Xg

+,v' ' ) •

We begin with the example of photoionization of N2, where for the sake of argument, we wish to measure the relative photoproduction of the V =1 and v' =2 levels versus the V =0 level of the N2+(B2£U

+) ion [14]. This is accomplished by measuring the intensities of fluorescence transitions originating from these levels. For this example, the process is summarized by Eq. 1, and is sketched in Fig. 1.

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N L ( x V ) ■+ hu > N + (B2E+ ,v) + e" 2V g7 exc 2V u '

1 N;J(xV,v") + hV y / ,

N0(X1S+) ■+ hu > N + (BZE+ ,v) + e" 2V g7 exc 2V u '

* 2, ) ■+ nv Q/ ex 2i ,v') + e

1 1 ' 7

X 2 £ + ,v") + hi/ , a' ' v '

') + (1)

The fluorescence intensity originating from level V is a measure of the rate of production of that level, i.e., its partial photoionization cross section, ov' [14]. Figure 2 is a portion of the fluorescence spectrum for N2+(B2Su

+,v/—>X2Sg+,v,/), and this spectrum shows transitions originating from the v' =0, 1, and 2 levels of N2+(B2SU

+). The relative intensities of fluorescence transitions from different upper vibrational levels provides a measure of the vibrational branching ratios [14], which serve as useful indicators of resonant ionization pathways.

Figure 2. Portion of N2+(B2Su+,v/ ~* X2Eg*,v /7) fluorescence spectrum with upper levels

v ' =0, v ' = l , and v '=2 .

While the ratio of fluorescence intensities from alternative vibrational levels is a measure of the vibrational branching ratio, it is not equal to the vibrational branching ratio. This is because different upper vibrational levels are connected to the lower electronic state's vibrational levels via Franck-Condon factors, so we correct for the fluorescence Franck-Condon factors (and the difference in transition frequencies) using Eq. 2 [14].

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(2) a u u

'u/ / ( v ■ V }

\>l> I <%>l> ' "U'l'3)

*

3x

Here, u and iT represent alternative vibrational levels for the upper electronic state. Similarly, £ and t' denote different vibrational levels for the lower electronic state. The Franck-Condon factor and the frequency of the fluorescence transition from upper level i to lower level f are denoted by qif and v\i, respectively. This equation converts ratios of fluorescence intensities into vibrational branching ratios. There is an obvious oversight in Eq. 2, namely, the possibility that different upper levels u and u' have different predissociation rates. This necessitates a correction factor, and is described elsewhere [21,28]. While Eq. 2 is easy to apply, a frequent problem is that the potential surfaces for polyatomic ions are not well-characterized. As a result, the necessary Franck-Condon factors are often unavailable. In such cases, photoelectron spectroscopy provides the necessary bridge. Specifically, vibrational branching ratios are frequently available at lower photon energies from photoelectron spectra. The fluorescence intensity ratio is simply scaled to the known vibrational branching ratio at this excitation energy [21].

Figure 3. Vibrational branching ratio curves for N2+(B2SU+).

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Figure 3 shows some branching ratio curves for our N2 example in the region of a broad autoionization resonance at hvexcx 22 eV, and we see that these curves exhibit considerable deviations from Franck-Condon behavior. The Franck-Condon approximation applied to photoionization dictates that these curves be constant with incident photon energy. Indeed, deviations from Franck-Condon behavior are ubiquitous, as some of the following sections will show.

This N2 example demonstrates that the information content in a dispersed fluorescence measurement is similar to that from photoelectron spectroscopy measurements [6]. However, there are qualitative differences between the techniques, and these differences must be appreciated for the methods to be exploited appropriately. First, we list features of fluorescence spectroscopy measurements that make them particularly useful for studies of molecular photoionization.

• The fluorescence detection bandwidth is determined by the optical system (i.e., monochromator, grating, slit width, etc.) used in the fluorescence channel, and therefore is not related to, or limited by the excitation bandwidth. As a result, high resolution data can be obtained on the photoions even when the excitation bandwidth is broad. This is the single most important instrumental characteristic of fluorescence measurements, and provides the basis for many studies that are not possible using existing electron spectroscopy technology. In practice, this feature allows fluorescence measurements to achieve sub-meV resolution regardless of the excitation bandwidth. By way of contrast, the energy bandwidth of the exciting radiation is the lower limit to the photoelectron bandwidth [29].

• Fluorescence measurements can be performed arbitrarily close to the ionization threshold [18], as the instrumental transmission for fluorescence is not affected by the electron kinetic energy.

• External electric and magnetic fields can be used for fluorescence studies [30], where such perturbations either degrade or preclude photoelectron spectroscopy studies.

• The collection efficiency is typically higher for fluorescence monochromators than for electron spectrometers [14]. A related point is that higher sample densities can be used in fluorescence measurements, providing that secondary processes (e.g., electron impact ionization) are not occurring. High sample densities introduce electron scattering for outgoing photoelectrons, which degrade electron spectroscopy measurements.

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On the other hand, some of these same features that make fluorescence spectroscopy useful can also function as obstacles under certain circumstances. The advantages of photoelectron spectroscopy relative to dispersed fluorescence spectroscopy for providing state resolved information on the photoions are listed below.

• Fluorescence studies are limited to excited states that fluoresce. Many excited states of ions decay via fragmentation rather than fluorescence. In fact, ion fragmentation is so common that it provides the basis for a separate area of research. Such studies are discussed by Leach [31] and others [32]. Thus, the range of sample systems for dispersed fluorescence measurements is limited.

• Uncoupling the excitation bandwidth from the fluorescence bandwidth also has drawbacks. For example, it is possible that states of interest are not exclusively created by direct photoionization, but rather, by production of more highly excited ionic states, followed by fluorescence cascades. Fortunately, this effect can be assessed in many cases, as comparisons between electron and fluorescence spectroscopy directly test for such effects [33,34]. These comparisons show that cascading has not measurably influenced any of these systems. (This point will be demonstrated for the N2O results presented in Sec. V.A.)

• Another complication introduced by uncoupling the excitation bandwidth from the fluorescence bandwidth is that the target state is uncertain [16,17]. For example, an excited vibrational level of an ion might be produced from photoionization of the ground state neutral, or vibrationally excited neutral molecules (i.e., hot band excitation). The fluorescence transition will occur at the same energy for both excitations, while they are readily distinguishable in photoelectron spectroscopy.

• The analysis of fluorescence results can be complicated by ionization induced by secondary electrons ejected from the primary photoions. Pressure dependent studies can test for such unwanted artifacts, and experiments are then performed at pressures sufficiently low to avoid these complications [24].

Thus, it is clear that dispersed fluorescence and photoelectron spectroscopy provide complementary benefits. For example, when vibrationally resolved measurements on the photoion are required at higher photon energies, fluorescence spectroscopy is preferable, as the incident energy bandwidth (typically rather large at higher

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energies) does not preclude vibrational resolution on the photoion. For studies at lower photon energies, photoelectron measurements are frequently more versatile.

Finally, we note that the two types of measurements provide qualitatively different types of dynamical information in their more highly differential configurations. As an example, angle-resolved photoelectron spectroscopy provides P asymmetry parameters, which are sensitive to information on the relative phases as well as the magnitudes of the photoelectron partial waves [1]; on the other hand, fluorescence polarization data can be used to separate the information due to the relative phases of the photoelectron partial waves [35-39]. (A polarization sensitive fluorescence measurement is equivalent to angle-resolved fluorescence detection [40].) Thus, the combination of angle-resolved photoelectron and fluorescence measurements can provide information that either method cannot generate independently.

HI. EXPERIMENTAL

This section describes the apparatus and technical experimental considerations relevant to dispersed fluorescence measurements. The experimental apparatus is sketched in Fig. 4 [14,17].

Figure 4. Experimental schematic

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The incident radiation originates from a synchrotron radiation source. The radiation is collimated by a plano-convex lens (typically with an optical aperture of f/4 or f/5), then exits the chamber through a window, encounters a shutter which is opened and closed under computer control to assess dark count contributions of the detector. Then the radiation is reflected into the horizontal plane and focused onto the entrance slit of the fluorescence monochromator (typically with an optical aperture of f/5). The dispersed radiation exiting the monochromator is refocused onto the photocathode of a cooled photomultiplier detector. [In place of the exit slit/phototube combination, it is preferable to use an optical multichannel analyzer (OMA).] A vacuum ultraviolet photodiode measures the incident intensity. The fluorescence signal, photodiode signal, shutter control, and monochromator controls are interfaced to a computer via standard CAMAC electronics. One item that is not shown in Fig. 4 is a convex spherical mirror which is placed in the vacuum chamber to collect the radiation that is emitted in the opposite direction from the collimating lens. In practice, this nearly doubles the observed fluorescence signal.

We now estimate the counting rates to illustrate the experimental capabilities and limitations for these measurements. The chamber pressure is adjusted to the highest pressure free of experimental artifacts, typically » 8-10"4 Torr , and we estimate that the sample pressure in the molecular jet is about a factor of 40 greater than this, or 3-10 "2 Torr. This corresponds to a nominal number density of 1015 cm-3. The number of excited state ions formed per second, Iexc, is the product of four factors.

I = In ■ N - a ■ I exc 0 (3) I = In ■ N - a ■ / exc 0

where I0 ( a 5-10" s"1), N ( « 1-10" cm**), a ( » MO"" cm2), and / (« 0.5 cm) denote the incident intensity, number density of target molecules, partial ionization cross section, and path length, respectively. So, the excitation rate is on the order of 2.5-108 Hz. The collection optics are approximately f/5, corresponding to a collection efficiency of 0.25%. The net detection efficiency, including reflective losses and detector response, is estimated at 5%. Once an excited state ion is created, there are several fluorescence pathways open, and it is assumed that the one monitored receives approximately 30% of the intensity. With these factors taken into account, the fluorescence counting rate is Inet » (2.5-108) • (3.7-10'5) « 104 Hz. This estimate is consistent with observed intensities for levels with relatively large photoproduction cross sections, providing that the experiment does not require extremely high resolution to separate the fluorescence transitions. Weaker channels and weaker transitions typically have counting rates of 50-500 Hz.

Of course, multichannel detection can generate data much more efficiently than single channel detection. First, it reduces the data acquisition time by roughly two orders of magnitude because fluorescence intensities are measured simultaneously for an entire spectrum. Secondly, the proper choice of OMA [41] also has the advantage that the background level per unit wavelength interval is

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much lower than for a photomultiplier tube, and the background level is frequently the limiting factor in determining the data quality for weaker signals. Specifically, cooled channel plate OMA's offer tremendous advantages, as the dark count rate integrated over the total area of the detector (»500 mm2) is less than 150 Hz, versus »5 Hz for a cooled photomultiplier tube detector. While this does not seem like a bargain, consider that the area of observation for a particular transition can be as low as 0.05mm x 2mm (i.e., 0.1 mm2) [17]. This implies an effective dark count rate of 0.03 Hz, and this is a critical improvement, as we show with a back-of-the-envelope calculation. The net signal is Snet=Stot-Sback, where Stot and Sback represent the total observed intensity (signal plus background) and background levels, respectively. Thus the relative uncertainty in the net signal is

A S ^ { [ A S to t ] 2 + [A Sback]2 } V 2 [ S t o t + S b a c k ] 1 / 2

net tot " back tot back

Assume for the sake of argument that we wish to investigate a weak channel with a net photon flux to the detector of only 1 Hz, and that the background level is 0.03 Hz (i.e., the OMA performance), it would take approximately 1/2 hour to obtain data with relative uncertainty, ASnet/Snet, less than 2.5%. Assuming a net flux of 1 Hz and a background level of 5 Hz (i.e., the photomultiplier tube performance), 5 days would be required to obtain this single data point with comparable statistical quality. Many such measurements are required to obtain branching ratio data; thus the microchannel plate OMA makes possible measurements that would otherwise be out of reach.

IV. BACKGROUND Much of the discussion in following sections describes how shape resonances

induce breakdowns in the Franck-Condon approximation. Before proceeding to these selected studies, we first review the Franck-Condon approximation applied to molecular photoionization, and then discuss background on molecular shape resonances that relates to deviations from Franck-Condon predictions.

A. Franck-Condon approximation applied to photoionization

The Franck-Condon approximation predicts that vibrational branching ratios are independent of the photon energy in the absence of resonant excitation. It is useful to review this prediction to illustrate how shape resonances induce deviations from Franck-Condon behavior, thereby coupling nuclear and electronic

AS , net S . net

{ [AStot]2 + [ASback]2 I ' 7 '

tot back atot back

|2 [ASt + back! 1/2

[ Stot + Sback ] 1/2

hart + \ > t ' [ Stot back

s t s,

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motion. The partial photoionization cross section for a selected vibrational level Vf is given by eq. 4 (dropping common constant factors).

avf = | < f | M | i > | 2 = | < X f | [ < e f | M d k i > ] U i > | 2 (4),

where i and f denote the initial and final states, respectively; <p\ is the initial bound state molecular orbital from which the electron is ejected and ef represents the continuum electron wavefunction; %i and Xf are the initial and final vibrational wavefunctions; /i is the dipole operator. Defining the term in brackets to be the electronic dipole matrix element, Pei, the Franck-Condon approximation states that Pel is independent of the internuclear configuration. Thus, the result of the Franck-Condon approximation is eq. [5], where the dependence of avf on the kinetic energy is contained completely in Pei. This electronic factor, Pei, is factored out from the Franck-Condon factor, | < Xf I Xi > 12» i-e-> t n e term containing the vibrational wavefunctions.

vtf-H'vl2 (5)

Finally, we arrive at the consequence of the Franck-Condon approximation for vibrational branching ratios in photoionization. We define the vibrational branching ratio, crVf/avf', as the relative rate of production for two vibrational levels of the ion, f and f'. Using eq. 5, the branching ratio is given by eq. 6,

I I2

^ f ' V f~ = " 2 («. V I <x{,\x{ > I

i.e., the ratio of Franck-Condon factors connecting the initial (target) vibrational level, i, to the alternative ionic vibrational levels, f and f'. This ratio is independent of the photoelectron kinetic energy, or alternatively stated, the incident photon energy. Equation 6 is the result of the Franck-Condon approximation applied to photoionization. This approximation frequently breaks down due to shape resonant processes, and this breakdown provides a useful means of studying the correlation of electronic and nuclear motion.

aVf

= | < f I H i > | 2 = |<Xf I [<ef|Mdki>] | ^ > | 2 a Vf

|<f|Hi: 12

<Xf I [<cfl^el^i>] I V f |2 [<eflMdki>] I (4),

a « P 2 - |<Xrlx .> | 2 Vf el I Af,/Vi I

2 < xf | xH |2 > i r « P

Vf e v * (5)

a Vf

v I < ^ i ^ > |

,2 <Xf\X:>

I <^{'^i> I :Xf,\X: > 2 (6),

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B. Shape resonances and Franck-Condon breakdown

It is well understood that non-Franck-Condon behavior is observed in the region of shape resonances for diatomic samples, and a particularly well-studied system has been the photoejection from N2 of a 3ag valence electron into a eau resonant continuum channel [3,11,42]. This example is reviewed briefly to provide background for the following sections. The explanation for the variation of the vibrational branching ratio relies on a simple qualitative description of the shape resonance dynamics. Specifically, the resonance enhancement in the cross section is due to the temporary trapping of the continuum electron by a potential barrier. Thus, a photoelectron has a significantly increased probability of remaining in the region of the molecule for a significant time (in a classical sense) at a particular photoelectron kinetic energy where the trapping by a barrier is effective. Hence, the wavefunction overlap between the initial and final states exhibits a resonance, as does the photoionization cross section. However, the trapping of the electron is sensitive to the shape of the potential sensed by the photoelectron, which in turn depends on the internuclear configuration. It is this dependence of the shape of the potential (experienced by the photoelectron) to the internuclear configuration that is the cause of the coupling between the electronic and nuclear motion. A frequently performed calculation for diatomic systems highlights this connection (e.g., see refs. 4, 11 and 42). Specifically, the internuclear distance is frozen and the photoionization cross section is calculated as a function of electron kinetic energy. The internuclear separation is then frozen at a new value, and another partial cross section curve is generated. This process is repeated many times until a family of partial cross section curves is generated. The Franck-Condon approximation dictates that all of these curves would be identical except for a scaling factor. However, these curves do not follow the Franck-Condon prediction, which breaks down because the resonance energy and width are sensitive to the internuclear separation. In other words, decoupling the electronic and nuclear motion, i.e., factoring out the electronic matrix element in Eq. 5, is not valid. Specifically, it has been shown [3,11,42] that the resonance position shifts to lower energy and the resonance width decreases as the bond length of the diatomic target molecule is increased. Extending these ideas to polyatomic systems is discussed for the test case of N2O in the following section.

V. SELECTED RESULTS

In order to illustrate how dispersed fluorescence measurements probe molecular ionization dynamics, several examples are described. We begin with the most straightforward extension to the N2 3<7g'1 example described above, namely polyatomic vibrationally resolved photoionization. Following that, coupling between ionization continua is covered, and finally a brief description of rotationally resolved aspects of photoionization resonances is presented.

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A. N<0: A vibrationally resolved polyatomic shape resonance

Deviation from Franck-Condon behavior is common, and is an indicator of resonance excitation, as demonstrated by the N2O shape resonance results discussed here [15,21]. The motivation for studying shape resonance ionization for a polyatomic molecule is that alternative vibrational modes may be explored, and facets that are nonexistent for diatomic systems — the only samples vibrationally resolved previously— may be revealed. Specifically, different internuclear configurations are probed by selectively sampling alternative vibrational levels of the ion. Thus, the continuum electron behavior can be mapped, and qualitative aspects of the electron ejection are illuminated. In the N2O study, electronically excited ions are produced via synchrotron radiation excitation and the ionic fluorescence is detected to provide relative cross section information.

N 2 0 ( X V ) + hvexc—* N 2 0 + [A 2 E + , v '=(n^,np] + e"

1 N 2 0 + [X 2 n,v"=(4Mi^' ,n- ) ] + h V v / / (7)

The three vibrational indices denote the number of quanta for the symmetric stretch, bend, and asymmetric stretching modes, respectively. As in the N2 example, the fluorescence intensity originating from level V is a measure of the rate of production of that level, i.e., its partial photoionization cross section, <V [14,21].

Figure 5. Portion of the fluorescence spectrum of N20+ photoions: N20+(A2E+-OC2II). Transitions of interest are labeled. The doubling of the features is due to spin-orbit splitting in the ground state, not the excited state [N20+(A2S+)] that is fluorescing.

N 20(X 1S+ ) + hvexc-^ N20+[A2E+,v'«(ni,n£,iip] + e' N 2 0 ( X V ) + hi/ex — N20+[A2S+>v'=(n^ (ii2,np] + e" f e* N„0 + [A2E+,v' = (n' nX.n'Y

I N 2 0 + [X 2 n,v" - ( n - ^ ' ^ ' ) I + l » V v " ( 7 ) ^ 0+[X2n,v"=(n'' ,n2 ' ,n' ')] + hv ^ 2 „ (7) = (n'\nX'.ni'YI + hv

Figure 5. Portion of the fluorescence spectrum of N2O* photoions: N20+(A2S*-*X2II). Transitions of interest are labeled. The doubling of the features is due to spin-orbit splitting in the ground state, not the excited state [N20+(A2S*)] that is fluorescing.

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Figure 5 shows a fluorescence spectrum from N20+ photoions, and fluorescence originating from the v' =(0,0,0), (1,0,0), and (0,0,1) levels are noted. (Fluorescence from the V =(0,1,0) level has also been investigated [16,21], but is not discussed here in the interest of brevity.) By measuring the fluorescence intensity for a selected transition as a function of excitation energy, we obtain a constant ionic state (CIS) spectrum (CIS spectroscopy is discussed in refs. 16,21, and 43-46.) CIS spectra are shown for the the 3 vibrational levels of interest in Fig. 6. These cross

Figure 6. Constant ionic state (CIS) spectra for vibrational levels of N2O (A2S ).

section curves are all similar, and a large shape resonance is clearly discernible in all three CIS scans near the ionization threshold for the N20+(A2E+) state (« 16.4 eV). There is also a weak shape resonance at higher energy (hvexc « 35 eV), although this higher-energy feature has a significant nonresonant contribution, as discussed by Braunstein and McKoy [47,48]. The ratios of CIS scans are scaled to generate vibrational branching ratio curves [14,21], which reveal resonant ionization pathways.

Figure 7 shows such branching ratio curves for N20+(A2S+), and the non-constant spectral behavior is a consequence of the shape resonance near the 7cr-i threshold [15,21,33,47,48]. The (l,0,0)/(0,0,0) ratio varies strongly with photon energy (i.e., non-Franck-Condon behavior), while the ratio of the (0,0,1) and (0,0,0)

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curves is comparatively constant. In other words, the shape resonance profile for the v7 =(1,0,0) cross section is different than either the (0,0,1) or (0,0,0) curves.

Figure 7. Vibrational branching ratios for N 20+ (A 2S+ ) : <7(100)/<7(000) and (7(001)/(7(000). Note that the (7(100)/a(000) ratio deviates from Franck-Condon behavior, while the (7(001)/(7(000) curve is essentially constant with photon energy.

The N2O results shown in Fig. 7 provide the basis for a microscopic understanding of polyatomic shape resonances. The earlier description of resonance-induced Franck-Condon breakdown indicates that shape resonance ionization is well understood for diatomics [1,3,4]. However, polyatomic systems have not been well characterized, and there have been serious disagreements as to the interpretations of shape resonance features for polyatomic systems. Specifically, investigators are studying shape resonant ejection of core electrons (i.e., NEXAFS spectroscopy, Near Edge X-ray Absorption Fine Structure), and are attempting to correlate the energy position of the shape resonance above the ionization potential with changes in specific molecular bond lengths (e.g., refs. 49-54). Such attempts at structure correlations are motivated by the need to characterize the structure of adsorbates on surfaces, as local probes of chemical structure are extremely powerful for such applications. These interpretations have been refuted by some [55,56] and modified by others [5].

Fortunately, the N2O results in Fig. 7 lend themselves to a direct and unambiguous microscopic interpretation [21], and this interpretation is supported by independent ab initio Schwinger variational calculations [48] (shown in Fig. 8) and photoelectron results [33]. Specifically, these N2O results imply that the resonant photoelectron enhancement extends over the whole molecular framework, and is not associated with a particular bond in the molecule. As a result, the (7(0,0,1) curve is similar to the (7(0,0,0) curve because the asymmetric stretching

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vibration of the ion does not affect the molecular "length" appreciably or, therefore, the barrier to photoelectron ejection. On the other hand, the ion in the V =(1,0,0) level undergoes a breathing motion, changing the overall length of the molecule, thereby shifting the spectral distribution for the resonance.

Figure 8. Theoretical results adapted from ref. [48]. The qualitative agreement with experiment is good, and the reasons for the differences are due to inaccuracies in the ionic potential surfaces used in the calculations.

Figure 9 shows a sketch representing these vibrational motions. The results shown in Fig. 7, in combination with theoretical results shown in Fig. 8 and discussed in Ref. [48], validate this interpretation. Thus, this dispersed fluorescence experiment has unambiguously elucidated the spatial extent of a polyatomic shape resonance for the first time. The implication of these results — i.e., shape resonance trapping of the photoelectron is not necessarily associated with a particular bond in a polyatomic molecule — is in stark contrast with interpretations of previous NEXAFS studies [49-54]. Specifically, these N2O fluorescence results demonstrate that, in general, shape resonance energy positions cannot be correlated with a specific bond length of a polyatomic molecule [55,56]. This microscopic picture of a polyatomic shape resonance has significant consequences for surface and materials science, as well as clarifying a fundamental phenomenon in gas-phase chemical physics. In so doing, this study motivates vibrationally resolved investigations of alternative polyatomic systems, so that reliable structure/dynamical correlations can be deduced.

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Figure 9. This sketch shows how the end-to-end length of N2O is affected by the symmetric and asymmetric stretching modes. This qualitative picture provides a straightforward explanation of the experimental results shown in Fig. 7, and is supported by theory [48].

This N2O fluorescence study is complemented by photoelectron work which generated P photoelectron asymmetry parameters and vibrational branching ratios at the lower photon energies [33]. We compare vibrational branching ratios obtained from the two methods in Fig. 10. The results are in excellent agreement, lending credibility to both data sets.

Figure 10. Comparison of photoelectron spectroscopy [33] and dispersed fluorescence spectroscopy [21] for the branching ratios <7(100)/a(000) and a(001)/a(000).

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A key point is that these results are accessible because dispersed fluorescence is capable of discerning molecular vibration even when the excitation bandwidth is broad [14]. This feature is critical, as the excitation bandwidth is larger than the ionic vibrational spacings at the higher photon energy [21,57]. This strategy of using dispersed fluorescence for decoupling the excitation and detection bandwidths can also be applied to core electron excitation processes [19,20,22,23], and preliminary work in this vein is described in Sec. V.C, following an introduction to continuum channel coupling phenomena in Sec.V.B.

B. Continuum channel coupling: Valence-hole/valence-hole coupling

The N2O results demonstrate how dramatically shape resonances can affect the deposition of vibrational energy into the molecular ion, and this process is well described at the independent particle level (i.e., Hartree-Fock level) of approximation [3,8,9,42]. The effects of shape resonances can be even more wide ranging, as channels that are nominally nonresonant at the Hartree-Fock level of approximation can "borrow" shape resonant character from other ionization channels via electron correlation, or continuum channel coupling. As a result, our description of shape resonances needs modifications that incorporate the sharing of oscillator strength between ionization channels. Before proceeding in detail, we stress that interchannel coupling between ionization continua is just beginning to receive experimental and theoretical attention, and that the current state of understanding is incomplete, at best. We begin with a classical picture of the process to highlight the physical origins of continuum channel coupling. The process is sketched in Fig. 11. Photoexcitation with hvexc% 30 eV creates a shape resonant ion/electron complex [N^^Og"1) + e~(e0u)L followed by a collision between the quasibound e<ru electron and a 2<ru valence electron [58,59]. This collision results in the ejection of the 2<7U electron while the excited electron drops into the 3ag vacancy. This collision has an appreciable cross section because the continuum electron is quasibound, i.e., there is considerable probability of finding the electron in the valence region of the ion even though it is a continuum electron [1,14,58-60]. In our experiments [24], we detect the dispersed fluorescence from the 2<ru-i hole state [i.e., N2

+(B2EU+,V) -» N2+(X2Eg

+,v") + h i V v " ] . The excitation, interchannel coupling decay, and fluorescence sequence for the N2 measurements is given by eq. 8.

N2(XiEg+,v=0) + hi/exc > [N2

+(2V) + e ^ i i ) ]

N2+(B2Eu

+,v) + e" I fluorescence

N ^ y ' l + h c ^ , , (8)

N2(X»Eg*,V = 0) + h«/exc [ N 2 ' ( 2 V ) + e-(€(T„)] ♦) + t\eav

I r.2-1

N2t(B2Su

t,v') + e" I fluorescence

N2+(X2Eg*,v-) + h i / v / v / /

N 2 i r > ^ u , v 1 T e

I fluorescence

N i W , v " ) + hi/ f I T I l f (8)

B. Continuum channel coupling: Valence-hole/valence-hole coupling

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Figure 11. Sketch showing oscillator strength being transferred from the shape resonant ejection of the 3<7g electron to the 2<TU

_1 continuum.

Figure 12. R-dependent continuum coupling: At every interauclear separation, oscillator strength is preferentially transferred from the shape resonant ejection of the 3<7g electron to specific vibrational levels of the the 2<7U"1 state.

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Eq. 8 indicates that this process can be investigated at the vibrationaUy resolved level of detail, as sketched in Fig. 12 [58]. The idea is the same as in the previous discussion of fixed-R channel coupling, except that for every value of R sampled in the target molecule, the resonance character is transferred preferentially to alternative vibrational levels of the 20V1 hole state. Thus, we expect that vibrational branching ratios for the N2

+(B2EU+) state will also exhibit

deviations from Franck-Condon behavior as oscillator strength is transferred from the 30g-»e<7u shape resonance, and the initial calculations confirm this expectation [58].

However, the agreement between experiment and theory is not satisfactory. Recent results [24] are shown in Fig. 13, and the V = l/v' =0 branching ratio for the 2cru -i hole state is very flat (i.e., Franck-Condon) except for a small resonance at hi/« 29 eV [14]. In other words, the 3ag*eau shape resonance is not strongly affecting this vibrational branching ratio for the 2au

_1 hole state. This contrasts strongly with theory, which predicts a large excursion (>60%) in this vibrational branching ratio at hi/ a 35 eV. On the other hand, the v' =2/v' =0 branching ratio does show significant non-Franck-Condon behavior, but there are not yet calculations available for comparison.

Figure 13. Experimental branching ratio results for the N2+(B2SU+) state (i.e., the 2(JU

_1 hole state). Also shown is a prediction for the v / = l / v / = 0 curve based on Schwinger variational calculations for the continuum wavefunctions [59].

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So, this discussion demonstrates that our understanding of molecular continuum channel coupling is not yet complete. It also shows that vibrationally resolved measurements provide a stringent test of continuum coupling, and in this case, provide guideposts for further theoretical efforts. For completeness, we note that the angularly resolved photoelectron results for this system [60] provide an independent test of theory, and that experimental photoelectron asymmetry parameters (i.e., /7s) do not agree satisfactorily with theory either [59]. Collectively, these results underscore the need for further studies of continuum channel coupling in molecular photoionization, as the results cannot be interpreted quantitatively without a picture of how resonance character is transferred between ionization continua. Moreover, an understanding of channel coupling is desirable for many reasons, including the need to characterize the role of electron correlation in scattering processes, and for applications in disentangling core-hole resonances, as discussed in the following section.

C. Continuum channel coupling: Core-hole/valence-hole coupling

The N2O study described in Sec. V.A underscores the point that even a qualitative understanding of the ionization dynamics is aided by resolving the ionic vibrational motion. Similarly, vibrationally resolved data for core electron excitation would be useful, but such results are elusive owing to severe constraints, both natural and instrumental. The first limitation is that vibrational structure of photoelectron spectra can be washed out following creation of a core-hole state because of lifetime broadening. Second, the excitation bandwidth in the energy range required for core-hole creation is usually broad, and this also restricts the photoelectron energy resolution following core-hole creation. Both sources of spectral broadening frequently preclude vibrationally resolved measurements using photoelectron methods. The work described on interchannel coupling in Sec. V.B showed that shape resonant character can be transferred from one ionization channel to another, and a corollary to this result is that the transfer of shape resonance character to nominally nonresonant channels can be exploited to gain R-dependent information on the channel which is sharing its shape resonant oscillator strength. So, this section shows that channel coupling can be exploited for obtaining R-dependent information on core-hole resonant excitations.

Preliminary studies have investigated the response of a core electron resonance to changes in the internuclear separation by detecting fluorescence from a valence-hole state that is populated via channel coupling [20,23]. The strategy is that interchannel coupling decay of a core-hole resonance populates excited valence-hole states of the ion [61-64]. The fluorescence from these valence-hole states can be vibrationally resolved, reflecting aspects of the resonant excitation of the core electron that depend on the internuclear separation. In our N2 study which serves as a test case [20,23], the resonance excitation for the Is electron is probed via its coupling to the 2^u

-1 valence-hole continuum [i.e., the N2+(B2SU+)

state]. The process may be viewed classically as excitation of the Is electron to a

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shape resonance state followed by a collision between the quasibound electron and a 2au valence electron. This interaction results in the ejection of the 2<ru electron while the quasibound electron drops into the Is vacancy.

Figure 14. Sketch of the process where resonance character is transferred from the shape resonant ejection of the Is electron to the the 2au

_1 continuum.

Figure 14 summarizes the individual steps in the process. This electron-electron interaction (i.e., channel coupling) provides an opportunity to circumvent the limitations associated with core electron excitation, because fluorescence from the resulting valence-hole state ion can be vibrationally resolved [19,20,23]. Though the excitation energy is » 420 eV and the bandwidth is w 2 eV, even rotationally resolved photoionization data are accessible via fluorescence from the valence-hole state [17]. The excitation, interchannel coupling decay, and fluorescence sequence for the N2 measurements is given by eq. 9.

N 2 ( X V ) + h^exc > [Nj^ls"1) + e-]

N2+(B2Su*,v) + e-

I valence-hole fluorescence

PVCls"1) + e-] 1 ru-i

N J W I V . V ) + e-I valence-hole fluorescence

N 2+ (XV,v" ) + h V v (9)

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In this process, photoexcitation creates a shape resonant complex [N2**(ls_1, shape resonant e") for hvexc% 420 eV] which decays via interchannel coupling to the N2+(B2SU

+) ionic continuum. The resulting valence-hole state ion fluoresces, and the dispersed fluorescence, mVv'' , is detected.

We show some recent data on this process [23], with the caveat that it is preliminary. Specifically, we have performed constant ionic state spectroscopy on the N2 system in the region of the nitrogen K-edge. Figure 15 shows CIS scans for the different vibrational levels of the N2+(B2SU

+) state, i.e., the valence-hole state.

Figure 15. Constant ionic state spectra for the N2+(B2EU+) state in the region of the nitrogen

K-edge (« 406 eV). The peak at hu « 401 eV is due to a Is -» lflg transition.

These CIS scans are plots of the production of specific vibrational levels of the valence-hole state as a function of photon energy in the region of the core-hole resonance. Note that the N2+(B2EU

+) partial cross section curves are changing substantially in the region of the core electron shape resonant excitation. Specifically, the shape resonant feature, i.e., the broad maximum located at

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h^exc* 420 eV, is clearly shifting among these CIS spectra. This is a significant observation, as it demonstrates that alternative vibrational levels of the valence-hole state (i.e., levels sampling different internuclear separations) shift the core-hole resonance to different energies.

Thus, these experimental results demonstrate that the vibrational branching ratios obtained for the valence-hole state are mediated by the core electron resonant excitation. The corollary is that information derived from valence-hole states of a molecular ion can shed light on core electron excitation phenomena. Thus, this example demonstrates the potential of using vibrationally resolved data on valence-hole states to probe aspects of the core-hole processes that vary with internuclear separation, including core electron shape resonant excitation.

These results underscore the need for developing an understanding of continuum channel coupling in molecular photoionization [58,59,65,66], as the results cannot be interpreted quantitatively without a picture of how resonance character is transferred between ionization continua. In addition to the need for theoretical progress, two experimental issues must also be considered. First is the possibility that the N2+(B2EU

+) ions are not populated by photoionization, but rather by high-energy secondary electrons produced by photoionization of N2. This possibility has been discounted for the V =0 and the v ' = l curves, as these excitation curves are independent of pressure, indicating that the fluorescence is not due to secondary electrons, but rather photoionization of the target N2 molecules. The pressure dependence for the v' =2 excitation curve has not yet been performed, although this work is in progress.

It is still possible that radiative cascading is complicating the results, i.e., the core-excited state decays to a highly excited valence-hole state of N2+ which then radiatively decays to N2+(B2EU

+). Further studies are required on this point. However, while cascading might complicate the detailed analysis of these results, it does not alter the principal conclusion. Specifically, the valence-hole state contains information on the core electron excitation process, as the vibrationally resolved CIS scans shown above are clearly displaying differences in the region of the core-hole resonance.

Thus, continuum channel coupling can be used to great advantage, as the results shown in this section demonstrate that core-hole resonances and dynamics can be probed on an R-dependent basis via interchannel coupling to valence-hole states. As in the previous examples in Sec. VA-C, this core electron study is an example of how vibrationally resolved data on the photoion provide a window into the microscopic aspects of the ionization dynamics. More specifically, such vibrationally resolved data show how resonances respond to changes in molecular geometries. Experimentally, it is possible to go beyond vibrationally resolved aspects of the ionization process, and the following section shows that it is both feasible and desirable to achieve rotationally resolved data on photoionization dynamics via dispersed fluorescence. V

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D. RotationaUy resolved studies

Rotationally resolved data on the photoion provides insights into the ionization dynamics, and the type of information that is accessed is qualitatively different from the vibrationally resolved examples. Rotationally resolved data on the photoion can be related to the photoelectron partial wave composition, and thereby to the ionization dynamics [67-74]. For example, it has been shown that the shape resonant wavefunctions can be dominated by a single partial wave with well-defined angular momentum [11,42]. Thus, the photoion's rotational motion is affected, as demonstrated by analogous REMPI (resonantly-enhanced multighoton ionization) photoelectron studies [74]. In this section, N2 results demonstrate that resonance excitation affects the deposition of rotational energy into the ion, and conversely, that rotationally resolved data on the ion can be used to disentangle the ionization dynamics. Moreover, these results show that dispersed fluorescence can generate rotationally resolved data on the photoion, and do so over a broad energy range, regardless of the incident bandwidth.

In this example, fluorescence originating from the ion in rotational level N ' is a measure of its rate of production, and the excitation/fluorescence sequence is

N 2 (xV,v=0 ,N) + hvcxc > N + ( B V , V ' = 0 , N ' ) + e"

4

N j ( x V , v " = 0 , N " ) + huN,N,, (10)

Figure 16 shows a rotationally resolved fluorescence spectrum. Important facets emerge from spectra obtained at different excitation energies. Specifically, the relative intensities of the fluorescence transitions vary with photoelectron energy.

N2(X1E^v = 0,N) + h , e x c , ( x V , v = 0,N) + hu > N + ( B V , V = Q , N ' ) + e " "S ,v'=0,N') + e"

1 N ^ x V . v ' ^ O . N " ) + h V N , , (10) -E- v"=Q,N") + h^ N / M , sr^v'

Figure 16. Rotationally resolved fluorescence spectrum from N2 photoions.

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An example of a rotational branching ratio spectrum is given in Fig. 17, where the intensity ratio I[R(4)]/I[band] is plotted as a function of the excitation wavelength. This rotational branching ratio exhibits a dip at hvexc% 23 eV, corresponding to the position of a broad autoionization resonance [75] with electron configuration (3<7g-ll7ru-ll7Tg2).

Figure 17. Rotationally resolved branching ratio. A resonance dip is discernible at hl/exc~ 23 eV, the position of an autoionization resonance [75].

One might suppose that dipole selection rules completely govern the angular momentum deposition for the ion; if this were the case, the resonance dip would not be observed in Fig. 17. However, dipole selection rules constrain the total angular momentum of the electron-ion complex, while the partitioning of angular momentum between the photoelectron and photoion depends on the photoejection dynamics. Alternatively stated, Fig. 17 demonstrates that photoelectron ejection can exert sufficient torque to change the rotational motion of the much more massive molecular ion, suggesting that measurement of the rotational distribution can provide insight into the photoionization dynamics.

While this N2 example demonstrates the potential of rotationally resolved photoionization experiments, the advent of suitable OMA systems and improvements in synchrotron radiation sources are making it possible to go beyond the demonstration phase, and employ rotationally resolved data for studying shape resonant photoionization of diatomic samples. This is one application of dispersed fluorescence that should and will be exploited. The examples in this section have shown only the beginning of what might be possible using dispersed fluorescence, and the following section describes other possibilities that build from these demonstrations.

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VL FUTURE DEVELOPMENTS

While Sec. V describes specific investigations into resonant ionization dynamics using dispersed fluorescence measurements, it is useful to examine possible outgrowths, particularly those that are more speculative or longer range in nature. Some of these possibilities are listed below, and they serve to place previous progress into a broader context. First, there are clear and necessary extensions of the previous work, such as investigating a wide variety of polyatomic systems' shape resonances with vibrational resolution. Such studies will make it possible to exploit shape resonances as reliable analytical tools for unusual chemical systems, including adsorbates in surface and aerosol chemistry. In particular, larger polyatomic samples should be investigated, as well as chemically homologous systems. For example, it is possible to alter the surroundings of a chemical moiety covalently. The shape resonant behavior for a group of compounds could then be compared. For example, one such series would include the -CN group, such as ICN, BrCN, and C1CN. Vibrationally resolved spectra would clarify the polyatomic nature of the shape resonance, including a critical assessment of whether it is reasonable to assign resonances to subgroups of molecules, such as the -CN moiety.

Similarly, interchannel coupling of continuum shape resonances requires further attention, as there is not yet sufficient agreement between theory and experiment. In particular, it is essential to build a broader data base, and this includes both theoretical and experimental efforts.

There are also new classes of experiments suggested by the previous studies. For example, the N2O study illustrates our current thinking on the microscopic picture of shape resonant ionization. It would be useful to extend these studies by altering the molecular environment — i.e., to solvate the target molecule — and investigate how the shape resonant dynamics are modified by such changes. This can be accomplished in a number of ways. For example, it is possible to change the molecular environment by introducing a van der Waals partner for the sample molecule. Other possibilities include embedding the sample molecules in a matrix [76,77] or supporting the sample on a solid surface.

Another pursuit that diverges from the past work involves vibrationally pumping the neutral target molecules before they undergo ionization. The studies discussed in Sec. V provide information on the ionization dynamics by discerning vibrational motion of the ion following its creation. It is possible to probe the response of the resonance to changes in molecular geometry with greater flexibility by selecting the vibrational level of the neutral target molecule. Currently, studies are restricted to ionization from the ground vibrational level of the ground state neutral sample. This selection of the target vibrational level can be accomplished using an F-center laser to excite target molecules in the ground electronic state manifold. Such studies would form a new class of measurements, and might be termed IR/VUV double resonance.

There is another benefit which can be derived by using an F-center pump laser to define the target molecules undergoing photoionization, namely, that the

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rotational level of the target could be state-selected. This has tremendous benefks for rotationally resolved fluorescence measurements on the photoion. Currently, the molecules undergoing photoionization are in a thermal distribution of rotational levels. By rotationally selecting the target molecule, complete state-to-state photoionization data could be obtained. This capability would provide data similar to that which is available from REMPI studies (e.g., ref. 74), where rotationally resolved electron spectra are obtained following rotational state selection of the target molecules undergoing ionization. The fluorescence studies have the advantage that a wider range of photon energies would be accessible; for example, shape resonant excitation could be investigated at the rotationally resolved level of detail.

The direction of future work is guided by both scientific and technical considerations. As the experiments described in this section rely exclusively on vacuum ultraviolet and x-ray radiation for creating the photoions, it must be noted that radiation sources in this energy range are improving in a variety of respects. For example, tripling of laser-generated ultraviolet light has become a reliable and very narrow bandwidth VUV tool for photoionization studies [78]. While the energy range is still limited by standards of photoionization work, it is constantly being improved. In a similar vein, the development of synchrotron radiation tools, including insertion devices and narrow bandwidth soft x-ray grating monochromators, has made synchrotron radiation probes of molecular photoionization more precise and sensitive [12]. Finally, there is the possibility of achieving free-electron laser radiation in the VUV region, and this could conceivably open up whole new areas, in that channels that are currently too weakly populated to be observed would be accessible for study. The variety of possible future directions is an indicator of the scientific potential of dispersed fluorescence for investigations of molecular photoionization. This breadth and flexibility provides the basis for continued research that generates important insights into existing problems, and also identifies new areas of future research.

ACKNOWLEDGNfENT

This work is supported by the National Science Foundation (NSF-CHE-9001590).

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