Line shape and lifetime in argon 2p electron spectroscopy

Journal of Electron Spectroscopy and Related Phenomena 120 (2001) 67–76 www.elsevier.nl / locate / elspec

Line shape and lifetime in argon 2p electron spectroscopy a b c d d e, T.X. Carroll , J.D. Bozek , E. Kukk , V. Myrseth , L.J. Sæthre , T.D. Thomas * b

a Keuka College, Keuka Park, NY 14478, USA Advanced Light Source, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA c Department of Physics, University of Oulu, FIN-90570 Oulu, Finland d Department of Chemistry, University of Bergen, N-5007 Bergen, Norway e Department of Chemistry, Oregon State University, Corvallis, OR 97331 -4003, USA

Received 15 March 2001; received in revised form 27 April 2001; accepted 2 May 2001

Abstract The argon 2p photoelectron spectrum and the argon L 3 M 23 M 23 1 S 0 Auger spectrum have been measured at several photon energies between 6 and 80 eV above the 2p 3 / 2 threshold with an instrumental line width significantly smaller then the natural line width. The spectra are described well by the theory of van der Straten et al. [Z. Phys. D 8 (1988) 35] provided that allowance is made for the instrumental resolution and measurements are made at a sufficiently low pressure. The lifetime (Lorentzian) line width determined from these measurements for the core-ionized atom is 11263 meV, in good agreement with the line width for the 2p 3 / 2 →4s core-excited state, 11462 meV, indicating that the 4s electron has little influence on the Auger decay rate. Remeasurement of the line width for the carbon 1s hole in carbon dioxide gives values in good agreement with the previous measurement of 99 meV.  2001 Elsevier Science B.V. All rights reserved. Keywords: Auger; Photoelectron; Linewidth; Lifetime; Post-collision interaction

1. Introduction Inner-shell photoelectron spectra are characterized by intensity, line position, line shape, and fine structure. The fine structure may reflect multiplet splitting, spin–orbit splitting, and, for molecules, vibronic excitation, inequivalent atoms of the same element, molecular-field splitting, or the effect of symmetric / antisymmetric combinations of atomic orbitals. The line positions reflect the chemical environments of the atoms and the intensities reflect cross sections and angular distribution parameters. *Corresponding author. Tel.: 11-541-737-6711; fax: 11-541737-2062. E-mail address: [email protected] (T.D. Thomas).

The line shape depends on the lifetime of the core hole as well as the interaction between the photoelectron and any Auger electrons (post-collision interaction, or PCI) [1,2]. Having a correct description of the line shape is key to understanding the other effects, and our focus here is on the lifetime and line shape. In the simplest approximation the line shape for inner-shell photoelectron spectroscopy is Lorentzian. The full width at half maximum of the Lorentzian, G, is related to the lifetime, t, by the relationship Gt 5 ". The shape is, however, distorted by the interaction of the photoelectron with the Auger electron that is emitted when the core hole deexcites. The distortion depends on the kinetic energies of the Auger and photoelectrons and on the lifetime of the core-hole. It is most

0368-2048 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 01 )00306-1

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pronounced near the ionization threshold and disappears when the kinetic energy of the photoelectron is greater than that of the Auger electron [2]. In addition to this intrinsic distortion of the Lorentzian line shape, there is an additional effect on the line shape due to the instrumental resolution of the experiment. The lifetimes of core holes in molecules and atoms have been the subject of many studies and many lifetimes of core holes have been reported. However, the uncertainties have often been large and the disagreements between values given by different investigators are significant. For instance, carbon 1s line widths reported for methane range from 83 to 120 meV [3–6], and for carbon dioxide from 70 to 99 meV [7–10]. Even for argon, where one might hope to find a reasonably simple situation, reported values of the width for a 2p hole range from 100 to 160 meV, with most values being near 120 meV [11–22]. In addition to the disagreements in values mentioned in the previous paragraph, we have found in recent measurements [6,10] that there is an apparent increase in the lifetime line width as the photon energy decreases towards the threshold for photoionization. Furthermore, the measurements on methane [6] show that there are small but systematic deviations between the line shapes observed experimentally and those predicted from the theory of post-collision interaction. Possible explanations for these observations are that the theory of post-collision interaction that we have used [23] does not accurately describe the line shape near threshold, or that there are experimental artifacts that we have not taken into account. Although the line width of the 2p hole in coreionized argon is not known accurately, that for the core-excited state obtained by exciting a 2p 3 / 2 electron to the 4s state is known with good accuracy. Several measurements of this quantity have been reported [24–27], and they agree with one another within a few meV, with a weighted average of 11462 meV. It is of interest to know the width for the core-ionized state with comparable accuracy in order to see if the additional 4s electron influences the Auger decay rate. To shed further light on the questions of lifetime and line shape, we have measured argon 2p photo-

electron and LMM Auger spectra at photon energies ranging from 6 to 80 eV above threshold and, in some cases, over a range of argon pressures. At the lowest energies the effects of post-collision interaction are very pronounced, and these measurements provide a useful test of PCI theory. If PCI theory is correct, they also provide a sensitive measurement of the core-hole lifetime. The Auger spectra are always at nearly the same kinetic energy, regardless of the photon energy, so these measurements are all made under exactly the same spectrometer conditions. In addition, for the Auger spectra there is no contribution to the resolution from the photon bandwidth. The photoelectron measurements, on the other hand, involve electrons ranging in energy from a few eV to 80 eV; these, therefore, involve different spectrometer conditions. Furthermore, in this case, the instrumental resolution includes a contribution from the photon bandwidth. The Lorentzian width derived from these measurements may, therefore, be differentially affected by the assumptions about and uncertainties in the instrumental line shapes. Comparison of the Auger and photoelectron spectra taken at the same photon energy should reveal such effects.

2. Experimental procedures and data analysis The experiments involved measurements of argon 2p 3 / 2 and 2p 1 / 2 photoelectron spectra, the L 3 M 23 M 23 1 S 0 line of the argon Auger spectrum, and the carbon1s photoelectron spectrum of carbon dioxide. Three sets of experiments were made. The first was with moderate resolution and covered photon energies between 6 and 80 eV above the 2p 3 / 2 threshold. Analysis of the data and separate measurements of the resolution indicated that the resolution was not as good as expected. A second set was taken at 11 and 80 eV above threshold after some improvements had been made to the experimental arrangements. A third set was made 10 months later with as a high a resolution as practical, but restricted to 12 and 80 eV above the 2p 3 / 2 threshold. The measurements were made using Beamline 10.0.1 of the Advanced Light Source of the Lawrence Berkeley National Laboratory. This beamline receives its radiation from an undulator (U10) with a 10-cm period. It is equipped with a spherical-grating

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monochromator that is capable of a resolving power of greater than 10 4 ; this was set to provide a resolution of either 25 or 40 meV for the photoelectron measurements. For the Auger measurements, resolution of the photon beam is not so important as intensity, so for these the resolution was set at 100 meV to provide greater intensity. For the argon spectra measurements were made at photon energies ranging from 255 to 330 eV, that is, 6–80 eV above the threshold for 2p 3 / 2 ionization. The carbon dioxide spectra were measured at a photon energy of 330 eV (for comparison with our previous measurements [10]). The electron spectra were measured with a Scienta SES-200 spectrometer [28]. This was set to have a pass energy of either 5, 20, or 40 eV and the entrance slit of the analyzer was chosen to give an expected resolution in the range of 20–40 meV. All measurements were made with the analyzer perpendicular to the beam direction and at an angle of 54.78 to the polarization direction. Both Ar and CO 2 were run at several pressures to ensure that pressure broadening would not complicate the line shape analysis even further. It is important to know the photon energy accurately, since the shapes of the photoelectron and Auger spectra depend critically on this energy, especially near threshold. For our experiments, the photon energy has been determined from the photoelectron spectrum, using the measured kinetic energy of the 2p 3 / 2 photoelectron line and its known ionization energy, 248.6 eV [15,24,29–33]. This procedure depends, in turn, on having calibrated the kinetic energy scale of the photoelectron spectrometer. For this, we measured the xenon N 4,5 OO Auger spectrum, which has many lines with known energies [34]. This procedure avoids the need to know the calibration and reproducibility of the monochromator. For the first and second series of measurements the monochromator slits were set to provide a nominal photon resolution of 40 meV. In the first series, the actual resolution of the photon beam was measured by collecting the photon absorption spectrum in the region of the 2p 3 / 2 →4s resonance of argon. The experimental resolution function for the photon beam was assumed to be Gaussian, and, accordingly, the absorption spectra were fit with

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Voigt functions to give the Lorentzian and Gaussian widths. These measurements indicated a resolution of about 70 meV, compared with the expected value of 40 meV. For the second series, absorption measurements were made for the same line in argon as well as for the 1s→p resonance of carbon monoxide. These were made at several pressures to assess the importance of saturation effects. The Lorentzian component of the argon absorption spectrum ranged from 110 to 115 meV; the most carefully measured absorption spectrum gave 112 meV. These values are in good agreement with those reported by others, with, as noted above, an average of 11462 meV [24–27]. The photon resolution determined in these experiments was about 50 meV, somewhat higher than the expected value of 40 meV. For the third series the monochromator slits were set to give a photon resolution of 25 meV; no measurements of the photon resolution were made for this series. The resolution of the electron spectrometer was determined for the first and second series by measuring the xenon 5p photoelectron spectrum at photon energies of 25 and 50 eV under conditions where we expect the contribution of the photon beam to be negligible. The spectra were fit with Gaussian functions, which fit them reasonably well. These measurements indicate that for the first series of argon measurements the resolution (full width at half maximum) was about 60 meV, compared with the expected value of 40 meV. The elements of the spectrometer were retuned to give a resolution of about 45 meV, and the second series of argon measurements was made. For the third series, an extensive set of measurements were performed using pass energies of 20 and 40 eV, at slit settings of 0.2, 0.3, 0.5, and 0.8 mm, and at photon energies of 22 and 50 eV. The overall results showed that the spectrometer was performing according to specifications. In detail, however, the line shapes were somewhat different from Gaussian, especially for the largest slit setting. Furthermore, the line widths were systematically higher at the higher photon energies (even after allowing for the greater Doppler width and greater contribution from the monochromator); this problem is discussed in more detail in Section 3.3. The photoelectron measurements were made with a pass energy of 20 eV and a 0.3-mm slit, for a spectrometer resolution of 22–26 meV. The Auger

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measurements were made with a pass energy of 40 eV and either a 0.2- or 0.3-mm slit, for a spectrometer resolution of 36 or 41 meV. For the Auger spectra, the expected overall instrumental resolution is given by the combination of the spectrometer resolution and the Doppler broadening (28 meV). For the three series of measurements, this gives an expected total resolution of 66, 53, and 45 meV. For the photoelectrons, it is necessary to include also the contribution for the photon bandwidth. For the three series of argon measurements, we have 93, 67–69, and 33–40 meV, and for the carbon dioxide measurements, 45 meV. The range of values reflects the effect of the variation in Doppler broadening with electron kinetic energy. In previous experiments [6,10], using the procedure outlined by Jauhiainen et al. [35], we have found that the analyzer transmission varies nearly as the reciprocal of the kinetic energy that the electron has before it enters the analyzer. The photoelectron spectra from the first two series of measurements were corrected using this assumption. At the time of the third series, we repeated these measurements and found that the transmission was constant over the kinetic-energy range of interest. Consequently, no corrections were made to these data. As a practical matter, the correction does not appear to be important. Even at the lowest kinetic energies considered here (7–9 eV), the results obtained from fitting the spectrum with and without the transmission correction are in close agreement. No correction was made for any of the Auger spectra since the width of the spectrum is small compared with the kinetic energy. The photoelectron and Auger spectra have been fit by least-squares using a fitting function that includes the effects of post-collision interaction and experimental resolution [36]. For this, we have used Eq. (8) of van der Straten et al. [23], which is expected to be valid even close to threshold, convoluted with a Gaussian to represent the experimental resolution. For the argon photoelectron spectra the 2p 3 / 2 and 2p 1 / 2 peaks are fit simultaneously; the fitting parameters are a linearly sloping background, peak heights, peak positions, and the Gaussian and Lorentzian widths. The same widths were used for the two peaks. The PCI profiles are, however,

different for the two peaks, since they are at different energies above threshold. For the Auger spectra the 1 S 0 peak is well isolated from other peaks, so only this single peak has been fit; the fitting parameters were the same as for the photoelectron lines, except that the background was assumed to be flat over the energy region of the fit. For the carbon dioxide photoelectron spectra three peaks were used to represent the vibrational progression observed in this spectrum. The relative intensities and positions of the peaks in this spectrum were fixed according to our earlier results [10].

3. Results

3.1. Pressure dependence of the photoelectron spectrum near threshold Measurements of photoelectron spectra near threshold involve low-energy electrons, which are easily scattered by the gas in the sample cell and in the spectrometer. Our first concern, therefore, was to measure the pressure dependence of the argon 2p photoelectron spectrum near threshold. This was done at a photon energy of 262 eV, 13.5 eV above the 2p 3 / 2 threshold and 11.4 eV above the 2p 1 / 2 thres26 25 hold. The pressures (1.0310 to 1.65310 Torr) were measured with an ion gauge attached to the vacuum chamber of the analyzer. The actual pressures in the sample region are unknown, but are estimated to be two to three orders of magnitude higher than in the vacuum chamber. The results of four such measurements are shown in Fig. 1. The data are shown as the open circles and the least-squares fits to the data as the solid lines. The ordinate is logarithmic, in order to show the extent of the agreement or disagreement between the fit and the data over a wide range of intensity. At the lowest pressure (Fig. 1a), there is good agreement between the fit and the data; x 2 is 0.9. As the pressure increases there is a change in the shape of the spectrum, and at the highest pressure, Fig. 1d, there are systematic deviations between the data and the fit over the entire spectrum. The value of x 2 increases with pressure to 4.8 at the highest pressure. The effect of pressure is further illustrated in Fig.

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Fig. 1. Pressure dependence of the argon 2p photoelectron spectrum at a photon energy of 262 eV. The open circles indicate the experimental data and the solid lines the results of least-squares fits to the data. The values of the Lorentzian line widths, G, derived from the fits as well as the values of x 2 for each fit are indicated.

2, where we compare the data for the lowest pressure (dashed line) with that for the highest(solid line). At high pressure, the photoelectron peak is both broadened and shifted relative to the low-pressure peak. In keeping with this difference, the value of the Lorentzian width, G, derived from the fit to the high-pressure data is significantly larger than is found in the lower-pressure measurements: 126 meV at high pressure as opposed to values between 116 and 118 meV for the other measurements. The value of the Gaussian width derived from the fits increases from 77 meV at the lowest pressure to103 meV at the highest. For most of the measurements, we have used a pressure of 4.0310 26 Torr as a reasonable compromise between minimizing the pressure effects while still maintaining a useful counting rate. The carbon dioxide measurements were made at four pressures between 1310 26 and 8310 26 Torr.

Fig. 2. Comparison of the argon 2p photoelectron spectra at the highest (solid line) and lowest (dashed line) pressures studied.

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No pressure effects were observed over this range. The values of the carbon 1s Lorentzian line width derived from fitting these data ranged from 97 to 101 meV, in good agreement with our previously reported value of 9962 meV.

3.2. Argon photoelectron and Auger spectra Typical examples of the photoelectron spectra are shown in Fig. 3a and b, and of the Auger spectra in Fig. 3c and d. At a given energy above threshold, the shapes of the photoelectron and Auger peaks are mirror images of one another, since any energy that is gained by the Auger electron is lost by the photoelectron. At low excess energies, post-collision interaction leads to significant transfer of energy from the photoelectrons to the Auger electrons, and there is, accordingly, a tail to high kinetic energies in

the Auger spectrum and to low kinetic energies in the photoelectron spectra. There is also a marked sharpening of the curves on the low-energy side of the Auger peak and on the high-energy side of the photoelectron peak. At higher energies, the PCI function approaches a Lorentzian shape, but even at the highest energy we have considered, there is still a noticeable asymmetry to the peaks. In Fig. 3, the open circles represent the data and the solid lines show the least-squares fits. Also shown in these graphs are the residuals from the fit, that is, the differences between the data and the fit. It is apparent that the theory of van der Straten et al. [23] fits the spectra very well. The only indications of systematic differences between the fits and the data are in the measurements close to threshold (Fig. 3a,c) in the region of the steep portions of the curves. Here the fit is particularly sensitive to the function

Fig. 3. Argon 2p photoelectron spectra (upper) and L 3 M 23 M 23 1 S 0 Auger spectra (lower) measured at 12 eV (left) and 80 eV (right) above the 2p 3 / 2 threshold. Open circles indicate the data and the solid lines indicate the results of the least-squares fits to the data.

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that has been chosen to describe the experimental resolution. At low photon energies the important feature of the data is the asymmetric tail, and in the fits the Lorentzian width is determined primarily by this tail. Fits that are restricted to the points on the highenergy side of the maximum in the Auger spectrum give values of the Lorentzian width that are essentially the same as those obtained from fitting the entire spectrum. Moreover, these values are nearly independent of the Gaussian width. The Gaussian width is determined primarily from the sharp rise on the low-kinetic-energy side. As a consequence, both of these parameters can be determined reasonably well from the data at low photon energies. At high photon energies the peaks become more symmetric, approaching Voigt functions. In this case, it is more difficult to determine the contributions of Gaussian and Lorentzian width accurately. Not surprisingly, there are correlations between the derived values of the Gaussian width, the Lorentzian width, and the background. As a result, the width parameters derived from the fits are influenced by the function that is chosen to represent the background (constant or sloping) and by the range of data selected for the fit. Different choices can lead to variation of a few meV in the derived values of the Lorentzian widths. For the 16 Auger spectra that we have analyzed, the average value of the Lorentzian width is 109 meV, with a root-mean-square deviation of 4 meV. For 21 photoelectron spectra, the corresponding values are115 and 4 meV. The difference between the values of G from the two types of measurements arises, in part, because of an apparent variation of the line width with photon energy; the width derived from the Auger spectra decreases and that from the photoelectron spectra increases with increasing excess energy. If we consider only the values for excess energies between 6 and 14 eV, then we have 111 meV from the Auger spectra and 114 meV from the photoelectron spectra. These trends with excess energy are not understood, but are real. In addition to the measurements discussed here, we have made many measurements of the argon 2p 3 / 2 photoelectron spectrum at an excess energy of 80 eV, since we have used this line extensively for energy calibration. The analysis of these spectra gives Lorentzian line widths that cluster

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within a few meV of 120 meV, significantly higher than the value 114 meV obtained as the average of the low energy data. A recent measurement by Jurvansuu et al. [22] at an excess energy of 40–50 eV gives a line width of 11864 meV, intermediate between these two values. A possible explanation is that the experimental resolution might not be accurately described by a symmetric function such as a Gaussian. An asymmetric tail on the instrument function would skew the spectra. Since the asymmetric tail that is produced by post-collision interaction in the spectra is to low kinetic energies for the photoelectrons and to high energies in the Auger spectra, an additional, instrumental asymmetry would add to this tail in one case but not in the other. For the measurements at low excess energies, the asymmetric tail is a major feature of the spectrum and a small perturbation might be insignificant. At high excess energies, however, the peaks are narrower and such a perturbation might be significant. A possible source of such an asymmetry is discussed in the following section.

3.3. Instrumental resolution The results described above are based on fits to the data in which the instrumental resolution (assumed to be Gaussian) was one of the fitting parameters. It is of interest to compare the Gaussian widths derived from the data with those expected from our ancillary measurements, and this comparison is made in Table 1. Here the values in the columns labeled ‘Expected’ have been calculated from the convolution of the Gaussian width determined in the xenon photoelectron measurements, the Doppler broadening, and, for the photoelectrons, the contribution from the monochromator. Those in the columns labeled ‘Found’ are the averages of the values found in the various fits, except for the three values for which an uncertainty is given, where each is the result of only one measurement. The uncertainty reflects only the statistical uncertainty, as given by the least-squares fitting procedure, and does not reflect any contribution from systematic errors. Looking first at the results from the Auger spectra, we note that the values from the fit are significantly larger than expected. The Auger electrons have a kinetic energy of 201 eV and are retarded to a pass

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Table 1 Expected instrumental resolution (full width at half maximum) compared with that found from fits to the spectra Series

1 2 2 3 3

Excess energy (eV) 6–80 11 80 12 80

Auger (meV)

Photoelectron (meV)

Expected

Found

Expected

Found

66 53 – 45 –

93 85 – 60 –

93 68 70 33 40

86 64 8062 3362 5067

energy of 40 eV. In the process, the product of linear and angular magnification increases by about 2.2, the square-root of the retarding ratio. For the measurements of the xenon photoelectrons, however, the corresponding quantities are 0.5 for the low-energy measurements and 1 for the higher-energy measurements. The effect of these differences depends on the details of the retarding system. At one extreme, constant angular magnification and the size of the image of the source always equal to or greater than the size of the entrance slit of the analyzer, there should be no variation of the resolution with kinetic energy. At another extreme, constant linear magnification, the angular magnification will increase significantly as we go to higher kinetic energies and the resolution may deteriorate in consequence. As noted in the discussion of experimental procedures, just such behavior is seen in the xenon photoelectron spectra as the kinetic energy is increased from 9 to 37 eV. Angular spread can lead to asymmetric peaks with a tail towards low kinetic energies, and the asymmetry would be more significant at high excess energies compared with the intrinsic structure of the Auger spectrum. A similar effect is seen in the Gaussian widths derived from the photoelectron spectra. Whereas those derived from low-kinetic-energy data are in reasonable agreement with expectations, those from the data at a kinetic energy of 80 eV are significantly greater than expected. The effect is less pronounced than for the Auger spectra, presumably because the 80-eV kinetic energy is closer to the energies of the xenon lines that were used to determine the expected resolution. As was suggested for the Auger electrons, this increase in width might be accompanied by an increase in asymmetry, and, also as noted above, such an asymmetry would affect the photoelectron

lines, which tail to low energies, differently from the way it would affect the Auger lines, which tail to high energies.

4. Discussion One goal of this work was to see if the existing theory of the interaction of Auger and photoelectrons (post-collision interaction) gives an accurate description of the experimental spectrum. Inspection of the results shown in Figs. 1 and 3 indicates that, except for some uncertainties in the contributions from instrumental resolution, the agreement between theory and experiment is excellent, as long as the sample pressure is sufficiently low. Second, we have endeavored to obtain a more accurate measure of the 2p core-hole lifetime in core-ionized argon. The uncertainties in our knowledge of the instrumental response function limit the accuracy with which this can be done, and as a result there is small disagreement between the average value obtained from the Auger measurements and that obtained from the photoelectron measurements. It is plausible that the instrumental problems affect one of these in one direction and the other in the opposite direction. In this case, it is reasonable to average the results from the two kinds of experiments, to give a Lorentzian line width of 112 meV with an estimated uncertainty of 3 meV. Third, we have asked whether the line width of the core-ionized state is different from that for the coreexcited state (2p 3 / 2 →4s). The two values are very close to one another, 11263 for the former and 11462 for the latter. It is easy to think of reasons why these widths might be different. On the one hand, the presence of the 4s electron in the excited

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atom opens up additional channels for Auger decay. Since the rate depends on a sum over final states, we might expect the presence of the 4s electron to increase the decay rate and, hence, the width. On the other hand, the Coulomb repulsion between the 4s electron and the valence electrons should lead to an expansion of the valence orbitals, making them less available to interact with the core hole, and lowering the decay rate and the width. The observation of similar widths for the two species indicates either that the 4s electron is so far from the atom that its effect on the transition rate is unimportant or that effects in one direction cancel those in the other. Measurements by Aksela et al. [37] indicate that there is little or no decay of the core-excited state involving the 4s electron as a participant. This result favors the first of these two explanations. Looking at the data as a whole, the root-meansquare deviations for the individual measurements is about 4 meV. This result gives an indication of the uncertainty of a single measurement. Argon, with well isolated lines, is a favorable case for such measurements. In molecules, where there may be vibrational structure with spacing comparable to the line width, we can expect that any individual measurement will be less accurate than this. In this light, the uncertainties we have reported for the carbon 1s lifetime in methane (9562) [6] and carbon dioxide (9962) [10] are unduly optimistic; a more realistic estimate is about 5 meV. Finally, we note the indications that measurements of the electron spectrometer resolution taken at low electron kinetic energies may not be transferrable to higher energies. It appears that the instrumental line width increases with the kinetic energy of the electron even if the pass energy and slits are held fixed.

Acknowledgements TXC and TDT acknowledge support by the National Science Foundation under Grant No. CHE9727471. EK and JDB acknowledge support from the Divisions of Chemical and Material Sciences, Office of Energy Research, of the US Department of Energy. LJS and VM thank the Research Council of Norway (NFR) for support.

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