WIDTHS OF THE ATOMIC K–N7 LEVELS

Atomic Data and Nuclear Data Tables 77, 1–56 (2001) doi:10.1006/adnd.2000.0848, available online at http://www.idealibrary.com on

WIDTHS OF THE ATOMIC K –N7 LEVELS J. L. CAMPBELL Guelph-Waterloo Physics Institute, University of Guelph, Guelph, Ontario, Canada N1G 2W1 and TIBOR PAPP Institute for Nuclear Research, Hungarian Academy of Sciences, Bem ter 18/c, H4001 Debrecen, Hungary

Atomic level widths obtained from experimental measurements are collected in Table I, along with the corresponding theoretical widths derived from the Evaluated Atomic Data Library (EADL) of Lawrence Livermore National Laboratory; these EADL values are based upon the Dirac–Hartree–Slater version of the independent-particle model. In a minority of cases, many-body theory predictions are also provided. A brief discussion of the manner in which the experimental widths were deduced from spectroscopic data is included. The bulk of the data are for elements in the solid state, but a few data for gases and simple compounds are included. For the K , L2, L3, and M5 levels, where Coster–Kronig contributions do not contribute or contribute only to a small extent to the overall widths, the EADL predictions appear satisfactory for elements in the solid state. For other levels, where Coster–Kronig and super-Coster–Kronig transitions have large probabilities within the independent-particle model, this model is not satisfactory. Table II provides a complete set of recommended elemental values based upon consideration of the available experimental data. ° 2001 Academic Press C

0092-640X/01 $35.00 C 2001 by Academic Press Copyright ° All rights of reproduction in any form reserved.

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Atomic Level Widths

CONTENTS INTRODUCTION .................................................................. Theoretical Calculations of Atomic Level Widths ....................... Previous Reviews.............................................................. Experimental Data ............................................................ Discussion of Tabulated and Recommended Widths.....................

2 2 2 3 3

EXPLANATION OF TABLES ....................................................

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TABLES I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels .................................................................. IIA. Recommended Widths (in eV) for the K –M5 Levels ........... IIB. Recommended Widths (in eV) for the N 1–N 7 Levels ..........

13 50 52

REFERENCES FOR TABLE I .............................................................

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INTRODUCTION Theoretical Calculations of Atomic Level Widths

[9, 10] (using the Hartree–Slater model with Kohn–Sham and Gaspar exchange) and of McGuire [11–14], who used the Herman–Skillman potential. In the case of subshells where Coster–Kronig and super-Coster–Kronig transitions can play a major role in the vacancy deexcitation, it has been widely observed that these IPM and two-potential calculations overestimate the level width. With that observation in mind, Ohno [15, 16] and Ohno and Wendin [17] have performed manybody-theory (MBT) calculations for a restricted subset of levels over restricted regions of atomic number, achieving much improved but not perfect agreement with experimental data.

The natural width 0 of an atomic level is given by the sum of the radiative width 0 R , the Auger width 0 A , and the Coster–Kronig width 0CK . These three components of the level width are related to the corresponding transition rates Si (i = R, A, CK ) for the filling of a hole in that level by 0i = h- Si , where h- is the Planck constant divided by 2π. These rates, and hence the individual and total widths, have been computed in several versions of the independentparticle model (IPM). The most recent comprehensive IPM calculation is that of Perkins et al. [1] at the Lawrence Livermore National Laboratory (LLNL); this work combined and extended the relativistic Dirac–Hartree–Slater (DHS) radiative rates of Scofield [2, 3] and the relativistic DHS nonradiative widths of Chen et al. [4–7]. Because the Perkins results are presented in the LLNL Evaluated Atomic Data Library, we will refer to them as EADL. The earlier work of Chen et al. had provided a more limited set of level widths based upon essentially the same approach, although in the K shell case these authors preferred to adopt the slightly more sophisticated Dirac–Fock (DF) radiative widths of Scofield [8] calculated in a two-potential formalism. Earlier, nonrelativistic IPM calculations include those of Walters and Bhalla

Previous Reviews In their 1974 review, Keski-Rahkonen and Krause [18] presented widths of the K , L, M, and N levels in graphical form, relying on theory supplemented by a small amount of experimental data. In 1979, Krause and Oliver [19] presented semiempirical widths for the K and L levels. In 1992, Al Shamma et al. [20] provided tables for the widths of the K –N 7 levels, drawing mainly upon the work of Krause and Oliver, but supplementing and correcting these via a small set of experimental data. Measured x-ray linewidths were compiled both by Pessa [21] and by Salem and Lee [22]. In 1995, Campbell and Papp [23] assembled a rather large set of experimentally measured level widths and x-ray line widths, and derived an internally consistent set of level widths, which 2

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Atomic Level Widths

of the best overall set of all the L1–N 5 level widths; these cases are identified in Table I. In several of the references used, widths of more than one transition from a specific core state to a sequence of Rydberg states are given. Following an argument of King et al. [24], we have selected in these cases the transition to the highest Rydberg state. These core states decay predominantly by the Auger process. When the excited electron is in lowlying Rydberg states, the proximity of the Rydberg electron to the outer shell might reduce the correlation between outershell electrons, thus altering the decay width. The choice of the highest possible Rydberg excitation minimizes error due to this effect. In the great majority of cases, the experimental widths refer to the elemental solid state, with the obvious exceptions of the inert gases. A small number of widths are included for simple compounds, but these were not invoked in our attempt to generate an internally consistent, recommended set of level widths. A number of the available measurements of x-ray linewidths in the literature were not used to derive level widths. For example, L3M5 and L2M4 x-ray linewidths were not used because in these cases one of the level widths involved is not significantly larger than the other. Other measurements were not employed because they had very large associated experimental uncertainty or because they deviated markedly from trends that were well-established by a significant number of other references.

they reported graphically; for each level the accuracy of the EADL computation was assessed and the MBT calculations of Refs. [15–17] were also tested and found to be quite successful. Campbell and Papp provided an extensive discussion of the manner in which they derived their internally consistent set of K –N 7 level widths, and they also provided estimates of uncertainties in these values; the present work is essentially an updating and extension of that effort. Experimental Data Measured widths are collected in Table I. They were obtained by x-ray photo-electron spectroscopy (XPS), x-ray emission spectroscopy (XES), x-ray absorption spectroscopy (XAS), Auger electron spectroscopy (AES), electron energy loss spectroscopy (EELS), measurements on Coster– Kronig transitions (C–K), resonant photoexcitation (RPE), x-ray emission intensity at the absorption edge (XEE), ion or electron yield at the absorption edge (IAE), resonant Raman scattering (RRS), photoelectron spectroscopy for analysis of x-rays (PAX), and internal conversion electron spectroscopy (ICES). The XES data are subdivided in the figures into XES1 (data since 1980), XES2 (1970s data), and XES3 (data before 1965). The overall data set results from a literature search that is extensive but not necessarily complete. Some spectroscopies, e.g., XPS, provide level widths directly, having invoked values for the spectrometer resolution and the energy width of the exciting radiation. Other spectroscopies provide combinations of two or even three level widths. XES provides an x-ray line width that is the sum of the widths of the initial and final levels involved in the transition. AES involves the widths of the initial state vacancy and the two vacancies in the final state. In these cases, it is necessary to assume particular level widths in order to derive others. The source of the assumed level width(s) is shown in the fifth column of Table I, and this width is usually either the EADL theoretical width or the width that is recommended from the present study. In many such cases, our so-derived level widths are not equal to those given in the original publications, because we have used more current values for those widths that must be assumed. In order to minimize error, the assumed level width in the case of an x-ray transition (X –Y ) was always the smaller of the level widths of X and Y . Similarly for an Auger transition (X – Y Z ), the two assumed widths were always the smallest of the three level widths. In almost all of the x-ray linewidth reports, measurements were conducted for a limited number of lines over a limited range of atomic number. However, in two particular instances, the widths of a very large number of L and M lines were measured for one element, and there were enough widths to permit a least-squares determination

Discussion of Tabulated and Recommended Widths In this section we shall have recourse to a few of the references that are employed in Table I and that are listed at the end of the paper.

K Level Many authors have shown that K x-ray spectra in the atomic number range 21 < Z < 30 are more complex than the simple groupings of diagram lines that are encountered elsewhere in the periodic table. The complexity in this region arises in large part from the coupling of the final state vacancy to the unfilled 3d subshell, but it has not had a complete explanation that covers all elements in the range cited. The measured K α x-ray line widths for each of these elements vary quite widely, with the lowest values being those that result when the spectra were fitted with multiple Lorentzians and the remaining, non-Lorentzian intensity was attributed to various subsidiary physical processes such as radiative Auger emission. In this region we derived our K level widths by 3

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Atomic Level Widths

radiative component of the L1 widths, which was taken as the EADL value. Our thorium and uranium data are taken from measured widths for the weak, dipole-forbidden L1M4 and L1M5 x-ray lines, assuming the present recommendations for M4 and M5 widths. The same sources (94Ho01 and 00Ra01) provide accurate widths for the more intense L1N 2 and L1N 3 lines, but we prefer to utilize these as a source of N 2 and N 3 widths assuming the L1 widths derived in this section. Table I also includes L1 widths derived from a 1944 set of XES measurements of the L1N 2,3 linewidth (44Co01), using our own recommended N 2 and N 3 level widths. These XES-derived numbers run 0.3–3.3 eV higher than the values derived from Coster–Kronig spectroscopy. We chose not to include these XES data in determining our overall recommendation, on account of their age, their Z -dependence, and because of the 0.5–1.0 eV uncertainty in our recommended N 2,3 widths. Nonetheless, the fact that the L1N 2,3 x-ray lines are free of Coster–Kronig satellites renders them potentially very reliable and so there would be merit in remeasuring them to ascertain if our recommendation of the trend determined by Coster–Kronig spectroscopy is indeed correct; in such a measurement the atomic number range 50 < Z < 56 where many-body effects play a major role (see below) would have to be excluded. The L1 data are compared to EADL predictions and recommended values in Fig. 2. XPS data for all three L subshells are available from work (98De01) that employed a titanium anode for excitation. In fitting the XPS spectra, the authors represented the Ti K α spectrum by two Lorentzians whose widths (1.45 and 2.13 eV) were taken from the 1976 review of Salem and Lee [22]. The work discussed above on the K x-ray spectra of the

FIG. 1. Width of the K level versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

subtracting our recommended L3 level widths from measured K α1 linewidths. Our recommended K level widths are the EADL values [1] with two adjustments. First, the DHS radiative component [2] is replaced by the corresponding DF value [8]. Because Scofield [8] only provided the DF radiative widths at selected values of atomic number, the full set was determined by interpolating in the ratio 0 R (DF)/ 0 R (DHS) over the atomic number range 10 < Z < 92. Second, the Auger component is replaced by the Auger component that was calculated in the earlier DHS work of Chen et al. [4]. Because these calculations do not extend to atomic numbers below Z = 18, our adjustment of the EADL widths is restricted to Z ≥ 18. The resulting recommended widths for Z ≥ 18 are slightly higher than the EADL widths, and agree slightly better with the widths derived from the minimum experimental K α1 linewidths. For Z < 18, we have no choice but to recommend the EADL widths, reflecting the restricted range of the earlier Auger calculations [4]. Figure 1 displays our recommended widths together with the measured data. L Levels At lower atomic numbers the majority of L1 data are from XPS measurements, and they join smoothly to a set of XES data in the region 40 < Z < 51. There is then a degree of choice in how one connects these data to very recent XES data for thorium and uranium. We have chosen to do so via a set of widths that were derived from measurements of L1 Coster–Kronig and relative fluorescence yields of elements in the range 62 < Z < 79. In order to convert the latter data to level widths, it was necessary to assume the

FIG. 2. Width of the L1 level versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

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The first of two exceptions to our empirical procedure of normalizing the EADL values to become equivalent to the older Chen et al. [5] values occurred for the L2 level in the atomic number region 21 < Z < 30. In that region the IPM, which describes isolated atoms, fails to predict the existence in the solid state of the L2L3M4, 5 Coster–Kronig transition. We have therefore set the L2 width equal to the L3 width generated above plus an additional Coster–Kronig width obtained from the table references 87So01, 97Ho01, 98Ku01, and 81Ny01. The recommended L2 and L3 widths, derived as outlined above, are in good agreement with the XPS and XES data between Z = 30 and Z = 55. A local maximum in measured L2M4 x-ray widths around Z = 44, 45 is explained by an observed local maximum in the measured M4 XPS widths in the same region, to be described below. At higher atomic numbers, the error estimates on experimental data are larger; however, the recommended widths are somewhat closer than the IPM values to the results of Coster–Kronig spectroscopy. From Z = 36 up to Z = 88, measured values [26] of the Coster–Kronig probability f23 fall typically 5–10% below the predictions of the original Chen et al. theory [5]. However, Papp et al. [26] have demonstrated that a significant part of this deficit may be due to the neglect by experimenters of Lorentzian lineshape and satellite contributions when analyzing L x-ray spectra. The Coster–Kronig component of the Chen et al. IPM L2 width therefore appears to be accurate up to Z = 88. The EADL tables predict the onset of L2L3M5 and L2L3M4 Coster–Kronig transitions at Z = 88 and Z = 91, respectively, while the earlier Chen et al. calculations suggest that the appropriate Z values are 91 and 94. Measurements [27] of L2–L3 Coster–Kronig transition probabilities demonstrate unambiguously that (a) the L2L3M5 process is not in play at Z = 88 but is in play at or before Z = 92; and (b) the L2L3M4 process is not in play at Z = 92 but is in play at Z = 94. The measured L2– L3 Coster–Kronig probabilities agree closely with the earlier Chen et al. predictions [5]. (For example at Z = 92 the f 23 values are EADL: 0.228; Chen et al.: 0.138; measured: 0.140 ± 0.002). EADL L2 widths seem unlikely to be correct insofar as the contribution from the Coster–Kronig process appears to be significantly overestimated. The difference in the two discontinuities prevents us from using the previous normalization approach to the DHS and DF treatments. For Z = 90, a recommendation can be attempted by taking the radiative and Auger widths from Chen et al. [5] and interpolating in published experimental data [27] to obtain a value for f 23 . If the L2L3M5 process is assumed not to occur, and f 23 is taken as 0.1, then the calculated L2 width of 7.73 eV is demonstrably low compared to the XES width

FIG. 3. Widths of the L2 and L3 levels versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

3d transition elements shows that these are better described by using two Lorentzians for each of the diagram lines K α1 and K α2 , together with significant satellite components. On this basis, we estimate that the L1, L2 and L3 widths of 98De01 might be low by 0.1–0.2 eV. The L2 and L3 data are shown in Fig. 3. For atomic numbers up to Z = 53, the earlier theoretical widths of Chen et al. [5] lie just 1–3% above the EADL values. Presumably some of this difference reflects the fact that Chen et al. used the more sophisticated DF wave functions of Scofield, whereas Perkins et al. [1] employed the DHS wave functions; the DF calculation has shown a marked superiority in the prediction of relative x-ray transition rates for each of the three L subshells [25]. But, at Z = 54, the difference between the two sets of IPM predictions jumps to about 7%, and then falls slowly back to 2–3% at Z = 83. Examination of Scofield’s radiative rates shows that the DF–DHS difference is not responsible for this effect, and the DHS and DF approaches generate essentially the same values for the L2–L3 Coster–Kronig transition probability. These observations suggest that the difference is caused by different predictions of the Auger rates. Inspection of the EADL Auger rates reveals a downward drop of several percent in an otherwise monotonic increase of each of the L2 and L3 Auger rates, occurring at Z = 52–53 for L2 and at Z = 53–54 for L3. We have therefore selected the earlier Chen et al. L2 and L3 widths as our recommended values. Because these are only given at selected atomic numbers, we plotted the ratio of the two predictions at these atomic numbers, interpolated, and then normalized the Chen et al. widths for all atomic numbers between Z = 30 and Z = 87. At lower atomic numbers we adopted the EADL values, except in the region 11 < Z < 17 where experimental data suggest the widths are larger than the EADL predictions. 5

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of 8.5 eV (00Ra01). If the L2L3M5 process is assumed to occur and the f 23 value is taken as 0.15, then a width of 8.2 eV is obtained, in somewhat better agreement. We might therefore deduce that the L2L3M5 process is indeed in play at Z = 90, but without an accurate L2–L3 Coster–Kronig probability we cannot derive an accurate recommended L2 width from the Chen et al. calculation and must rely upon the XES measurement of 00Ra01. In the case of Z = 92, where it is established from the measured f 23 values that only the L2L3M5 process is in play, our calculated value is 8.64 eV, which clearly does not agree with the XES width measurement of 10.0 eV (00Ra01). Agreement could only be obtained if both Coster–Kronig channels were open, which the f 23 data suggest not to be so. Another possible explanation is that the M4 and M5 binding energies are sufficiently altered in the radioactive compounds employed in the Coster–Kronig measurements that the onset of the L2L3M4,5 transitions is different from that in the pure element. For the moment, we have no choice but to use the measured XES values at Z = 90 and 92 as our recommended values and to interpolate graphically for nearby atomic numbers.

Atomic Level Widths

FIG. 5. Width of the M2 level versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

The M1 data are shown in Fig. 4. Below Z = 55, the M1 data are predominantly from XPS, with a few recalculated XES values that have 10–20% uncertainties. Above Z = 55 there is a serious dearth of modern data; we have used ten XES data points for the L3M1 transition from seven references (assuming our recommended L3 widths) to define a curve that connects smoothly to the data below Z = 55. It is worth remarking on how well some very old x-ray measure-

ments (34Ri01, 38Pa01, 61Me01) fit with more recent data. We did not permit the L3M1 and L2M1 linewidth measurements of 74Sa01 to influence our recommendations, because these data give L1 widths that fall markedly lower than our recommended trend and have uncertainties of 30–40% based on the originally quoted experimental errors. The low intensity of the L3M1 line relative to the strong, neighboring L3M4,5 line renders measurements difficult, but there is merit in further measurements to test the values of M1 widths recommended here in the region of large atomic numbers. For M2 and M3 (Figs. 5 and 6), the data for the lower half of the periodic table are again predominantly XPS measurements, and those in the upper half are derived from XES measurements. The majority of these XES results are L1M2

FIG. 4. Width of the M1 level versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

FIG. 6. Width of the M3 level versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

M Levels

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and L1M3 widths from two sources (44Co01 and 74Sa01); we have to assume our own recommended L1 level widths, which we have already suggested merit further experimental testing. Our M2 and M3 recommendations appear superficially accurate to 1.0–1.5 eV on the basis of the scatter within the two XES data sets, but the real error may be larger, reflecting the significant uncertainty in our recommended L1 widths. We have excluded from our tables the uranium XES results of Williams [28] because they are clearly inconsistent with the trend of other measurements. Like the L3 level, the M5 level cannot de-excite by Coster–Kronig transitions, and so the EADL values, which tend to agree with the rather limited experimental data, are recommended. In the lanthanide region, the unfilled 4 f shell causes multiplet effects that broaden observed 3d linewidths (78Cr01, 81Ka01) and so the data in the 58 < Z < 70 region are not used in reaching our recommendations for M4 and M5 widths. The EADL calculations for M4 appear to be appropriate up to Z = 57, but they fail to predict the observed enhanced M4 width in the region 41 < Z < 45 that is caused by the M4M5N 4,5 super-Coster–Kronig process, and so here our recommended values are larger than those of the EADL. This local effect is also observed, as mentioned above, in L2M4 x-ray linewidths, which are entirely consistent with the XPS measurements. The EADL values for the M4 width show a maximum between Z = 70 and 80, in contrast to a monotonic increase in the M5 case; this maximum is due to the M4M5 Coster–Kronig process becoming energetically possible in the EADL calculation. But PAX and XES data for both tungsten and gold suggest that this maximum is an erroneous prediction, and that the M4 and M5 widths are in fact very similar in the region of high atomic number. Our recommended M4 width above Z = 58 is therefore the EADL M5 value. The M4 and M5 results are summarized in Fig. 7.

Atomic Level Widths

FIG. 7. Widths of the M4 and M5 levels versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

51 < Z < 54 that is established as discrepant, and Z = 70, there are no experimental data, and then above Z = 70 there are limited XPS data with considerable scatter. Lacking any other information, we have used the MBT datum at Z = 54 to anchor curves that run monotonically through the XPS data and join smoothly to the very limited XES data that are available for thorium and uranium. Some of the latter are determined by assuming our recommended L1 level widths and therefore have a corresponding degree of uncertainty. The results are shown in Fig. 9. N 4 and N 5 widths from XPS in the region 70 < Z < 83 cluster quite closely, with the exception of the data of 80Fu01 which tend to be lower than the overall trend and to have larger attached uncertainties. A small number of AES

N Levels As Fig. 8 shows, the measured N 1 widths, largely from XPS measurements, are very much smaller than the EADL predictions, the difference being a factor of 5 around silver. The XPS data join smoothly to recent XES measurements of L2N 1 and L3N 1 x-ray linewidths for thorium and uranium. Between Z = 40 and Z = 50, the N 2 and N 3 widths rise steeply. Then, from Z = 51 to Z = 54, extremely wide peaks are observed in XPS and these are no longer Lorentzian in nature, showing that the independent-particle model has broken down. Ohno [29] has shown that the core hole fluctuates between complex configurations of the atomic system, with consequent strong effects upon its decay and upon the resultant level widths. Between this “anomalous” region

FIG. 8. Width of the N 1 level versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

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of these data sets has been included in Table I or utilized in constructing Table II. The excess of the 44Co01 data is reminiscent of the similar excess observed in the L1 case and suggests that resolution corrections by this author are less than they should have been. A third, older set [30] of x-ray linewidths has not been invoked, as these data also lie significantly higher than the XPS trend; this exclusion of the x-ray linewidths of Williams [30] is supported by the observation that his uranium L3N 5 and L2N 4 linewidths [28] are dramatically higher than the recent measurements included in Table I. It would be desirable to have a modern set of measurements of the L2N 4 and L3N 5 x-ray linewidths spanning a broad region of the upper half of the periodic table. The N 6 and N 7 data are compiled exclusively from XPS measurements, and for some elements they show a very wide scatter. Widths of atoms below Z = 70 are broadened by multiplet effects due to the open 4 f shell, and so our discussion is restricted to Z > 70. Presumably the higher results in this region reflect that the data analysis did not separate the narrow bulk component from the broad surface component, a separation which is now accepted. In the N 7 case, where the data, shown in Fig. 11, are much more numerous, we have therefore drawn a smooth curve through minimum measured values up to Z = 78, and then accepted the EADL values, which agree well with the data, at higher atomic numbers. References 75Hu02, 82Ve01, and 84We01 show that the N 6 width exceeds the N 7 width systematically in the region 72 < Z < 79, due to the presence of N 6N 7O4,5 Coster–Kronig transitions, and this fact is reflected in our recommended N 6 widths, which otherwise are the EADL values.

FIG. 9. Widths of the N 2 and N 3 levels versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

measurements lie high relative to the XPS trend. The XES measurements of the L3N 5 x-ray linewidth at Z = 77–79 (we assume our recommended L3 level widths) reported in 88Am01 give N 5 widths that lie above the trend defined by XPS data; therefore for the thorium and uranium cases, we have favored other, lower XES values than those of 88Am01. As Fig. 10 shows, the data follow the EADL predictions below Z = 60 but with increasing atomic number, they fall well below the EADL predictions. An extensive set of L3N 4 and L3N 5 x-ray linewidths reported in 74Sa01 gives N 4 and N 5 level widths that run up to 3 eV higher than the trend of the XPS data. Another set of L3N 4 and L3N 5 x-ray linewidths, reported in 44Co01, runs typically 1.5–2 eV higher than the XPS data. Neither

FIG. 10. Widths of the N 4 and N 5 levels versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

FIG. 11. Width of the N 7 level versus atomic number Z . Refer to Explanation of Tables for the abbreviations.

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TABLE A

Estimates of Uncertainty (in eV or %) for Recommended Widths of the K –N 7 Atomic Levels Level K L1

Error estimate in width 10 < 30 < 10 < 30 < 40 < 56 < 75 <

L2, L3

M1

M2, M3

M4, M5

20 < 40 < 50 < 20 < 40 < 55 < 20 < 40 < 55 < 30 < 40 < 55 <

Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z

< 30 : < 92 : < 30 : < 40 : < 56 : < 75 : < 92 : < 20 : < 40 : < 50 : < 92 : < 40 : < 55 : < 92 : < 40 : < 55 : < 92 : < 40 : < 55 : < 92 :

Level

± 5–25% ± 5–10% ± 10% ± 25% ± 10–20% ± 1.5 eV ± 2 eV ± 30% ± 10–30% ± 5–10% ± 10% ± 10% ± 5% ± 2 eV ± 10% ± 5–10% ± 5–25% ± 30% ± 0.05 eV ± 10%

Many-Body Theory Predictions

Error estimate in width

N1

35 < Z < 92 : ± 10%

N2

40 < Z < 55 : ± 10–15% 60 < Z < 92 : ± 0.8 eV

N3

40 < Z < 50 : ± 10–15% 60 < Z < 83 : ± 0.5 eV 83 < Z < 93 : ± 1 eV

N 4, N 5

50 < Z < 70 : ± 30% 70 < Z < 92 : ± 0.5 eV

N 6, N 7

70 < Z < 92 : ± 0.05 eV

stead, we present, in Table A, an overview of our uncertainty estimates for different levels in different atomic number regions. These estimates are offered as suggestions and are not intended to be used rigorously.

MBT predictions are available only in limited atomic number ranges. They are usually quite successful, for example in the M2, M3 and N 2–N 5 levels, but they are by no means in perfect agreement with the measured data. More detailed discussion of the assumptions of the various MBT calculations and their degree of success is given by Campbell and Papp [23].

Acknowledgments Both authors acknowledge the support of the Natural Sciences and Engineering Research Council of Canada. T.P. acknowledges support from the Hungarian Research Foundation through OTKA T-026514.

Error Estimates References We have not attempted to provide an individual error estimate for each of the recommended values in Table II. For some of the levels, a simplistic error estimate for the recommended level width might be obtained just by examining the scatter of experimental data relative to the recommended values in the pertinent region of atomic numbers in the appropriate figure. The error is likely to be smallest in regions where there is good agreement among different techniques. But many of the plotted widths have been derived by subtracting our recommended width for some other level from the linewidth measured using a particular spectroscopy; in these cases the error estimate for that subtracted width is an important component of the sought-after uncertainty. A systematic and precise derivation of the uncertainties, free of subjectivity, appears to us an intractable challenge. In-

1. S. T. Perkins, D. E. Cullen, M.-H. Chen, J. H. Hubbell, J. Rathkopf, and J. H. Scofield, Tables and Graphs of Atomic Subshell Relaxation Data derived from the LLNL Evaluated Atomic Data Library, Lawrence Livermore National Laboratory Report UCRL-50400, Vol. 30 (1991) 2. J. H. Scofield, Phys. Rev. 179, 9 (1969) 3. J. H. Scofield, ATOMIC DATA AND NUCLEAR DATA TABLES 14, 121 (1974) 4. M. H. Chen, B. Crasemann, and H. Mark, Phys. Rev. A 21, 436 (1980) 9

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5. M. H. Chen, B. Crasemann, and H. Mark, Phys. Rev. A 24, 177 (1981)

19. M. O. Krause and J. H. Oliver, J. Phys. Chem. Ref. Data 8, 329 (1979)

6. M. H. Chen, B. Crasemann, and H. Mark, Phys. Rev. A 21, 449 (1980)

20. F. Al Shamma, M. Abbate, and J. C. Fuggle, Appendix B of Topics in Applied Physics: Vol. 69: Unoccupied Electronic States; edited by J. C. Fuggle and J. E. Inglesfield (Springer-Verlag, Berlin, 1992)

7. M. H. Chen, B. Crasemann, and H. Mark, Phys. Rev. A 27, 2989 (1983)

21. V. M. Pessa, X-ray Spectrometry 2, 169 (1973) 8. J. H. Scofield, Phys. Rev. A 9, 1041 (1974) 22. S. A. Salem and P. L. Lee, ATOMIC DATA DATA TABLES 18, 234 (1976)

9. D. L. Walters and C. P. Bhalla, Phys. Rev. A 3, 1919 (1971)

AND

NUCLEAR

23. J. L. Campbell and T. Papp, X-ray Spectrometry 24, 307 (1995)

10. D. L. Walters and C. P. Bhalla, Phys. Rev. A 4, 2164 (1971)

24. G. C. King, M. Tronc, F. H. Read, and R. C. Bradford, J. Phys. B 12, 2479 (1977)

11. E. J. McGuire, Phys. Rev. 185, 1 (1969)

25. T. Papp, J. L. Campbell, and S. Raman, J. Phys. B 26, 4007 (1993)

12. E. J. McGuire, Phys. Rev. A 2, 273 (1970) 13. E. J. McGuire, Phys. Rev. A 3, 587 (1971)

26. T. Papp. J. L. Campbell, and S. Raman, Phys. Rev. A 49, 729 (1994)

14. E. J. McGuire, Phys. Rev. A 5, 1043 (1972)

27. P. L. McGhee and J. L. Campbell, J. Phys B 21, 2295 (1988)

15. M. Ohno, J. Phys. B 17, 195 (1984) 16. M. Ohno, Phys. Rev. B 29, 3127 (1984)

28. J. H. Williams, Phys. Rev. 43, 71 (1934) 17. M. Ohno and G. Wendin, Phys. Rev. A 31, 2318 (1985) 29. M. Ohno, Phys. Scripta 21, 589 (1979) 18. O. Keski-Rahkonen and M. O. Krause, ATOMIC DATA AND NUCLEAR DATA TABLES 14, 139 (1974)

30. J. H. Williams, Phys. Rev. 37, 1431 (1931)

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Atomic Level Widths

EXPLANATION OF TABLES TABLE I.

Measured and Theoretical Level Widths for the K–N7 Atomic Levels Z 0

Atomic number and element symbol Atomic level width, in eV, for the K through N7 (sub)shell Value determined here by digitizing graphs of width versus Z. Fuggle and Alvarado (80Fu01) determined this value by inspection of spectra in the cited reference Assuming our recommended value for width of indicated level Spectrometer resolution was not deconvoluted

d i r s Method

Measured data are from the following techniques: AES C-K EELS IAE ICES PAX RPE RRS XAS XEE XES

XPS

Auger electron spectroscopy Derived from Coster–Kronig transition probabilities Electron energy loss spectroscopy Ion or electron yield at the x-ray absorption edge Internal conversion electron spectroscopy Photo-electron spectrometry for analysis of x-rays Resonant photo-excitation Resonant Raman scattering x-ray absorption edge x-ray emission intensity at the absorption edge x-ray emission spectroscopy (in the figures, XES1 comprises data since 1980; XES2 comprises data published between 1965 and 1980; XES3 comprises data published before 1965) x-ray photoelectron spectroscopy

Theoretical predictions are from: EADL MBT

Evaluated Atomic Data Library tabulation of Lawrence Livermore National Laboratory [1] Many-body theory (FC: frozen core approximation; FCE: frozen core approximation excluding monopole relaxation and relativistic effects; FCI: frozen core approximation including monopole relaxation energy shift and relativistic energy shift; FC.VN : final state taken as neutral atom; FC.VN−1 : final state taken as atom with one vacancy; FC.VN−2 : final state taken as atom with two vacancies)

The recommended value is identified by: Rec Reference ra

The experimental or theoretical value adopted as the recommended width The original source of the experimental data (see References for Table I) Original data reanalyzed here using present width database

Comment

Details on the experiment or the treatment of the data, e.g.:

H2S gas (DS) (EADL) (M) (Rec) KL3-L3(Rec)

H2 S gas was used as a target Spectrum fitted using Doniach–Sunjic lineshape Assuming the EADL width value (91Pe01) for width of indicated level Assuming McGuire value (74Mc01) for width of indicated level Assuming the present recommended value for width of indicated level K level width is obtained by subtracting recommended L3 width from measured width of K L3 x-ray line 11

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EXPLANATION OF TABLE continued NL (1L) (mL) LSD 2p−1 1/2 6d Rydberg 70 K Approximate resolution Assume radiative width

The lineshape is not Lorentzian and no width is given Spectrum fitted using one Lorentzian line Spectrum fitted using multiple Lorentzian lines Obtained through a least-squares determination of widths using many x-ray transitions Transitions from the L2 level to the unoccupied 6d state Temperature of experimental sample Measured level or line width was corrected only in approximate fashion for spectrometer resolution Radiative widths of L levels are assumed from 91Pe01 in analyzing Coster–Kronig probability data

TABLE IIA.

Recommended Widths (in eV) for the K –M5 Atomic Levels

TABLE IIB.

Recommended Widths (in eV) for the N1–N7 Atomic Levels Z K, . . . , N7

Atomic number Level width 0(K), . . . , 0(N7) in eV

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE I. Measured and Theoretical Level Widths for the Atomic K –N 7 Levels See page 11 for Explanation of Tables

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TABLE IIA. Recommended Widths (in eV) for the K –M5 Levels See page 12 for Explanation of Tables

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TABLE IIA. Recommended Widths (in eV) for the K -M5 Levels See page 12 for Explanation of Tables

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TABLE IIB. Recommended Widths (in eV) for the N 1–N 7 Levels See page 12 for Explanation of Tables

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REFERENCES FOR TABLE I [34Ri01] [38Pa01] [44Co01] [61Me01] [70Fa01] [71Da01] [71Kr01] [71La01] [71Wu01] [72Kr01] [73Le01] [73Yi01] [73Sc01] [74Ci01] [74Ge01] [74Mc01] [74Sa01] [74Sp01] [74Yi01] [74We01] [75Hu01] [75Hu02] [75La01] [75On01] [75We01] [76Ba01] [76Ch01] [76Ko01] [76Ne01] [76Sv01] [76Sv02] [76We01] [77Ak01] [77An01] [77Ci01] [77Gr01] [77Ha01] [77Ke01] [77Ki01] [77Kr01] [77No01] [77Va01] [77Ya01]

F. K. Richtmeyer, S. W. Barnes and E. Ramberg, Phys. Rev. 46, 843 (1934) L. G. Parratt, Phys. Rev. 54, 99 (1938) J. N. Cooper, Phys. Rev. 65, 15 (1944) J. Merrill and J. W. M. Dumond, Annals. Phys. 14, 166 (1961) C. S. Fadley and D. A. Shirley, Phys. Rev. A2, 1109 (1970) G. Dannhauser and G. Wiech, Phys. Lett. 35A, 208 (1971) M. O. Krause, Chem. Phys. Lett. 10, 65 (1971) K. Lauger, J. Phys. Chem. Solids 32, 609 (1971) F. Wuilleumier, J. Phys. 32, C4-88 (1971) M. O. Krause, F. Wuilleumier and C.W. Nestor, Phys. Rev. A6, 871 (1972) L. Ley, S. P. Kowalczyk, F. R. McFeely, R. A. Pollak and D. A. Shirley, Phys. Rev. B8, 2392 (1973) L. I. Yin, I. Adler, M. H. Chen and B. Crasemann, Phys. Rev. A7, 897 (1973) G. Sch¨on, Acta Chem. Scand. 27, 2623 (1973) H. Citrin, P. M. Eisenberger, W. C. Marra, T. Aberg, J. Utriainen and E. Kallne, Phys. Rev. B10, 1762 (1974) U. Gelius, J. Electron Spectrosc. 5, 985 (1974) E. J. McGuire, Phys. Rev. A9, 1840 (1974) I. Salem and P. L. Lee, Phys. Rev. A10, 2033 (1974) D. P. Spears, H. J. Fishbeck and T. A. Carlson, Phys. Rev. A9, 1603 (1974) I. Yin, I. Adler, T. Tsang, M. H. Chen, D. A. Ringers and B. Crasemann, Phys. Rev. A9, 1070 (1974) G. K. Wertheim, M. Campagna and S. Hufner, Phys. Condens. Matter 18, 133 (1974) S. Hufner, G. K. Wertheim, and J. H. Wernick, Solid State Commun. 17, 417 (1975) S. Hufner and G. K. Wertheim, Phys. Rev. B11, 678 (1975) W. C. Lang, B. D. Padalia, L. M. Watson, D. J. Fabian and P. R. Norris, Discuss. Faraday Soc. 60, 37 (1975) Y. Onodera, J. Phys. Soc. Japan 39, 1482 (1975) G. K. Wertheim and S.Hufner, Phys. Rev. Lett. 35, 53 (1975) A. Barrie and N. E. Christensen, Phys. Rev. B14, 2442 (1976) M. H. Chen, B. Crasemann, L. Y. Yin, T. Tsang, and I. Adler, Phys. Rev. A13, 1435 (1976) S. P. Kowalczik, Ph.D. thesis Lawrence Berkeley Lab. Report No. LBL 4319, (1976)(unpublished); data, derived by inspection of spectra, are in 80Fu01 H. Neddermeyer, Phys. Rev. B13, 2411 (1976) S. Svensson, N. Martensson, E. Basilier, P. A. Malmqvist, U. Gelius and K. Siegbahn, Phys. Scripta 14, 141 (1976) S. Svensson, N. Martensson, E. Basilier, F. P. A. Malmqvist, U. Gelius, and K. Siegbahn, J. Electron Spectrosc. 9, 51 (1976) P. Weightman, J. F. McGilp, and C. E. Johnson, J. Phys. C9, L585 (1976) H. Aksela, S. Aksela, J. S. Jen and T. D. Thomas, Phys. Rev. A15, 985 (1977) E. Antonides, E. C. Janse and G. Sawatzky, Phys. Rev. B15, 4596 (1978): deconvoluted data taken from 80Fu01 P. H. Citrin and G. K. Wertheim, Phys. Rev. B16, 4256 (1977) G. Graeffe, H. Juslen and M. Karras, J. Phys. B: At. Mol. Phys. 10, 3219 (1976) D. Hausamann, B. Breuckmann and W. Melhorn, Abstracts of contributed papers, X ICPEAC, Paris, 1977 O. Keski-Rahkonen and M.O. Krause Phys. Rev. A15, 959 (1977) G. C. King, M. Tronc, F. H. Read and R.C. Bradford, J. Phys. B: At. Mol. Opt. Phys. 12, 2479 (1977) M. O. Krause, C. W. Nestor, Jr. and J. H. Oliver, Phys. Rev. A15, 2335 (1977) J. Nordgren, H. Agren, C. Nordberg and K. Siegbahn, Phys. Scripta 16, 280 (1977) J. Vayrynen, S. Aksela and H. Aksela, Phys. Scripta 16, 452 (1977) Y. Yafet and G. K. Wertheim, J. Phys. F: Met. Phys. 7, 357 (1977)

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Atomic Level Widths

REFERENCES FOR TABLE I continued [78An01] [78Ci01] [78Cr01] [78La01] [78St01] [78We01] [79Be01] [79Ci01] [79Tr01] [80Al01] [80Ca01] [80Cr01] [80Fu01] [80Ha01] [80Ho01] [80Va01] [80Ny01] [80Ra01] [80Ve01] [81Co01] [81Ka01] [81La01] [81Ma01] [81Me01] [81Ny01] [81Va01] [82Ap01] [82Ba01] [82De01] [82Ka01] [82Ke01] [82So01] [82So02] [82So03] [82Ve01] [83Ak01] [83Ch01] [83Ci01] [84Ke01] [84Ma01] [84Ny01] [84Oh01] [84Oh02] [84Oh03]

J. F. McGilp and P. Weightman, cited by P. T. Andrews and P. Weightman, J. Phys. C11, L559 (1978) P. Citrin, G. K. Wertheim and Y. Baer, Phys. Rev. Lett. 41, 1425 (1978) G. Crecelius, G. K. Wertheim and D. N. E. Buchanan, Phys. Rev. B18, 6519 (1978) R. E. Lavilla, Phys. Rev. A17, 1018 (1978) P. Steiner, F. J. Reiter, H. Hochst, S. Hufner and J. C. Fuggle, Phys. Lett. 66A, 229 (1978) G. K. Wertheim and P. H. Citrin, in Photoemission in Solids I, edited by M. Cardona and L. Ley (Springer, Berlin, 1978) p. 197 A. Berndtsson, R. Nyholm, N. Martensson, R. Nilsson and J. Hedme, Phys. Stat. Sol. (b) 93, K103 (1979) P. H. Citrin, G. K. Wertheim and Y. Baer, Phys. Rev. Lett. 20, 1425 (1978) M. D. Tran, C. Guillot, Y. Lassailly, J. Lecante, Y. Jugnet and J. C. Vedrine, Phys. Rev. Lett. 43, 789 (1979) S. F. Alvarado, M. Campagna and W. Gudat, J. Electron Spectrosc. 18, 43 (1980) J. L. Campbell and C. W. Schulte, Phys. Rev. A22, 609 (1980) R. S. Crisp, J. Phys. F: Met. Phys. 10, 511 (1980) J. C. Fuggle and S. F. Alvarado, Phys. Rev. A22, 1615 (1980) C. F. Hague, J.-M. Mariot and G. Dufour, Phys. Lett. 78A, 328 (1980) H. Hochst, private communication quoted in 80Fu01 J. V¨ayrynen, S.Aksela, M. Kellokumpu and H. Aksela, Phys. Rev. A22, 1610 (1980) R. Nyholm and N. Martensson, Chem. Phys. Lett. 74, 337 (1980) K. J. Rawlings, B. J. Hopkins and S. D. Foulias, J. Electron Spectrosc. 18, 213 (1980) J. F. van der Veen, F. J. Himpsle and D. E. Eastman Phys. Rev. Lett. 44, 189 (1980) J. P. Connerade and R. C. Kartanak, J. Phys. F: Met. Phys. 11, 1539 (1981) R. C. Kartanak, J. M. Esteva and J. P. Connerade, J. Phys. B: At. Mol. Phys. 14, 4747 (1981) J. K. Lang, Y. Baer and P. A. Cox, J. Phys. F: Met. Phys. 11, 121 (1981) N. Martensson and R. Nyholm, Phys. Rev. B24, 7121 (1981) W. Menzel and W. Melhorn, in Inner-Shell and X-ray Physics of Atoms and Solids, eds. D. J. Fabian, H. Kleinpoppen and L.M. Watson, (Plenum Press, New York, 1981), p. 319 R. Nyholm, N. Martensson, A. Lebugle and U. Axelsson, J. Phys. F: Met. Phys. 11, 1727 (1981) J. Vayrynen and S. Aksela, J. Electron Spectrosc. 23, 119 (1981) G. Apai, R. C. Baetzold, E. Shustorovich and R. Jaeger, Surf. Sci. 116, L191 (1982) G. Barreau, H. G. Borner, T. von Egidy and R. W. Hoff, Z. Phys. A308, 209 (1982) M. Deutsch and M. Hart, Phys. Rev. B26, 5558 (1982) R. Kammerer, J. Barth, F. Gerken, C. Kunz, S. A. Flodstr¨om and L. I. Johansson, Phys. Rev. B26, 3491 (1982) E. G. Kessler, Jr., R. D. Deslattes, D. Girard, W. Schwitz, L. Jacobs and O. Renner, Phys. Rev. A26, 2696 (1982) H. Sorum, O. M. Weng and J. Bremer, Phys. Stat. Sol. (b) 109, 335 (1982) H. Sorum, Phys. Stat. Sol. (b) 113, 197 (1982) H. Sorum and J. Bremer, J. Phys. F: Met. Phys. 12, 2721 (1982) J. F. Van der Veen, F. J. Himpsel and D. E. Eastman, Phys. Rev. B25, 7388 (1982) H. Aksela and S. Aksela, J. Phys. B16, 1531 (1983) I. Chorkendorff, J. N. Onsgaard, H. Aksela and S. Aksela, Phys. Rev. B27, 945 (1982) P. H. Citrin, G. K. Wertheim and Y. Baer, Phys. Rev. B27, 3160 (1983) O. Keshki-Rahkonen, G. Materlik, B. Sonntag and J. Tulkki, J. Phys. B: At. Mol. Phys. L121 (1984) N. Martensson, P.-A. Malmqvist, S. Svensson and B. Johansson, J. Chem. Phys. 80, 5458 (1983) R. Nyholm and J. Schmidt-May, J. Phys. C17, L113 (1984) M. Ohno, J. Phys. B: At. Mol. Phys. 17, 195 (1984) M. Ohno, Phys. Rev. B29, 3127 (1984) M. Ohno, P. Putila-Mantyla and G. Graeffe, J. Phys. B: At. Mol. Phys. 17, 1747 (1984)

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REFERENCES FOR TABLE I continued [84Pu01] [84We01] [85Fi01] [85Ho01] [85La01] [85Oh01] [85Oh02] [85We01] [85Wi01] [86Oh01] [87La01] [87Ma01] [87Ny01] [87So01] [88Am01] [88We01] [88We02] [89Ha01] [89Je01] [89Ri01] [90Ar01] [90Ha01] [90Ik01] [90Ko01] [90Ri01] [90Wa01] [91Me01] [91Pe01]

[92Ca02] [92La01] [92Oh01] [92Pa01] [92Sa01] [92St01] [93Gl01] [93Ko01] [93Le01] [93Te01] [93Th01]

P. Putila-Mantyla, M. Ohno and G. Graeffe, J. Phys. B: At. Mol. Phys. 17, 1735 (1984) G. K. Wertheim, P. H. Citrin and J. F. Van der Veen, Phys. Rev. B25, 4343 (1984) J. Fink, Th. M¨uller-Heinzerling, B. Scheerer, W. Speier, F. U. Hillebrecht, J. C. Fuggle, J. Zaanen and G. A. Sawatzky, Phys. Rev. B32, 4899 (1985) S. E. Hornstrom, L. Johansson, A. Flodstrom, R. Nyholm and J. Schmidt-May, Surf. Sci. 160, 561 (1985) A. Laakonen, A. Vuoristo and G. Graeffe, Proc. 19th Ann. Conf. Finnish Physical Society 3:4 (1985) M. Ohno and G. Wendin, Phys. Rev. A31, 2318 (1985) M. Ohno, J.-M. Mariot and C. F. Hague, J. Electron Spectrosc. 36, 17 (1985) G. K. Wertheim and S. Hufner, Phys. Rev. Lett. 35, 53 (1975) J. Wigger, Dissertation, University of Muenster (1985): results communicated by B. Cleff (private communication, 1994); see also 92Me01 M. Ohno, A. Laakonen, A. Vuoristo and G. Graeffe, Phys. Scripta 34, 146 (1986) A. Laakonen and G. Graeffe, Jour. de Physique C9-405, 48 (1987) N. Martensson, S. Svensson and U. Gelius, J. Phys. B: At. Mol. Opt. Phys. 20, 6243 (1987) R. Nyholm and N. Martensson, Phys. Rev. B36, 20 (1987) H. Sorum, J. Phys. F: Met. Phys. 17, 417 (1987) P. Amorim, L. Salgueiro, F. Parente and J. G. Ferreira, J.Phys. B: At. Mol. Opt. Phys. 21, 3851 (1988) U. Werner and W. Jitschin, Phys. Rev. A38, 4009 (1988) G. K. Wertheim and P. H. Citrin, Phys. Rev. B38, 7820 (1988) K. Hamalainen, S. Manninen, P. Suortti, S. P. Collins, M. J. Cooper and D. Laundy, J. Phys.: Cond. Matt. 1, 5955 (1989) E. Jensen, R. A. Bartynski, S. L. Hulbert, E. D. Johnson and R. Garrett, Phys. Rev. Lett. 62, 71 (1989) M. Riffe, G. K. Wertheim and P. H. Citrin, Phys. Rev. Lett. 63, 1976 (1989) U. Arp, G. Materlik, M. Richter and B. Sonntag, J. Phys. B: At. Mol. Phys. 23, L811 (1990) K. Hamalainen, S. Manninen, S. P. Collins and M. J. Cooper, J. Phys.: Cond. Matt. 2, 5619 (1990) T. Ikeda, K. Okada, H. Ogasawara and A. Kotani, J. Phys. Soc. Japan 59, 622 (1990) L. Kover, I. Cserny, V. Brabec, M. Fiser, O. Dragoun and J. Novak, Phys. Rev. B42, 643 (1990) K. H. Richter, Surf. Interface Anal. 15, 705 (1990) a N. Wassdahl, J.-E. Rubensson, G. Bray, P. Glans, P. Bleckert, R. Nyholm, S. Cramm, N. Ma rtensson and J. Nordgren, Phys. Rev. Lett. 64, 2807 (1990) Meierkord, T. Blumke, M. Brussermann, J. Hofste, H.-U. Menzebach, J. F. Pennings, Z. Stachura, W. Vollmer, J. Wigger and B. Cleff, Z. Phys. D18, 75 (1991) S. T. Perkins, D. E. Cullen, M. H. Chen, J. H. Hubbell, J. Rathkopf and J. H. Scofield, Tables and graphs of atomic subshell relaxation data derived from the LLNL evaluated atomic data library Z = 1 − 100. Lawrence Livermore National Laboratory Report UCRL50400 Vol. 30, 1991 R. Cao, X. Yang, J. Terry and P. Pianetta, Phys. Rev. B45, 13749 (1992) G. Le Lay, J. Kanski, P. O. Nilsson, U. O. Karlsson and K. Hricovini, Phys. Rev. B45, 6692 (1992) M. Ohno and R.E. LaVilla, Phys. Rev. A45, 4713 (1992) T. Papp, J. Campbell, J. A. Maxwell, J.-X. Wang and W. J. Teesdale, Phys. Rev. A45, 1711 (1992) A. Santoni, A. Derossi, P. Finetti, R. G. Agostino and B. Luo, Phys. Rev. B46, 15660 (1992) R. Stotzel, U. Werner, M. Sarkar and W. Jitschin, J. Phys. B25, 2295 (1992) P. Glans, R. E. LaVilla, M. Ohno, S. Svensson, G. Bray, N. Wassdahl and J. Nordgren, Phys. Rev. A47, 1539 (1993) L. Kover and I. Cserny, J. Electron Spectrosc. 63, 31 (1993) J. A. Leiro, M. Heinonen, F. Werfel, E. G. Nordstrom and K. H. Karlsson, Phil. Mag. Lett. 68, 153 (1993) C. M. Teodorescu, R. C. Kartanak, J. M. Esteva, A. El-Alif and J. P. Connorade, J. Phys. B26, 4019 (1993) W. Theis and K. Horn, Phys. Rev. B47, 16060 (1993)

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Atomic Data and Nuclear Data Tables, Vol. 77, No. 1, January 2001

J. L. CAMPBELL and T. PAPP

Atomic Level Widths

REFERENCES FOR TABLE I continued [94He01] [94Ho01] [94Hu01] [94Ki01] [94Ne01] [95Ar01] [95Av01] [95De01] [95Ja01] [95Ko01] [95Ma01] [95Mo01] [95We01] [95Os01] [96Ah01] [96An01] [96Ki01] [96Lo01] [96Me01] [96Pa01] [96Sa01] [96Sh01] [96Ya01] [97Ho01] [97Zh01] [98De01] [98Ha01] [98Ku01] [98Pa01] [98Vl01] [99Ji01] [99Le01] [99Pa01] [00Ra01]

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