Evaluation of the mean excitation energies of gaseous and liquid argon

Current and future experiments need to know the stopping power of liquid argon. It is used directly in calibration, where commonly the minimum-ionizing portion of muon tracks is used as a standard candle. Similarly, muon range is used as a measure of muon energy. More broadly, the stopping power figures into the simulation of all charged particles, and so uncertainty propagates widely throughout data analysis of all sorts. The main parameter that controls stopping power is the mean excitation energy, or I-value. Direct experimental information for argon's I-value come primarily from measurements of gaseous argon, with a very limited amount of information from solid argon, and none from liquid argon. A powerful source of indirect information is also available from oscillator strength distribution calculations. We perform a new calculation and find that from oscillator strength information alone, the I-value of gaseous argon is (187 ± 5) eV. In combination with the direct measurements and other calculations, we recommend (187 ± 4) eV for gaseous argon. For liquid argon, we evaluate the difference in central value and uncertainty incurred by the difference of phase and recommend (197 ± 7) eV. All uncertainties are given to 68% C.L.


Introduction
The International Commission on Radiation Units and Measurements (ICRU) recommended values and uncertainties for the mean excitation energy of gaseous argon twice, once in 1984 [1] and again in 2016 [2].The first of these was in Report 37 which gives an evaluated value of (188 ± 10) eV.The uncertainty is not at 68% C.L., but is a "[figure] of merit, arrived at by subjective judgments, and with a meaning that is not easily defined."The report further explains that errors are given at roughly 90% C.L., and that one "could convert them to 'standard deviations' by multiplying them by a factor of about one half."These two statements indicate difference confidence levels.However, ICRU-37 derives from NBSIR 82-2550 [3], which gives only the first of these uncertainty interpretations, so this note will consider ICRU-37 uncertainties to be at 90% C.L.; this also agrees with ICRU-90's comments on ICRU-37.The 68% C.L. uncertainty is therefore 6 eV.
ICRU-37 uses four experimental results for stopping power and range [4][5][6][7] in their evaluation.Other methods of estimating I-values are cited, such as the semi-empirical oscillator strength distribution calculated in Ref. [8], but they are not used in the evaluation.
The authors give a detailed list of sources of uncertainty as well as a discussion of theoretical difficulties in calculating corrections at low energy needed to obtain the I-value for argon.The confidence level of their result would seem to be subjective -"obtained by estimating the maximum and minimum slopes consistent with the errors displayed."This note's evaluation treats the uncertainty as being at 68% C.L., but this may be very conservative.Like the previous experiment, this is a stopping power measurement and is relatively less vulnerable to uncertainties related to very slow particles.

Hanke & Bichsel 1970
In another stopping power measurement, Hanke & Bichsel [6] used alpha particles from radioactive decay to measure the I-value of gaseous argon.The authors quote 182 eV and 167 eV as their results, for two evaluations of shell corrections.ICRU-37 uses a re-evaluation of (188 ± 10) eV.Hanke & Bichsel provides the most information on gaseous argon's I-value (given that we have used the correct uncertainty of 17 eV from Ref. [5]).From context, the ICRU quoted uncertainty is probably meant to be at 68% C.L., but unfortunately it is not clear how it was obtained.

Besenbacher et al 1979
Ref. [7] reports on a measurement of stopping power for protons in the range 40 keV to 1 MeV and alpha particles in the range 100 keV to 2.4 MeV.The I-value of 194 eV is quoted with no error in their Table II.ICRU has not evaluated an uncertainty either, nor is it clear how it would be done.At such low energies, shell corrections and other complications are very important.For the purpose of this note's evaluation, it is assumed that this experiment is a factor of several less precise than those that report uncertainties, and an error of ±30 eV has been assigned.The final result below is insensitive to the precise value of this error; so long as it is several times larger than the uncertainty of the more reliable inputs, this note's evaluation of the central value and uncertainty are both unchanged to within the precision displayed.

Baumgart et al 1983
Ref. [9] (not used in ICRU-37) reports on a measurement of the stopping power of argon to protons of between 60 and 800 keV.Similarly to the previous experiment, a value of 190 eV is given, but no uncertainty is quoted, and it is not clear how one would be extracted.Shell corrections are, again, a major concern.An error of ±30 eV has again been assigned for this note's evaluation.

Oscillator strength distribution
ICRU-37 says that the most reliable calculations of I-value come from semi-empirical dipole oscillator strength distributions (OSD), i.e. the photoabsorption cross section as a function of energy.ICRU-37 does not use OSD calculations as part of its evaluation of the recommended Ivalue for argon, but ICRU-90 does, with much of the reason for its small recommended uncertainty of 3 eV being its adopted uncertainty of 2 eV for the calculation of Kamakura et al 2006 [11], who reported 191 eV.However, neither this reference, nor the older calculations from Kumar & Meath 1985 [12] and Eggarter 1975 [8], report an uncertainty themselves.ICRU-90 explains its own by saying that it is "based on those quoted for similar results."This is on very shaky ground.Similar results would only have similar uncertainties if the uncertainties in the underlying photon cross section data were similar between the various materials.But the underlying data for Kamakura come from the review of Berkowitz 2002 [13], who cautions that "Information on the oscillation strengths [of argon] is still rather limited", a warning that does not appear for similar cases (e.g.O, O 2 , N, N 2 , Ne).Moreover, ICRU-90 averages several OSD calculations, then expands all the errors such that the reduced  2 is unity.But the calculations are not independent, being based on mostly the same underlying data, so they cannot be validly combined in this way.
The calculation of Kamakura is based on the recommended oscillator strengths from Berkowitz.Here we will repeat the calculation, adding more recent experimental data, and estimating uncertainties.The result is (187 ± 5) eV, and is found by where and in each case the sum is over discrete states and the integral is over the continuum from the ionization potential to infinity. is the incoming photon energy and  is the oscillator strength, i.e.
where  is the photoabsorption cross section,  0 is the permittivity of free space,   is the mass of the electron,  is the speed of light, and  is the elementary charge.By the Thomas-Reiche-Kuhn sum rule, (0) = , i.e. 18 for argon, up to relativistic and multipole effects that are expected to be negligible for low- elements.We find (0) to be 17.8±0.8, in good agreement with the sum rule.No explicit correction to the oscillator strengths to make (0) equal to 18 is made, as the I-value is invariant under a uniform scaling of oscillator strengths, and we do not impose additional constraints that would motivate any non-uniform scaling.
The following discussion examines energy ranges from lowest to highest.Our method for adopting central values for each part of the spectrum will closely follow the choices and methods of Berkowitz's review, updated with newer data.
First, the discrete spectrum.The values listed in table 1 were chosen.The uncertainties adopted are primarily those stated by the experimental groups.As an exception, the uncertainties for the 5d and 5 d levels are expanded by a factor of two because Berkowitz finds the values suspiciously large.Within each of the two experimental groups, Chan et al [15] and Gibson & Risley [14], we conservatively take the uncertainties to be fully correlated.The final entry in the table is Berkowitz's estimate for all unresolved discrete transitions close to the ionization potential.Two uncertainties are assigned to Berkowitz's estimate, a 10% uncertainty fully correlated to the discrete transitions attributed to Chan, since Berkowitz's number is an extrapolation based primarily on Chan's measurements, and an uncorrelated 10% uncertainty to cover the extrapolation procedure.Despite the For the narrow energy range between the 2 P 3/2 and 2 P 1/2 ionization potentials, Berkowitz assumes a constant cross section of 20.75 Mb.We accept this and assign a 20% uncertainty to this cross section to cover the data of Samson 1966 [16] as shown in figure 1.This section does not contribute significantly to the I-value or its uncertainty.
Following Berkowitz, the continuum is partitioned into several energy ranges, and the oscillator strength data fit to polynomials within these ranges.1.This motivates refitting, and we have found that a substantially better fit results from adding two additional terms to Berkowitz's polynomial.The coefficients are shown in table 3. The region of window resonances from 26.6 to 29.2 eV is excluded from the fit; these are treated as separate discrete transitions below.Samson 1966 andSamson 2002 are used in the fit, but the Samson 1966 data from 29 to 30 eV is excluded from the fit for both this energy range and the following range, as it is in substantial conflict with other measurements.The   [19].This note's evaluation is shown as the solid red line and Berkowitz 2002's evaluation [13] in dot-dashed red.The shaded energy range from 26.6 to 29.2 eV is handled specially; see the text.The vertical line at 29.3295 eV is the boundary between polynomial fits used in the evaluations.The bottom pane, on this plot and the following plots, shows the fractional differences between the present evaluation and the various data and other evaluations.
data of Carlson et al 1973 [17] is not directly used, but is displayed to illustrate the consistency and to guide the choice of adopted uncertainty.The window resonances evident in figure 1 are included as discrete transitions with total oscillator strength of −0.055, following Berkowitz.Given that two experimental groups, Madden et al 1969 [20] and Berrah et al 1996 [21] have results within 10% of each other, we assign a 10% uncertainty.This is a tiny contributor to the overall uncertainty on the I-value, and so it is not examined more closely.
In the following range, 29.3295-48.0eV, we performed the fit on the data of Samson 1966 Given the less-good agreement between experiments in this region, a 4% uncertainty is adopted.We note the rather large fractional difference between our evaluation and that of Berkowitz towards the end of this range.Our evaluation is clearly a better fit to all of the data, but in any case the absolute difference is very small since there is little oscillator strength between 45 and 48 eV.
Since both the 15.9371-29.3295eV and 29.3295-48.0eV ranges are dominated by the work of Samson, their uncertainties are treated as fully correlated.The 15.9371-48 eV range is the dominant contributor of uncertainty to the I-value, giving ±3.6 eV.
For 48.0 eV to 79.3 eV, we fit a 4-term polynomial to the data of Watson 1972 [23], Samson 2002 and Suzuki & Saito 2005 [24].See figure 2. Watson states 3% uncertainty.Suzuki says that uncertainties are between 0.05% and 2%, and within 1% for most energies, but gives no information as to which energies have which uncertainties.Accordingly, we assign 2% uncertainties in the fit.[24], as well as the evaluations of Henke et al 1993 [25] and Berkowitz 2002 [13].Between 230 and 336 eV, Berkowitz uses the data of Chan 1992 without a functional form.
The three experiments have good agreement, with only one point of Watson lying more than 2% from the fit.With this robust confirmation from different groups, we adopt a 2% uncertainty for this range.
From 79.3 to 243 eV, the data of the same three groups is fit, plus that of Henke et al 1967 [22].This latter data is treated as having 5% uncertainties, despite the very small errors reported by the authors in this unpublished report.There is somewhat more disagreement between the various results in this range, and so we adopt a 3% uncertainty.As nearly all the information comes from the same groups as the previous energy range, the two are treated as fully correlated.
From 243 to 250 eV, the L-edge, we directly use the data of Suzuki 2005 shown in figure 3. From 250 to 336 eV, we directly average Suzuki 2005 with Chan 1992, without any functional form, scaled by their stated uncertainties.Although Chan's data covers the entire range from the ionization potential to 500 eV, we do not display it for the L-edge because with a resolution of 1 eV, it lacks the ability to resolve the structure of the edge.(We have not displayed it for lower energies because it would add little information.) From 336 to 500 eV, we display Chan's data, but do not use it.Above 336 eV, it rises steadily away from the work of other groups, and, as Berkowitz states, its use in this region would give too much contribution to the sum rule.We fit the data of Suzuki to a polynomial, as above.From 243 to 500 eV, we assign an uncertainty of 5%, given that the evaluation rests heavily on a single group's data, Suzuki's, and the main second source, Chan, does not agree very well, even in the 250-336 eV range.Two points from Henke 1967 do agree well with Suzuki, but this is quite sparse.We also display on the plot the Henke et al 1993 [25] evaluation for comparison only.
From 500 to 929 eV, we again fit a polynomial to Suzuki's data.See figure 4. In this range there are four points by Henke 1967 which agree very well, and we choose an uncertainty of 3%, fully correlated with the 243-500 eV range.For this range and the following, The evaluation of Chantler et al 1995 [30] is displayed along with Henke's evaluation, for comparison.
From 929 to 3202 eV, just before the K-edge, we fit the data of Wuilleumier 1965 [26], Henke 1967, Suzuki 2005, and Zheng et al 2006 [29] to a polynomial.Given the level of agreement between these several groups, we assign a 3% uncertainty, uncorrelated with the previous regions.
Between 3202 and 3206 eV, we treat the oscillator strength as consisting of the discrete 1s→4pm resonance, measured by Deslattes et al 1983 [31], with a strength of 0.0022 and a 10% uncertainty.This is for completeness only, as it has a negligible impact on the I-value or its uncertainty.[28] are shown, along with the evaluations of Henke 1993 [25] and Chantler [30].Subtraction to obtain oscillator strength from attenuation measurements is done as in figure 4. The Chantler evaluation is used directly in the present evaluation.
1974 [28] and McCrary et al 1970 [27].(Here we depart from direct use of Berkowitz's energy divisions by using a single fit for this range, which Berkowitz divides into two sections.)For the higher energy data of Millar and McCrary, we use the evaluations of Chantler to subtract the nonphotoabsorption portion of the cross section.Again an uncertainty of 3% is assigned based on the agreement between groups.Given the overlap of the experimental groups between the 3206 eV to 10 keV range and the 929 to 3202 eV range, we treat these two ranges as fully correlated.This choice is not crucial; a less conservative choice to consider them uncorrelated would lower the uncertainty on the I-value by only 0.2 eV.
From 10 to 100 keV, we follow Berkowitz and directly use Chantler's evaluation.We assign a 3% uncertainty based on agreement with the data of Millar and McCrary, being somewhat conservative because of the subtraction procedure necessary to isolate the photoabsorption component of attenuation at high energies.See figure 5.
Above 100 keV, we are unaware of any photoabsorption data, and we follow Berkowitz, using the formula of Bethe & Salpeter [32], directly evaluating it up to 1 GeV and then integrating the asymptotic form from there to infinity.Because the range from 100 keV to infinity gives almost no contribution to the I-value, changing it by only 0.1 eV if it is neglected entirely, no uncertainty is assigned.
As stated above, the result for the I-value from combining all of these energy ranges is (187 ± 5) eV.There are several energy ranges each contributing significantly to the uncertainty on the Ivalue.From the ionization potential to 48 eV has the biggest contribution because of the large amount of oscillator strength present.The range from the L-edge to 929 eV contributes near the second most because of its fairly large oscillator strength and larger fractional uncertainties.Similarly, the range just above the K-edge is a significant contributor to the uncertainty.Discrete transitions below the IP are next most important given their substantial contribution to the total oscillator strength and 10% uncertainties.In contrast, the range 48-243 eV has a very small contribution because of the fairly small oscillator strengths coupled with low uncertainties, and above 10 keV, the contribution to the uncertainty is small because the oscillator strength is small.
As a byproduct of this calculation, we can estimate the quantities  (−1) and  (1), where  ( ) is defined as: and such that the I-value that is the focus of this note is  (0).We find  (−1) = 26.51± 0.28.For  (−1), the lower energies are more important.The uncertainty comes almost entirely from discrete transitions below the IP and from the region just above the L-edge, in equal proportions.
The result for  (1) is (3600 ± 80) eV 2 .For  (1), higher energies are more important.Nearly all of the uncertainty comes from the region above the L-edge (±60 eV 2 ) and from the 10-100 keV range where we use the evaluation of Chantler (±40 eV 2 ).This assumes an uncertainty below ∼10% above 100 keV where we use the formula of Bethe and Salpeter.Unlike for  (0), the region above 100 keV is not negligible for  (1); neglecting it reduces the result by 200 eV 2 .For this reason, we do not venture an estimate for  (2) since it is even more sensitive to high energies and we are unaware of any photoabsorption data above 100 keV where the majority of the uncertainty is most likely to lie.

Comparison with other results
In 2010, Kumar and Thakkar gave another estimate of argon's I-value, 186.3 eV with an estimated ±2% (±3.7 eV) uncertainty [33].There are three major differences between their evaluation and ours.First, their method uses the sum rule and molar refractivity data as constraints.We choose to use oscillator strengths alone, without constraints from molar refractivity data.
Second, for any given energy interval, they choose a single data set or evaluated set of oscillator strengths for their fit.This has the effect of discarding modern oscillator strength data in many energy ranges.For instance from 319.9 eV to 100 keV, the 1973 evaluation of Veigele [34] is used even though data from Millar 1974, Suzuki 2005and Zheng 2006 all exist in this range.In contrast, we include all modern data, and in each energy range use a fit to all data judged as reliable.Third, we display the underlying uncertainties assigned to each part of the oscillator strength distribution and the effect that each has towards the final uncertainty on the I-value.It is not clear how to trace Kumar and Thakkar estimated uncertainty on the I-value back to the underlying data.
Despite all these differences, the present evaluation arrives at a very similar result for the I-value.For  (1), Kumar and Thakkar find 3620 eV 2 ±3% (±110 eV 2 ), also very similar to our result.For  (−1), they find 26.53 ±1% (±0.27), essentially identical to our result.

Periodic trends
As an independent method of estimating the I-value, an interpolation can be done from nearby elements.First, using the I-values for aluminum, silicon and calcium, a simple interpolation on a plot of Z vs. I/Z can be made.The result is 189 eV.I-values certainly do not lie on a smooth curve, so this result cannot be taken too literally.Nevertheless, it would be surprising, given the clear periodic trends, if argon's I-value lay much above 200 eV or much below 170 eV, even in the abscense of other methods of evaluation.
A more sophisticated treatment is given in eq.4.1 of ICRU-37, where  is the atomic number of the element whose I-value is to be interpolated,  1 and  2 are the atomic numbers of the next lower and next higher element with experimentally determined I-values,   indicates a calculated I-value and a bare  indicates an experimental I-value.ICRU's choice of calculated I-values for gasses are the set from Chu & Powers 1972 [35], and for solids those from Ziegler 1980 [36], displayed in ICRU-37 Fig 3 .2and reproduced here in figure 6.Another set of calculated I-values are those from Dehmer et al 1975 [37] and Inokuti et al 1981 [38], where the former covers  = 1-18 and the latter 19-38; these are also shown in figure 6.
The uncertainties on the experimental data of silicon and calcium (the nearest elements with experimental data on each side of argon) contribute 3 eV to the uncertainty of this interpolation.The choice of theoretical input is much more important.If, instead of the ICRU recommendation, Dehmer and Inokuti are used (the unused curve of their Fig.3.2), the result shifts 20 eV upwards to 214 eV.These inputs are assumed to be worse, but still represent a reasonable calculation, and so we may qualitatively take the theory uncertainty to be somewhat smaller than the difference.Therefore, this evaluation includes the I-value interpolated from periodic trends as (194 ± 12) eV.

Hartree-Fock wave functions
Only two calculations for argon listed in ICRU-90 come with uncertainties stated by the original authors.One has such large uncertainties as to be irrelevant.The other is Bell et al 1972 [39], which uses a method involving Hartree-Fock wave functions.Since it does not share underlying data with the OSD calculations, it can be included separately in this note's evaluation.Bell's result, as given by the ICRU table, is (174 ± 3.5) eV.What Bell actually says is 12.8 Ry, that "the predictions of different representations [agreed] to within 2% in all cases," and that a "full error analysis [...] is beyond the scope of the present paper."Bell goes on to compare the calculation for helium with a more sophisticated treatment, finding that the difference is 6% and "Errors in  arising from the Hartree-Fock approximation are probably similar for the other atoms considered here".Since both the 2% and 6% errors are relevant, an uncertainty of 11 eV is more correct, and is used in the evaluation in this note.

Evaluation for gaseous argon
The five direct experimental results are combined with the three indirect methods to produce this note's evaluation (see figure 7).Each underlying result is represented as a PDF which is the sum of a Gaussian plus a uniform distribution.The Gaussian's mean and standard deviation are the quoted central value and uncertainty of the given result.The uniform distribution has the range 130-240 eV and a normalization representing a subjective judgment about how likely the result is to be incorrect (through any means, e.g., unaccounted for systematic error, incorrect calculation, typographic error, etc.), typically 5-10%.This reflects the tendency of older papers (and sometimes newer papers) to have results that are incompatible with each other at many times the stated errors.The Gaussian is assigned the remainder of the normalization.
The underlying PDFs are multiplied together to produce the evaluated PDF, which is integrated from the mean to find the evaluated uncertainty.The present evaluation for gaseous argon is (187 ± 4) eV.
Since the method just described unfortunately must include subjective estimates of the correctness of past experiments and calculations, a second method was used to check how robust the result is.In this method, it is assumed that exactly one of the input experiments or calculations is incorrect.[4][5][6][7]9], interpolation from periodic trends, and calculations [11,39].The ICRU-90 recommendation is shown for comparison, interpreting their central value and uncertainty as a Gaussian PDF.All curves except for the one for ICRU-90 share a normalization.
The average is taken with Gaussian distributions only, but with each input experiment or calculation dropped in turn, producing several results.A weighted average is then produced from these results with the weights set by the uncertainty of the experiment or calculation that was excluded.The result of this alternate procedure is (187 ± 5) eV, which does not differ significantly from the main procedure.If our own OSD calculation is exempted from this procedure, the result is (187 ± 4) eV, identical to the main result.
Our answer is ultimately very similar to ICRU-90's, with the same central value and an uncertainty just 1 eV larger.It has, however, been arrived at through a substantially different process.Our uncertainty is larger than ICRU-90's for several reasons: First, the ICRU misread the Martin & Northcliffe's error as 7 eV rather than 17 eV.Second, the present note's OSD evaluation is (187 ± 5) eV, which has a larger uncertainty than ICRU assigned to the several OSD calculations used in their evaluation.Finally, ICRU-90 misunderstood the uncertainty of the Bell calculation, understating it by a factor of three.This note's evaluation for gaseous argon is dominated by the OSD calculation presented above.If it is excluded from the average, the result is instead (187 ± 6) eV.If only direct experimental evidence from range and stopping power measurements is used, the value (189 ± 8) eV.It can be seen that there is good agreement among the several methods used to estimate the I-value.

Evaluation for liquid argon
Liquid argon is not just a very dense gaseous argon; there is binding energy associated with the phase change.Naively, if electrons are bound more strongly, the stopping power should decrease.Data on this effect is limited, but instructive.This effect is predicted to be large for strongly bound systems such as metals, and smaller for molecular substances.Examples of the latter: • Hydrogen: ICRU-37 (Table 5.7) recommends 19.2 eV for gaseous H 2 and 21.8 eV for liquid hydrogen (14% higher).
• Water: The ICRU-90 recommended value for liquid water is (78 ± 2) eV.ICRU-37 gives (71.6 ± 2) eV for water vapor and (75 ± 3) eV for liquid water.The addendum for ICRU-73 [40] gives 69.1 eV for water vapor and 78 eV for liquid water.ICRU-90 cites this without recommending a value for water vapor.The phase effect on the I-value ranges from 5% to 13% depending on the numbers chosen.For the purposes of this evaluation, the phase effect is considered to be (9 ± 4)%.
• n-propane, n-pentane, n-hexane, n-heptane: ICRU-37 recommends I-values differing by 10% or 11% between the liquid and gas phases.All of the gaseous measurements were performed by the same group, as were all of the liquid measurements, so the uncertainties are considered fully correlated.Averaging them gives (11 ± 5)%.
• Bromine: ICRU-37 recommends 343 eV for gaseous bromine and 357 eV for condensed bromine, although both are interpolations from adjacent elements.Taking into account the uncertainties of this procedure as was done for argon in section 3.2, this is considered to be a change of (4 ± 6)%.
at 400 MeV.Across these energies, range increases by between 0.6% and 0.7% with the largest change around 100 MeV.Since the change in the I-value is 9 eV and the recommended uncertainty is 7 eV, the uncertainties on all these ranges and stopping powers are nearly as large as the shifts quoted above.Notably, the effect of a change in I-value on calorimetric energy calibration with muon / and the muon energy reconstruction with range have the same sign: the whole neutrino event energy is overestimated by using gaseous argon's I-value.Nor is there any cancellation of this kind of uncertainty from use of a liquid argon near detector.
Energy reconstruction has many uncertainties besides those from the I-value, but the author's estimate is that the I-value dominates muon energy estimation uncertainty below 1 GeV.Most of the information about   energy comes from the muon, and Δ 2  32 is directly proportional to the measured energies of oscillation minima and maxima.All other oscillation parameters rest, if not as directly, on energy reconstruction as well.The I-value is, therefore, a critical parameter for DUNE and other liquid argon detectors.
To conclude, this note recommends a new value and uncertainty for the mean excitation energies of gaseous and liquid argon, (187 ± 4) eV and (197 ± 7) eV, respectively.The central value for liquid argon is significantly higher than that most recently recommended by the ICRU for gaseous argon, and the uncertainty is substantially larger.While this recommendation is believed to be a useful improvement, it is notable that it rests strongly on an indirect calculation based on oscillator strength distributions.Direct experimental evidence is also used, but none of the inputs are clean.Three of the five experiments lack any original statement of uncertainty, while the remaining two give numerical uncertainties, but without confidence levels.Of these latter two, only one directly states an I-value.With so much freedom of interpretation, another evaluation could easily arrive at a different result.This fact should further motivate experimental work to improve the uncertainty.

Figure 5 .
Figure 5. Oscillator strength distribution for gaseous argon from 10 4 to 10 5 eV.The data of McCrary et al 1970[27], and Millar & Greening 1974[28] are shown, along with the evaluations of Henke 1993[25] and Chantler[30].Subtraction to obtain oscillator strength from attenuation measurements is done as in figure4.The Chantler evaluation is used directly in the present evaluation.

Figure 8 .
Figure 8.Effect of phase on I-value.The points with error bars are each discussed in the text.For compounds water and the hydrocarbons,  is a weighted average of the constituent elements.The atomic number of argon is shown as a vertical dotted line.A smooth curve is drawn to give an estimate of the effect for argon.

Table 1 .
[15]llator strengths for discrete transitions.The rightmost column indicates the primary source of information.Uncertainties are judgments made here based on consistency between several measurements or as stated by the original experimental group[14][15].

Table 2 .
Contributions to the uncertainty on the I-value in the OSD calculation, by energy range.Groups of ranges treated as fully correlated are shown without separating horizontal lines and with subtotals.The total uncertainty is found by adding each group in quadrature.

Table 3 .
Coefficients for the piecewise polynomial fit to various energy ranges, used in the OSD calculation.
Figure 1.Oscillator strength distribution for gaseous argon, 15-48 eV, showing data of Samson 1966 [16], Carlson et al 1973 [17], Samson et al 1991 [18], and Samson & Stolte 2002 The older two measurements are largely within 3% of Samson 2002 and within 3% of the fit, with the largest difference between the fit and Samson 1966 being 6% around 26 eV and the largest difference for Carlson being 4% around 19 eV.We adopt 3% as the uncertainty for this range.Here and in the following, the number given indicates the uncertainty on the overall normalization of the range.
Samson 1966does not state an uncertainty except to suppose that the overall error on the sum of all continuous oscillator strengths is about 5%.Samson 2002 says that uncertainties range from 1 to 3% but unfortunately does not specify which energies have the lower or higher uncertainties.Carlson states no uncertainties. , Carlson 1973cillator strength distribution for gaseous argon, 48-230 eV, showing the data of Samson 1966 [16], Henke et al 1967 [22], Watson 1972 [23], Samson et al 1991 [18], Samson & Stolte 2002 [19], and Suzuki & Saito 2005[24].The evaluation ofBerkowitz 2002 [13]is also shown.The conventions are the same as for figure1.Note suppressed zero.excluding29-30eV,Carlson 1973, excluding >37 eV where evidently background dominates, Samson 1991, and Samson 2002.We note that the very low point for 43.8 eV from Samson 1966 is a probable typo -the original data table gives 23 cm −1 , but 32 cm −1 would be much more consistent with both the surrounding points and later experimental results.Since a 6-term polynomial gave very similar results to a 4-term polynomial, the latter was used; this reasoning holds for each of the following energy ranges as well.Nearly the same result is obtained if Samson 2002 is fit alone.
Evaluation of the mean excitation energy of gaseous argon, using experimental results