NISTIR 7887

Correction Factors for the NIST 

Free-Air Ionization Chambers Used 

to Realize Air Kerma from

W-Anode X-Ray Beams

Stephen M. Seltzer

http://dx.doi.org/10.6028/NIST.IR.7887
NISTIR 7887

Correction Factors for the NIST 

Free-Air Ionization Chambers Used 

to Realize Air Kerma from

W-Anode X-Ray Beams

Stephen M. Seltzer

Radiation and Biomolecular Physics Division

Physical Measurement Laboratory

http://dx.doi.org/10.6028/NIST.IR.7887

October 2012

U.S. Department of Commerce 

Rebecca M. Blank, Acting Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
1

Correction Factors for the NIST Free-Air Ionization Chambers Used to 

Realize Air Kerma from W-Anode X-Ray Beams

October 2, 2012

Stephen M. Seltzer

Guest Researcher

Dosimetry Group

Radiation and Biomolecular Physics Division

Physical Measurement Laboratory

National Institute of Standards and Technology

Gaithersburg, MD USA

Abstract

This report details analyses in the development of certain correction factors for 

free-air ionization chambers used by the National Institute of Standards and Technology 

to realize air kerma for its measurement standards and calibrations of W-anode x-ray 

beams. The correction factors dealt with in this report are the electron-loss correction, kel, 

the photon-scatter correction, ksc, the fluorescence-reabsorption correction, kfl, and the 

bremsstrahlung-reabsorption correction, kbr. 
2

Introduction

This report documents the development of certain correction factors for the 

parallel-plate free-air chambers (FACs) used by the National Institute of Standards and 

Technology (NIST) to realize air kerma for W-anode x-ray beams. These FACs are the 

Lamperti chamber for x-ray beams of 10 kV to 50 kV, the Ritz chamber for x-ray beams 

of 20 kV to 100 kV, and the Wyckoff-Attix chamber for x-ray beams of 50 kV to 300 kV. 

Because this report restricts itself to new evaluations of particular FAC-geometrydependent correction factors, the reader is referred to previous publications (Lamperti et 

al., 1988; Lamperti and O’Brien, 2001) for more general descriptions of the FACs and 

the evaluation of the complete list of correction factors, including the historical methods 

some of which the present report replaces.

The quantity kerma is defined (ICRU, 2011) for ionizing uncharged particles as

the quotient of dEtr by dm, where dEtr is the mean sum of the initial kinetic energies of all 

the charged particles liberated in a mass dm of a material by the uncharged particles 

incident on dm, thus

m

E

K

d

d tr = . (1)

In the International System of Units (SI) (BIPM, 2006) kerma has units of J kg-1

; the 

special name for this unit is gray (Gy).

Technically, air kerma, Kair, is realized through a measurement of the related 

quantity exposure. Exposure, X, is the quotient of dq by dm, where dq is the absolute 

value of the mean total charge of the ions of one sign produced when all the electrons and 

positrons liberated or created by photons incident on a mass dm of dry air are completely 

stopped in dry air, thus

m

q X

d

d = . (2)

The SI unit of exposure is C kg-1 (however, the older unit of Roentgen (R) is still used by 

some, where 1R = 2.58x10-4 C kg-1). The ionization produced by electrons emitted in 

atomic/molecular relaxation processes is included in dq. The ionization due to photons 

emitted by radiative processes (i.e., bremsstrahlung and fluorescence photons) is not to be 

included in dq. Except for this difference, significant at high energies, the exposure, as 

defined above, is the ionization analogue of the dry-air kerma.

The quantities exposure and air kerma can be related through use of the mean 

energy expended in a gas per ion pair formed, divided by the elementary charge, W/e, 

where W is the mean energy expended in air per ion pair formed when the initial kinetic 
3

energy of a charged particle is completely dissipated in the air, and e is the elementary 

charge. Then

( /e)/(1 ) . air K ≈ X ⋅ W − g (3)

The quantity g is the fraction of the kinetic energy of electrons (and positrons) liberated 

by the photons that is lost in radiative processes (mainly bremsstrahlung) in air. In 

Eq. (3), g is the mean value of g averaged over the distribution of the air kerma with 

respect to electron energy.

A schematic of a generic parallel-plate FAC is shown in Fig. 1. The FAC is a 

shielded container open to the atmosphere into which a portion of the x-ray beam enters 

through a defining aperture, passes between parallel collecting and high-voltage plates, 

and leaves through an exit aperture. The dimensions of the components are designed to 

allow complete slowing down of all electrons produced, which are collected by the 

electric field across the collecting volume.

The results of a FAC measurement for x-ray beams are then analyzed according 

to the measurement equation

, (1 ) ( /e)

air eff

net

air ≈ − ∏

i

i k

V g

Q K W

ρ (4)

where Qnet is the measured net ion current (corrected for cosmic-ray and systemgenerated background), ρair is the density of air, and Veff is the product of the aperture 

area and the length of the collecting volume. Equation (4) is an elaboration of combining 

Eqs. (2) and (3) in which the mass has been replaced by the product ρair Veff and the 

application of the various necessary corrections is shown. The radiative-loss correction 

g is very small, effectively zero, for these x-ray beams, and ki are correction factors for 

air attenuation, photon scatter, electron loss, etc., within the FAC. It is assumed that the 

correction factors include also those for humidity, ion recombination, and ambient 

pressure and temperature (to correct to reference conditions), but these are not the subject 

of this report (the correction for humidity was discussed in Seltzer et al. (2003), in which 

the value of 0.998 used by the NIST was verified).

Before continuing, it should be noted that the approximate equality in Eqs. (3) and 

(4) is used here to reflect the fact that exposure includes the charge of electrons or ions 

liberated by the incident photons whereas W pertains only to the charge produced during 

the slowing down of these electrons. Thus the initial charge created by the interaction of 

the photons should be discounted when transferring the exposure measurement for the 

determination of air kerma. This difference, although relatively small, tends to become 

more significant as the photon energy decreases. Additionally, W is not constant as 

perhaps implied in Eqs. (3) and (4) , but is known to increase at low energies (ICRU, 

1979). At energies for which the variation of W with energy becomes important, one 
4

should consider also the effect of this increase. The initial-ion correction has been 

considered by Büermann et al. (2006), and by Takata and Begum (2008). The NIST does 

not yet include this correction; it appears to be relatively small, i.e., rather close to unity, 

but does seem to become more significant, approaching about 0.995 for standard x-ray 

beams with the lowest mean energies.

Correction Factors

The correction factors of concern in this report are mainly those for electron loss, 

photon scatter, fluorescence reabsorption, and bremsstrahlung reabsorption. The first two 

of these have been evaluated and used for more than 50 years (see Lamperti et al., 1988; 

Lamperti and O’Brien, 2001; and references therein), but the advent of reliable radiationtransport Monte Carlo calculations has allowed more accurate and consistent data, 

including that for the latter two correction factors, which although small had not been 

considered until about a decade ago.

Electron-loss correction, kel. Energetic electrons can leave (and enter) the collection 

volume, with only a portion of their energy expended in ionization being collected. The 

collecting volume is defined by the area of the collecting plate (collector length ×

collector width in Fig. 1) and the electrode separation.

Photon-scatter correction, ksc. Ionization produced by electrons resulting from photons 

scattered out of the aperture-defined beam is not included in the definitions of exposure 

and of air kerma.

Fluorescence-reabsorption correction, kfl. The ionization collected due to reabsorption 

of fluorescence photons is not included in the definitions of exposure and of air kerma.

Bremsstrahlung-reabsorption correction, kbr. The ionization collected due to 

reabsorption of bremsstrahlung photons is not included in the definitions of exposure and 

of air kerma. This is associated with but separate from the (1 - g) correction. The NIST 

currently assumes g in Eq. (4) is identically zero for its calibration x-ray beams. If the 

appropriate small values were to be used, then the use of kbr would correct for effects of 

reabsorption. Although the following analyses will carry along results for kbr, the final 

recommendation will be an estimated uncertainty associated with the assumption that 

kbr/(1- g ) = 1.

Data for kel, ksc, kfl, and kbr for Monoenergetic Photons

The source of data for the NIST correction factors is the Monte Carlo calculations 

reported by Burns (2001) for the FACs of NIST and other national metrology institutes. 

These calculations were a follow-on to earlier work (Burns, 1999), but using a Version 

VI of the EGSnrc code that included the transport of fluorescence x rays and of Auger 
5

and Coster-Kronig electrons. The critical dimensions used for the NIST FACs are listed 

in Table 1. In addition to these dimensions, Burns used a gap between electrodes and 

side walls of 2 cm for the Lamperti and Ritz chambers, and of 5 cm for the WyckoffAttix chamber. He assumed electrodes and wall materials to be aluminum and an 

electrode thickness of 1 cm. The composition of air was taken as that listed in ICRU 

Report 37 (ICRU, 1984), and the histories of photons and electrons were terminated at a 

kinetic-energy cut-off of 1 keV. The number of histories was such that Burns states that 

the relative statistical standard uncertainty of all results is less than 0.01 %. 

Burns (1999) performed some sensitivity studies to assess uncertainties arising 

from his model of the chambers. He estimates the relative standard uncertainties to be 

0.05 % for kel and 0.03 % for ksc (kfl and kbr were not considered in this earlier study). In 

a later report, Burns (2003) used the Monte Carlo code PENELOPE to re-evaluate the 

correction factors for the BIPM FACs. From comparisons among the various results, he 

estimates a relative uncertainty of 0.03 % for ksc and from 0.03 % to 0.05 % for kfl, 

depending on the chamber size. Moreover, now with results from different methods of 

electron transport, he then estimates a relative uncertainty in kel of from 0.01 % to 0.09 

%, depending on the x-ray beam energy and thus the chamber used. These latter results 

are difficult to transfer to the NIST chambers, as the dimensions differ somewhat. 

However, it seems reasonable to assign to the NIST chambers the relative standard 

uncertainties due to the computational models employed to be those given in Table 2.

The data supplied by Burns (private communication, 2001) were in the form of 

tables for each of the NIST FACs, and are reproduced in Table 3. These monoenergetic 

data were, however, processed by Burns from his Monte Carlo scores in terms of a 

concatenation of separate classes of energy deposition whose ratios yield the desired 

quantities. Using his notation and the quantities listed in Table 3, we can recover the 

essential scores, each as a function of photon energy:

eq

rel

dep

(1 )

k

g P

P − = ,

eq el

rel

col

(1 )

k k

g P

P − = ,

eq el

rel

sc

col

(1 ) 1 1

k k

g P

k

S −















 = − , (5)

eq el sc

rel

fl

col

(1 ) 1 1

k k k

g P

k

F −















 = − ,

eq el sc fl

rel

br

col

(1 ) 1 1

k k k k

g P

k

G −















 = − .
6

The normalization of the quantities given in Eqs. (5) (governed by that of Prel) is 

unimportant, as we are ultimately interested only in their ratios. Indeed, we see then that 

the monoenergetic results are simply:

( )

( ) ( )

col

dep

el P E

P E

k E = ,

( ) ( )

( ) ( )

col col

col

sc P E S E

P E k E

+ = ,

( ) ( ) ( )

( ) ( ) ( )

col col col

col col

fl P E S E F E

P E S E k E

+ +

+ = , (6)

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

col col col col

col col col

br P E S E F E G E

P E S E F E k E

+ + +

+ + = .

For a photon spectrum, however, it is formally required to integrate over the 

numerators and denominators of Eqs. (6). In order to facilitate interpolation for such 

integration, it was decided to fit and thus smooth the quantities on the right-hand side of

Eqs. (6). It was noticed that some of the quantities reconstructed from Eqs. (5) displayed 

inconsistent results at the lowest energy or energies (possibly due to energy cut-offs in 

the Monte Carlo calculations); in particular, there should be no contribution by 

fluorescence re-absorption below the K-edge energy of 3.206 keV for Ar. Therefore in 

some cases the fitted data were extrapolated down to these lower energies to insure 

smoothness. Issues of accuracy for these lowest energies are unimportant because x-ray 

spectra of NIST calibration beams rarely extend down to these energies and, in any case, 

the relative energy fluence would be quite small.

The original and adopted smoothed data are given in Tables 4 and 5, respectively. 

Reconstructed results for the monoenergetic-photon correction factors from the smoothed 

data via Eq. (6) are given in Table 6. These are compared with the original Burns data in 

Figs. 2 - 4. The modified data are not necessarily better, but they do follow the original 

rather closely and are indeed smoother. Table 7 gives estimated relative uncertainties due 

to the smoothing process, calculated as the relative root-mean-square deviation between 

the data of Tables 3 and 6. These are combined (in quadrature) with the results that were 

given in Table 2 for the estimated total relative standard uncertainties inherent in the 

basic data adopted for calculating correction factors for the NIST FACs, and these are 

listed in Table 8. That is, it is assumed that any additional uncertainty is to be 

contributed by that in the input spectra for the incident x-ray beam.

As regards kbr, one can form the product kbr/(1-g) from Burns’ Monte Carlo results 

in Table 3, and investigate its difference from unity. Such results suggest an estimate of

the relative standard uncertainties associated with the assumption that kbr/(1- g ) = 1 of 

0.02 % for the Lamperti chamber, 0.02 % for the Ritz chamber, and 0.03 % for the 

Wyckoff-Attix chamber. These have been added to Table 8 for completeness.
7

Results for the NIST Standard Beam Qualities

There has developed a fair amount of information on the W-anode x-ray fluence 

spectra that the NIST uses in its measurement standards and calibration services (see, 

Seelentag et al., 1979; Eisenhower et al., 1983; Iles, 1987; Peaple et al., 1989; Laitano et 

al., 1989; 1991; Ankerhold, 2000), as well as the tools to estimate such fluence spectra 

for a wide range of conditions (see, e.g., Cranley et al., 1997). C.G. Soares of the NIST 

collected much of this information in digital form and made it available (private 

communication, 1994). These spectra, including the NIST traditional and ISO beams 

(ISO, 1996), number some 200 versions from independent measurements (from the 

institutions GSF, Harwell, ENEA, PTB, and NIST) and calculations (from the NRPB), 

thus often providing multiple versions (up to 5) for many of the NIST beam qualities.

The smoothed data in Table 5 were integrated over these available fluence 

spectra, the ratios of the integrated values were taken as indicated in Eq. (6), and the 

results from multiple versions of the spectra were averaged. The adopted results are 

listed in Table 9 for the traditional NIST beams qualities, in Table 10 for the ISO beam 

qualities, and in Table 11 for the BIPM/CCRI beam qualities used for international 

comparisons. There were no fluence spectra available for the more recently added NIST 

beam qualities M80 and M120, so the correction factors were obtained by interpolation as 

a function of the half-value layer for the Ritz and for the Wyckoff FACs. 

The variations in results from multiple spectra for the same beam quality suggest 

that a reasonable estimate of the relative standard uncertainty of the results is 20 % of the 

(absolute) difference of the correction factor from unity. Because the correction factors 

are so close to unity, this estimated relative standard uncertainties of the correction 

factors themselves due to assumed fluence spectrum is never more than about 0.01 %. 

This then suggests that the uncertainties listed in Table 8 are appropriate for the final 

results in Tables 9 and 10.

Final Remarks

This work is the culmination of efforts started in 2001 to produce correction 

factors for the NIST FACs. The results produced in various analyses over the last decade 

are rather consistent, but the present results should be considered as the most complete, 

with a perhaps more careful uncertainty analysis. The analyses have also included the 

correction for attenuation within the FAC, kat, using standard reference data for the 

photon attenuation coefficients, presumably consistent with the Monte Carlo calculations 

by Burns. Because of ambiguity on the role of coherent scattering in the analytical 

calculations of the attenuation, and on the uncertainty of the underlying photoninteraction cross sections, the calculated kat values were intended only to confirm 

measured values, which could be readily obtained (although not without some difficulty). 

Thus these values are not presented here, although agreement with measured values is 

reasonably good.
8

Acknowledgements

This work was conducted over the years in close collaboration with Michelle 

O’Brien, the NIST expert for air-kerma measurement standards for x-ray beams and 

ultimate user of these results. Of course, this work would not have been possible without 

the Monte Carlo results and background explanations supplied by David Burns of the 

BIPM, nor without the collection of x-ray-beam fluence spectra provided by Christopher 

Soares of the NIST. The efforts of the author were partially supported through contract 

SB1341-11-RQ-0398 with the Dosimetry Group, Radiation and Biomolecular Physics 

Division, National Institute of Standards and Technology.
9

References

Ankerhold, A. (2000). Catalogue of X-Ray Spectra and their Characteristic Data - ISO 

and DIN Radiation Qualitites, Therapy and Diagnostic Radiation Qualities, 

Unfiltered X-Ray Spectra, PTB Report PTB-Dos-34, Physikalisch-Technische 

Bundesanstalt, Braunschweig, Germany.

Büermann, I., Grosswendt, B.,. Kramer, H.-M., Selbach, H.-J., Gerlach, M., Hoffmann, 

M., and Krumrey, M. (2006). “Measurement of the x-ray mass energy-absorption 

coefficient using 3 keV to 10 keV synchrotrton radiation,” Phys. Med. Biol. 51, 

5125–5150.

BIPM (2006). Bureau International des Poids et Mesures, Le Systéme International 

d’Unités (SI), The Initernational System of Units (SI), 8th edition (Bureau 

International des Poids et Mesures, Sèvres).

Burns, D.T. (1999). “Consistent set of calculated values for electron-loss and photonscatter corrections for parallel-plate free-air chambers,” CCRI(I)/99-4, BIPM, 

Sèvres, France.

Burns, D.T. (2001). “Free-air chamber correction factors for electron loss, photon scatter, 

fluorescence and bremsstrahlung,” CCRI(I)/01-36, BIPM, Sèvres, France.

Cranley,K., Gilmore, B.J., Fogarty, G.W.A., and Desponds, L. (1997). Catalogue of 

Diagnostic X-ray Spectra and Other Data, Report No. 78, Institute of Physics and

Engineering in Medicine, York, UK.

Eisenhower, E.H., Ehrlich, M., Soares, C., Schima, F.J., and Seltzer, S.M. (1983). Quality 

Assurance for Measurements of Ionizing Radiation (Annual Report for FY 1982), 

USNRC Report NUREG/CR-3120, Washington, D.C.

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Energy Required to Produce an Ion Pair, ICRU Report 31 (International 

Commission on Radiation Units and Measurements, Bethesda, MD).

ICRU (2011). International Commission on Radiation Units and Measurements, 

Fundamental Quantities and Units for Ionizing Radiation, ICRU Report 85a

(International Commission on Radiation Units and Measurements, Bethesda, MD).

Iles, W.J. (1987). The Computation of Bremsstrahlung X-Ray Spectra over an Energy 

Range 15 keV to 300 keV. Document NRPB-R204, National Radiological 

Protection Board, Chilton, UK.
10

ISO (1996). International Organization for Standardization, X and gamma reference 

radiations for calibrating dosimeters and dose rate meters and for determining 

their responses as a function of photon energy -- Part 1.: Radiation 

characteristics and production methods, ISO/IS 4037-1:1996 (International 

Organization for Standardization, Geneva).

Laitano, R.F. Pani, R. Pellegrini, R., and Toni, M.P. (1989). Energy Distributions and Air 

Kerma Rates of ISO and BIPM Reference Filtered X-Radiations, Technical 

Report ENEA RT/PAS(89), ENEA (National Agency for Atomic Energy), Rome, 

Italy.

Laitano, R.F. Pani, R. and Pellegrini, R.(1991). “Determination od x-ray spectra and of 

the scattered component up to 300 kV,” Med. Phys. 18, 934–938.

Lamperti, P.J., Loftus, T.P., and Loevinger, R. (1988). NBS Measurement Services: 

Calibration of X-Ray and Gamma-Ray Measuring Instruments, National Bureau of 

Standards Special Publication 250-16, Gaithersburg, MD.

Lamperti, P.J., and O’Brien, M. (2001). NIST Measurement Services: Calibration of XRay and Gamma-Ray Measuring Instruments, National Institute of Standards and 

Technology Special Publication 250-58, Gaithersburg, MD.

Peaple, L.H.J., Birch, R., and Marshall, M. (1989). Measurement of the ISO Series of 

Filtered Radiations, Report AERE-R-13424, Atomic Energy Research 

Establishment, Harwell, England.

Seelentag, W.W., Panzer, W., Drexler, G., Platz, L., and Santner, F. (1979). A Catalogue 

of Spectra for the Calibration of Dosemeters, GSF Bericht 560. Gesellschaft fur 

Strahlen und Umweltforschung MBH, Munchen, Germany.

Seltzer, S.M., Lamperti, P.J., Loevinger, R., Mitch, M.G., Weaver, J.T., and Coursey, 

B.M. (2003). “New National Air-Kerma-Strength Standards for 125I and 103Pd 

Brachytherapy Seeds,” NIST J. Res. 108, 337–358.

Takata, N., and Begum, A. (2008). “Corrections to air kerma and exposure measured 

with free air ionization chambers for charge of photoelectrons, Compton electrons 

and Auger electrons,” Radiat. Prot. Dosim. 130, 410–418.
11

Table 1. Critical dimensions for the NIST parallel-plate free-air chambers. All 

dimensions are in units of cm.

Lamperti

(10 kV – 50 kV)

Ritz

(20 kV – 100 kV)

Wyckoff-Attix

(50 kV – 300 kV)

Aperture diameter 0.5 1.0 1.0

Collector length 1.0 7.0 10.1

Collector width 5.0 9.0 27.0

Electrode separation 4.0 9.0 27.0

Attenuation length 3.9 12.7 30.8

Table 2. Estimated relative standard uncertainties due to computational models adopted 

for the NIST FACs.

Correction

Factor

Lamperti

(10 kV – 50 kV)

Ritz

(20 kV – 100 kV)

Wyckoff-Attix

(50 kV – 300 kV)

kel 0.05 % 0.05 % 0.09 %

ksc 0.03 % 0.03 % 0.03 %

kfl 0.05 % 0.05 % 0.03 %
12

Table 3. Original data from Burns’ Monte Carlo calculations for NIST FACs. Note that 

values of kel shown as 1.0 indicate that Burns evidently imposed this lower limit 

rather than giving the results from the ratio shown in Eq. (6). The various 

quantities are indicated in the text. The large number of significant figures is to 

preserve the data as transmitted.

a. Lamperti chamber.

E/keV (1-g)

-1 keq kel ksc kfl kbr Prel

2 1.0000000 0.9997988 1.0 0.9980880 1.0000000 1.0000000 4.969E-19

4 1.0000028 0.9999972 1.0 0.9969588 0.9942037 0.9999959 8.651E-18

6 1.0000010 0.9997953 1.0 0.9976122 0.9956900 1.0000000 4.908E-18

8 1.0000120 0.9993245 1.0 0.9980929 0.9964462 0.9999954 3.012E-18

10 1.0000282 1.0005597 1.0 0.9982881 0.9970240 0.9999870 1.702E-18

12 1.0000557 0.9991425 1.0 0.9986930 0.9973521 0.9999813 1.246E-18

14 1.0000841 0.9999159 1.0 0.9985291 0.9975836 0.9999881 9.803E-19

16 1.0000991 0.9986722 1.0 0.9986802 0.9979104 0.9999662 6.502E-19

18 1.0001212 1.0010093 1.0 0.9988290 0.9980633 0.9999629 5.313E-19

20 1.0001339 1.0049185 1.0 0.9989213 0.9982463 0.9999654 3.978E-19

22 1.0001722 0.9986311 1.0 0.9989377 0.9984463 0.9999728 3.338E-19

24 1.0001486 0.9998514 1.0 0.9990345 0.9985611 0.9999669 2.889E-19

26 1.0001149 0.9975016 1.0 0.9989899 0.9986761 0.9999650 2.511E-19

28 1.0001800 0.9975803 1.0 0.9988816 0.9987150 0.9999731 2.227E-19

30 1.0002288 0.9980142 1.0 0.9987269 0.9988919 0.9999514 1.704E-19

32 1.0002138 1.0010957 1.0 0.9990631 0.9988387 0.9999615 1.529E-19

34 1.0002050 1.0002259 1.0002797 0.9990535 0.9990175 0.9999753 1.408E-19

36 1.0002150 1.0043660 1.0016750 0.9989713 0.9990364 0.9999441 1.285E-19

38 1.0003100 1.0024512 1.0056470 0.9990027 0.9991120 0.9999691 1.197E-19

40 1.0001991 1.0002266 1.0135405 0.9987202 0.9991943 0.9999642 1.016E-19

42 1.0002144 0.9989974 1.0267239 0.9991060 0.9992517 0.9999659 9.620E-20

44 1.0003089 1.0018165 1.0445255 0.9990351 0.9992840 0.9999639 9.136E-20

46 1.0002494 0.9993876 1.0702046 0.9989927 0.9993256 0.9999588 8.719E-20

48 1.0002166 0.9935509 1.0982407 0.9990157 0.9992944 0.9999566 8.383E-20

50 1.0002638 0.9995694 1.1251879 0.9988022 0.9993390 0.9999602 7.821E-20
13

b. Ritz chamber.

E/keV (1-g)

-1 keq kel ksc kfl kbr Prel

2 1.0000000 1.0000000 1.0 1.0000000 1.0000000 1.0000000 1.156E-21

4 1.0000002 0.9998972 1.0 0.9938854 0.9912199 0.9999996 9.745E-17

6 1.0000000 1.0000000 1.0 0.9947642 0.9934328 1.0000000 1.052E-16

8 1.0000017 0.9997311 1.0 0.9953721 0.9945537 0.9999994 7.485E-17

10 1.0000300 0.9999700 1.0 0.9962687 0.9953324 0.9999838 4.523E-17

12 1.0000530 0.9999470 1.0 0.9966030 0.9959413 0.9999818 3.365E-17

14 1.0000669 0.9999331 1.0 0.9966397 0.9965215 0.9999747 2.653E-17

16 1.0000837 0.9999163 1.0 0.9973156 0.9968536 0.9999656 1.790E-17

18 1.0001129 0.9998871 1.0 0.9972494 0.9970578 0.9999562 1.464E-17

20 1.0001163 1.0007919 1.0 0.9974290 0.9973274 0.9999609 1.102E-17

22 1.0001580 1.0007055 1.0 0.9974093 0.9975435 0.9999519 9.271E-18

24 1.0001782 0.9996965 1.0 0.9973497 0.9977324 0.9999524 7.977E-18

26 1.0001747 0.9996822 1.0 0.9974738 0.9978967 0.9999474 6.984E-18

28 1.0001876 1.0006199 1.0 0.9976103 0.9980685 0.9999508 6.196E-18

30 1.0001765 0.9998235 1.0 0.9974863 0.9981725 0.9999493 4.734E-18

32 1.0002152 1.0002538 1.0 0.9976880 0.9983247 0.9999464 4.266E-18

34 1.0002219 1.0010609 1.0 0.9976233 0.9984074 0.9999460 3.902E-18

36 1.0002177 1.0003426 1.0 0.9976737 0.9985103 0.9999538 3.571E-18

38 1.0002195 1.0000822 1.0 0.9977673 0.9985991 0.9999480 3.316E-18

40 1.0002196 0.9997804 1.0 0.9977829 0.9987117 0.9999522 2.828E-18

42 1.0002471 1.0005024 1.0 0.9977390 0.9988409 0.9999419 2.670E-18

44 1.0002448 1.0009426 1.0 0.9977765 0.9988952 0.9999538 2.529E-18

46 1.0002358 1.0009991 1.0 0.9977629 0.9989872 0.9999522 2.432E-18

48 1.0002475 1.0010392 1.0 0.9979882 0.9990457 0.9999486 2.334E-18

50 1.0002315 1.0002255 1.0000036 0.9978334 0.9991229 0.9999506 2.172E-18
14

b. Ritz chamber (cont’d).

E/keV (1-g)

-1 keq kel ksc kfl kbr Prel

52 1.0002478 1.0011245 1.0000683 0.9977577 0.9992061 0.9999582 2.085E-18

54 1.0002291 0.9994704 1.0003007 0.9978193 0.9992720 0.9999563 2.038E-18

56 1.0002138 1.0001679 1.0011186 0.9978974 0.9993310 0.9999646 2.002E-18

58 1.0002026 1.0004479 1.0028882 0.9978886 0.9994012 0.9999637 1.984E-18

60 1.0002126 0.9995248 1.0058850 0.9980641 0.9994235 0.9999619 1.968E-18

62 1.0002041 1.0019827 1.0099604 0.9980151 0.9994735 0.9999633 1.913E-18

64 1.0002198 0.9994224 1.0152254 0.9980040 0.9995188 0.9999619 1.912E-18

66 1.0001914 1.0012683 1.0219123 0.9980829 0.9995702 0.9999653 1.924E-18

68 1.0002134 0.9996194 1.0288651 0.9981840 0.9995912 0.9999676 1.936E-18

70 1.0001747 1.0007563 1.0362296 0.9981151 0.9996009 0.9999580 1.952E-18

72 1.0002137 1.0005539 1.0436668 0.9981675 0.9996438 0.9999603 1.973E-18

74 1.0002108 1.0007109 1.0501383 0.9981279 0.9996798 0.9999586 1.995E-18

76 1.0002157 1.0000510 1.0566075 0.9980965 0.9996931 0.9999611 2.025E-18

78 1.0002004 0.9991657 1.0622996 0.9982181 0.9997184 0.9999643 2.050E-18

80 1.0001732 0.9998784 1.0665093 0.9981366 0.9997411 0.9999615 2.083E-18

82 1.0001922 0.9996665 1.0644509 0.9981675 0.9997723 0.9999629 2.069E-18

84 1.0001958 0.9991964 1.0655565 0.9982435 0.9997869 0.9999638 2.100E-18

86 1.0001971 1.0003183 1.0668154 0.9982933 0.9998000 0.9999599 2.139E-18

88 1.0001926 1.0000736 1.0682423 0.9983000 0.9998231 0.9999626 2.183E-18

90 1.0002114 0.9996883 1.0691059 0.9983129 0.9998289 0.9999608 2.231E-18

92 1.0002297 1.0001402 1.0691534 0.9983458 0.9998507 0.9999616 2.276E-18

94 1.0001832 1.0003445 1.0684333 0.9984353 0.9998598 0.9999562 2.324E-18

96 1.0002108 1.0005231 1.0672652 0.9983771 0.9998686 0.9999589 2.370E-18

98 1.0002106 1.0007573 1.0663093 0.9983969 0.9998776 0.9999623 2.425E-18

100 1.0002088 1.0008069 1.0612865 0.9984623 0.9998840 0.9999633 2.453E-18
15

c. Wyckoff-Attix chamber.

E/keV (1-g)

-1 keq kel ksc kfl kbr Prel

10 1.0000330 0.9999670 1.0 0.9907690 0.9940463 0.9999788 5.798E-17

20 1.0001388 0.9998612 1.0 0.9931947 0.9965738 0.9999412 1.547E-17

30 1.0001677 0.9999816 1.0 0.9936727 0.9976644 0.9999263 6.699E-18

40 1.0002682 0.9997319 1.0 0.9942618 0.9983533 0.9999264 4.032E-18

50 1.0002738 0.9997263 1.0 0.9948802 0.9988959 0.9999395 3.080E-18

60 1.0002159 0.9997841 1.0 0.9948538 0.9992142 0.9999491 2.807E-18

70 1.0001906 0.9987293 1.0 0.9953227 0.9995257 0.9999541 2.774E-18

80 1.0002135 1.0001245 1.0 0.9958322 0.9996827 0.9999550 2.959E-18

90 1.0002143 0.9999362 1.0001646 0.9958384 0.9997936 0.9999433 3.174E-18

100 1.0002133 0.9994791 1.0014520 0.9965291 0.9998543 0.9999365 3.501E-18

110 1.0001829 0.9995988 1.0035905 0.9966065 0.9998860 0.9999414 3.869E-18

120 1.0002313 0.9986789 1.0064862 0.9967747 0.9999239 0.9999418 4.291E-18

130 1.0002146 0.9994416 1.0082342 0.9969651 0.9999394 0.9999385 4.728E-18

140 1.0002621 1.0006219 1.0093889 0.9969887 0.9999578 0.9999416 5.208E-18

150 1.0002698 0.9987145 1.0090913 0.9972348 0.9999717 0.9999310 5.624E-18

160 1.0003211 0.9995951 1.0083436 0.9973493 0.9999718 0.9999227 6.104E-18

170 1.0003654 0.9996044 1.0078491 0.9974998 0.9999710 0.9999254 6.574E-18

180 1.0003565 1.0006345 1.0076882 0.9975126 0.9999792 0.9999258 7.083E-18

190 1.0003243 1.0002534 1.0070050 0.9976046 0.9999827 0.9999269 7.570E-18

200 1.0003849 0.9999461 1.0059281 0.9977399 0.9999860 0.9999271 8.036E-18

210 1.0003957 1.0000261 1.0053400 0.9978109 0.9999856 0.9999244 8.550E-18

220 1.0004213 1.0005860 1.0052143 0.9978718 0.9999867 0.9999237 9.049E-18

230 1.0004783 0.9982574 1.0059085 0.9979129 0.9999880 0.9999225 9.535E-18

240 1.0004632 1.0014876 1.0080831 0.9980811 0.9999882 0.9999160 1.005E-17

250 1.0005391 1.0021819 1.0126576 0.9980923 0.9999903 0.9999170 1.054E-17

260 1.0005314 0.9999220 1.0208533 0.9981757 0.9999895 0.9999147 1.102E-17

270 1.0006003 0.9985523 1.0322657 0.9981898 0.9999899 0.9999156 1.150E-17

280 1.0006393 1.0016764 1.0482707 0.9981886 0.9999920 0.9999226 1.202E-17

290 1.0006469 0.9971620 1.0671867 0.9982480 0.9999928 0.9999191 1.248E-17

300 1.0006639 1.0016564 1.0899844 0.9983040 0.9999927 0.9999090 1.299E-17
16

Table 4. Reconstructed data from Burns’ Monte Carlo calculations for NIST FACs, using 

Eqs. (5). The quantities are defined in the text.

a. Lamperti chamber.

E/keV Pdep Pcol Scol Fcol Gcol

2 4.970E-19 4.970E-19 9.521E-22 0 0

4 8.651E-18 8.651E-18 2.639E-20 5.059E-20 3.561E-23

6 4.909E-18 4.909E-18 1.175E-20 2.130E-20 0

8 3.014E-18 3.014E-18 5.759E-21 1.077E-20 1.386E-23

10 1.701E-18 1.701E-18 2.917E-21 5.086E-21 2.217E-23

12 1.247E-18 1.247E-18 1.632E-21 3.315E-21 2.347E-23

14 9.803E-19 9.803E-19 1.444E-21 2.378E-21 1.172E-23

16 6.510E-19 6.510E-19 8.603E-22 1.365E-21 2.206E-23

18 5.307E-19 5.307E-19 6.222E-22 1.031E-21 1.976E-23

20 3.958E-19 3.958E-19 4.274E-22 6.961E-22 1.373E-23

22 3.342E-19 3.342E-19 3.554E-22 5.206E-22 9.124E-24

24 2.889E-19 2.889E-19 2.792E-22 4.167E-22 9.574E-24

26 2.517E-19 2.517E-19 2.545E-22 3.340E-22 8.836E-24

28 2.232E-19 2.232E-19 2.499E-22 2.875E-22 6.020E-24

30 1.707E-19 1.707E-19 2.176E-22 1.896E-22 8.321E-24

32 1.527E-19 1.527E-19 1.432E-22 1.777E-22 5.891E-24

34 1.407E-19 1.407E-19 1.333E-22 1.385E-22 3.484E-24

36 1.279E-19 1.277E-19 1.315E-22 1.233E-22 7.159E-24

38 1.194E-19 1.187E-19 1.185E-22 1.056E-22 3.676E-24

40 1.016E-19 1.002E-19 1.284E-22 8.090E-23 3.592E-24

42 9.628E-20 9.377E-20 8.391E-23 7.028E-23 3.204E-24

44 9.117E-20 8.728E-20 8.430E-23 6.260E-23 3.160E-24

46 8.722E-20 8.150E-20 8.218E-23 5.506E-23 3.362E-24

48 8.436E-20 7.681E-20 7.568E-23 5.429E-23 3.341E-24

50 7.822E-20 6.952E-20 8.337E-23 4.604E-23 2.770E-24
17

b. Ritz chamber.

E/keV Pdep Pcol Scol Fcol Gcol

2 1.156E-21 1.156E-21 0 0 0

4 9.746E-17 9.746E-17 5.996E-19 8.686E-19 3.981E-23

6 1.052E-16 1.052E-16 5.537E-19 6.991E-19 0

8 7.487E-17 7.487E-17 3.481E-19 4.119E-19 4.656E-23

10 4.523E-17 4.523E-17 1.694E-19 2.129E-19 7.375E-22

12 3.365E-17 3.365E-17 1.147E-19 1.376E-19 6.186E-22

14 2.653E-17 2.653E-17 8.945E-20 9.292E-20 6.771E-22

16 1.790E-17 1.790E-17 4.818E-20 5.665E-20 6.187E-22

18 1.464E-17 1.464E-17 4.038E-20 4.332E-20 6.447E-22

20 1.101E-17 1.101E-17 2.838E-20 2.958E-20 4.331E-22

22 9.263E-18 9.263E-18 2.406E-20 2.287E-20 4.478E-22

24 7.978E-18 7.978E-18 2.120E-20 1.818E-20 3.815E-22

26 6.985E-18 6.985E-18 1.769E-20 1.476E-20 3.692E-22

28 6.191E-18 6.191E-18 1.483E-20 1.201E-20 3.060E-22

30 4.734E-18 4.734E-18 1.193E-20 8.689E-21 2.411E-22

32 4.264E-18 4.264E-18 9.881E-21 7.172E-21 2.293E-22

34 3.897E-18 3.897E-18 9.284E-21 6.231E-21 2.113E-22

36 3.569E-18 3.569E-18 8.322E-21 5.337E-21 1.656E-22

38 3.315E-18 3.315E-18 7.418E-21 4.661E-21 1.731E-22

40 2.828E-18 2.828E-18 6.284E-21 3.656E-21 1.356E-22

42 2.668E-18 2.668E-18 6.046E-21 3.103E-21 1.555E-22

44 2.526E-18 2.526E-18 5.629E-21 2.800E-21 1.170E-22

46 2.429E-18 2.429E-18 5.446E-21 2.468E-21 1.164E-22

48 2.331E-18 2.331E-18 4.699E-21 2.231E-21 1.201E-22

50 2.171E-18 2.171E-18 4.714E-21 1.910E-21 1.076E-22
18

b. Ritz chamber (cont’d).

E/keV Pdep Pcol Scol Fcol Gcol

52 2.082E-18 2.082E-18 4.678E-21 1.487E-21 8.718E-23

54 2.039E-18 2.037E-18 4.452E-21 1.340E-21 8.927E-23

56 2.001E-18 1.998E-18 4.210E-21 1.187E-21 7.088E-23

58 1.983E-18 1.976E-18 4.182E-21 1.131E-21 7.186E-23

60 1.969E-18 1.957E-18 3.796E-21 9.978E-22 7.484E-23

62 1.909E-18 1.890E-18 3.760E-21 9.090E-22 6.959E-23

64 1.913E-18 1.884E-18 3.769E-21 8.104E-22 7.193E-23

66 1.921E-18 1.881E-18 3.613E-21 7.712E-22 6.534E-23

68 1.936E-18 1.882E-18 3.424E-21 7.527E-22 6.116E-23

70 1.950E-18 1.882E-18 3.553E-21 6.741E-22 7.914E-23

72 1.971E-18 1.888E-18 3.467E-21 6.086E-22 7.516E-23

74 1.993E-18 1.897E-18 3.557E-21 5.893E-22 7.876E-23

76 2.024E-18 1.916E-18 3.654E-21 5.454E-22 7.462E-23

78 2.051E-18 1.933E-18 3.451E-21 5.077E-22 6.919E-23

80 2.083E-18 1.957E-18 3.653E-21 4.427E-22 7.557E-23

82 2.069E-18 1.940E-18 3.562E-21 4.203E-22 7.206E-23

84 2.101E-18 1.968E-18 3.463E-21 4.011E-22 7.148E-23

86 2.138E-18 2.002E-18 3.422E-21 3.620E-22 8.036E-23

88 2.182E-18 2.043E-18 3.479E-21 3.581E-22 7.653E-23

90 2.231E-18 2.089E-18 3.530E-21 3.185E-22 8.205E-23

92 2.275E-18 2.130E-18 3.529E-21 3.055E-22 8.190E-23

94 2.323E-18 2.175E-18 3.409E-21 2.921E-22 9.552E-23

96 2.368E-18 2.220E-18 3.608E-21 2.788E-22 9.143E-23

98 2.423E-18 2.274E-18 3.652E-21 2.681E-22 8.583E-23

100 2.451E-18 2.307E-18 3.553E-21 1.487E-21 8.474E-23
19

c. Wyckoff-Attix chamber.

E/keV Pdep Pcol Scol Fcol Gcol

10 5.798E-17 5.798E-17 5.402E-19 3.505E-19 1.248E-21

20 1.547E-17 1.547E-17 1.060E-19 5.355E-20 9.189E-22

30 6.698E-18 6.698E-18 4.265E-20 1.578E-20 4.982E-22

40 4.032E-18 4.032E-18 2.327E-20 6.689E-21 2.988E-22

50 3.080E-18 3.080E-18 1.585E-20 3.422E-21 1.875E-22

60 2.807E-18 2.807E-18 1.452E-20 2.219E-21 1.436E-22

70 2.777E-18 2.777E-18 1.305E-20 1.324E-21 1.282E-22

80 2.958E-18 2.958E-18 1.238E-20 9.428E-22 1.338E-22

90 3.174E-18 3.173E-18 1.326E-20 6.578E-22 1.807E-22

100 3.502E-18 3.497E-18 1.218E-20 5.115E-22 2.229E-22

110 3.870E-18 3.856E-18 1.313E-20 4.410E-22 2.266E-22

120 4.296E-18 4.268E-18 1.381E-20 3.257E-22 2.494E-22

130 4.730E-18 4.691E-18 1.428E-20 2.850E-22 2.896E-22

140 5.203E-18 5.155E-18 1.557E-20 2.180E-22 3.022E-22

150 5.630E-18 5.579E-18 1.547E-20 1.586E-22 3.859E-22

160 6.105E-18 6.054E-18 1.609E-20 1.714E-22 4.691E-22

170 6.574E-18 6.523E-18 1.635E-20 1.894E-22 4.880E-22

180 7.076E-18 7.022E-18 1.751E-20 1.467E-22 5.222E-22

190 7.566E-18 7.513E-18 1.804E-20 1.302E-22 5.508E-22

200 8.033E-18 7.986E-18 1.809E-20 1.118E-22 5.834E-22

210 8.546E-18 8.501E-18 1.865E-20 1.227E-22 6.444E-22

220 9.040E-18 8.993E-18 1.918E-20 1.199E-22 6.877E-22

230 9.547E-18 9.491E-18 1.985E-20 1.140E-22 7.375E-22

240 1.003E-17 9.950E-18 1.913E-20 1.177E-22 8.378E-22

250 1.051E-17 1.038E-17 1.984E-20 1.013E-22 8.633E-22

260 1.102E-17 1.079E-17 1.972E-20 1.139E-22 9.217E-22

270 1.151E-17 1.115E-17 2.022E-20 1.133E-22 9.429E-22

280 1.199E-17 1.144E-17 2.076E-20 9.174E-23 8.876E-22

290 1.251E-17 1.172E-17 2.057E-20 8.445E-23 9.501E-22

300 1.296E-17 1.189E-17 2.020E-20 8.681E-23 1.084E-21
20

Table 5. The adopted, smoothed data from Burns’ Monte Carlo calculations for NIST 

FACs.

a. Lamperti chamber.

E/keV Pdep Pcol Scol Fcol Gcol

2 1.539E-17 1.539E-17 7.104E-20 1.272E-19 3.256E-23

4 8.684E-18 8.684E-18 2.666E-20 4.921E-20 2.872E-23

6 4.891E-18 4.891E-18 1.152E-20 2.159E-20 2.567E-23

8 2.901E-18 2.901E-18 5.638E-21 1.058E-20 2.313E-23

10 1.842E-18 1.842E-18 3.073E-21 5.706E-21 2.096E-23

12 1.249E-18 1.249E-18 1.840E-21 3.343E-21 1.902E-23

14 8.955E-19 8.955E-19 1.193E-21 2.101E-21 1.726E-23

16 6.718E-19 6.718E-19 8.274E-22 1.402E-21 1.562E-23

18 5.222E-19 5.222E-19 6.071E-22 9.822E-22 1.408E-23

20 4.176E-19 4.176E-19 4.665E-22 7.166E-22 1.262E-23

22 3.419E-19 3.419E-19 3.720E-22 5.400E-22 1.125E-23

24 2.854E-19 2.854E-19 3.055E-22 4.175E-22 9.978E-24

26 2.422E-19 2.422E-19 2.566E-22 3.292E-22 8.801E-24

28 2.084E-19 2.084E-19 2.193E-22 2.636E-22 7.730E-24

30 1.814E-19 1.814E-19 1.898E-22 2.135E-22 6.772E-24

32 1.593E-19 1.593E-19 1.659E-22 1.745E-22 5.930E-24

34 1.411E-19 1.411E-19 1.461E-22 1.437E-22 5.202E-24

36 1.261E-19 1.259E-19 1.295E-22 1.192E-22 4.586E-24

38 1.139E-19 1.132E-19 1.156E-22 9.964E-23 4.078E-24

40 1.042E-19 1.028E-19 1.041E-22 8.413E-23 3.673E-24

42 9.679E-20 9.431E-20 9.470E-23 7.193E-23 3.365E-24

44 9.142E-20 8.747E-20 8.745E-23 6.253E-23 3.152E-24

46 8.742E-20 8.171E-20 8.234E-23 5.555E-23 3.036E-24

48 8.368E-20 7.619E-20 7.954E-23 5.073E-23 3.026E-24

50 7.844E-20 6.972E-20 7.938E-23 4.798E-23 3.140E-24
21

b. Ritz chamber.

E/keV Pdep Pcol Scol Fcol Gcol

2 2.608E-16 2.608E-16 2.206E-18 2.994E-18 7.171E-22

4 1.663E-16 1.663E-16 1.104E-18 1.411E-18 7.503E-22

6 1.071E-16 1.071E-16 5.738E-19 7.147E-19 7.623E-22

8 7.064E-17 7.064E-17 3.156E-19 3.876E-19 7.547E-22

10 4.807E-17 4.807E-17 1.851E-19 2.240E-19 7.306E-22

12 3.386E-17 3.386E-17 1.159E-19 1.372E-19 6.935E-22

14 2.470E-17 2.470E-17 7.715E-20 8.860E-20 6.474E-22

16 1.862E-17 1.862E-17 5.428E-20 5.993E-20 5.958E-22

18 1.447E-17 1.447E-17 4.005E-20 4.222E-20 5.419E-22

20 1.155E-17 1.155E-17 3.077E-20 3.081E-20 4.882E-22

22 9.439E-18 9.439E-18 2.443E-20 2.316E-20 4.365E-22

24 7.868E-18 7.868E-18 1.992E-20 1.785E-20 3.882E-22

26 6.673E-18 6.673E-18 1.659E-20 1.406E-20 3.439E-22

28 5.742E-18 5.742E-18 1.406E-20 1.126E-20 3.040E-22

30 5.005E-18 5.005E-18 1.209E-20 9.157E-21 2.685E-22

32 4.412E-18 4.412E-18 1.052E-20 7.537E-21 2.374E-22

34 3.930E-18 3.930E-18 9.253E-21 6.268E-21 2.103E-22

36 3.535E-18 3.535E-18 8.222E-21 5.260E-21 1.869E-22

38 3.209E-18 3.209E-18 7.378E-21 4.449E-21 1.668E-22

40 2.941E-18 2.941E-18 6.684E-21 3.790E-21 1.496E-22

42 2.719E-18 2.719E-18 6.113E-21 3.251E-21 1.350E-22

44 2.537E-18 2.537E-18 5.644E-21 2.808E-21 1.226E-22

46 2.388E-18 2.388E-18 5.258E-21 2.441E-21 1.121E-22

48 2.267E-18 2.267E-18 4.942E-21 2.136E-21 1.033E-22

50 2.194E-18 2.193E-18 4.683E-21 1.882E-21 9.589E-23
22

b. Ritz chamber (cont’d).

E/keV Pdep Pcol Scol Fcol Gcol

52 2.113E-18 2.112E-18 4.470E-21 1.669E-21 8.974E-23

54 2.048E-18 2.047E-18 4.294E-21 1.489E-21 8.467E-23

56 1.998E-18 1.995E-18 4.148E-21 1.338E-21 8.052E-23

58 1.962E-18 1.956E-18 4.025E-21 1.209E-21 7.720E-23

60 1.938E-18 1.927E-18 3.920E-21 1.098E-21 7.458E-23

62 1.925E-18 1.906E-18 3.830E-21 1.003E-21 7.260E-23

64 1.922E-18 1.893E-18 3.752E-21 9.198E-22 7.118E-23

66 1.926E-18 1.886E-18 3.684E-21 8.467E-22 7.026E-23

68 1.938E-18 1.884E-18 3.625E-21 7.817E-22 6.979E-23

70 1.954E-18 1.886E-18 3.575E-21 7.233E-22 6.972E-23

72 1.974E-18 1.891E-18 3.535E-21 6.702E-22 7.001E-23

74 1.995E-18 1.899E-18 3.505E-21 6.215E-22 7.063E-23

76 2.018E-18 1.910E-18 3.487E-21 5.765E-22 7.154E-23

78 2.040E-18 1.923E-18 3.479E-21 5.348E-22 7.269E-23

80 2.063E-18 1.938E-18 3.481E-21 4.961E-22 7.405E-23

82 2.087E-18 1.957E-18 3.492E-21 4.602E-22 7.558E-23

84 2.114E-18 1.980E-18 3.508E-21 4.271E-22 7.723E-23

86 2.144E-18 2.008E-18 3.524E-21 3.969E-22 7.895E-23

88 2.180E-18 2.041E-18 3.536E-21 3.696E-22 8.070E-23

90 2.222E-18 2.080E-18 3.538E-21 3.453E-22 8.241E-23

92 2.270E-18 2.125E-18 3.530E-21 3.240E-22 8.403E-23

94 2.323E-18 2.175E-18 3.515E-21 3.059E-22 8.550E-23

96 2.376E-18 2.227E-18 3.506E-21 2.907E-22 8.675E-23

98 2.421E-18 2.273E-18 3.531E-21 2.784E-22 8.773E-23

100 2.450E-18 2.306E-18 3.641E-21 2.687E-22 8.838E-23
23

c. Wyckoff-Attix chamber.

E/keV Pdep Pcol Scol Fcol Gcol

3.206 2.035E-16 2.035E-16 2.737E-18 1.710E-18 3.140E-21

5 1.414E-16 1.414E-16 1.691E-18 1.073E-18 2.601E-21

10 5.800E-17 5.800E-17 5.382E-19 3.383E-19 1.606E-21

20 1.548E-17 1.548E-17 1.083E-19 5.682E-20 7.284E-22

30 6.665E-18 6.665E-18 4.110E-20 1.611E-20 4.041E-22

40 4.041E-18 4.041E-18 2.322E-20 6.548E-21 2.656E-22

50 3.105E-18 3.105E-18 1.678E-20 3.381E-21 2.011E-22

60 2.794E-18 2.794E-18 1.408E-20 2.039E-21 1.708E-22

70 2.778E-18 2.778E-18 1.293E-20 1.355E-21 1.592E-22

80 2.928E-18 2.928E-18 1.254E-20 9.573E-22 1.595E-22

90 3.186E-18 3.183E-18 1.256E-20 7.035E-22 1.688E-22

100 3.514E-18 3.506E-18 1.284E-20 5.319E-22 1.859E-22

110 3.889E-18 3.873E-18 1.326E-20 4.120E-22 2.102E-22

120 4.296E-18 4.271E-18 1.378E-20 3.269E-22 2.416E-22

130 4.726E-18 4.691E-18 1.436E-20 2.660E-22 2.796E-22

140 5.172E-18 5.128E-18 1.496E-20 2.223E-22 3.236E-22

150 5.632E-18 5.581E-18 1.556E-20 1.910E-22 3.726E-22

160 6.104E-18 6.049E-18 1.616E-20 1.686E-22 4.249E-22

170 6.585E-18 6.529E-18 1.674E-20 1.527E-22 4.790E-22

180 7.073E-18 7.019E-18 1.731E-20 1.414E-22 5.328E-22

190 7.564E-18 7.514E-18 1.784E-20 1.333E-22 5.847E-22

200 8.056E-18 8.011E-18 1.833E-20 1.274E-22 6.332E-22

210 8.547E-18 8.504E-18 1.876E-20 1.229E-22 6.778E-22

220 9.036E-18 8.991E-18 1.910E-20 1.192E-22 7.182E-22

230 9.527E-18 9.470E-18 1.936E-20 1.158E-22 7.552E-22

240 1.002E-17 9.936E-18 1.955E-20 1.127E-22 7.900E-22

250 1.052E-17 1.038E-17 1.971E-20 1.095E-22 8.241E-22

260 1.102E-17 1.080E-17 1.991E-20 1.061E-22 8.597E-22

270 1.152E-17 1.116E-17 2.019E-20 1.024E-22 8.990E-22

280 1.201E-17 1.146E-17 2.054E-20 9.788E-23 9.443E-22

290 1.248E-17 1.169E-17 2.074E-20 9.169E-23 9.978E-22

300 1.297E-17 1.190E-17 2.017E-20 8.262E-23 1.062E-21
24

Table 6. The monoenergetic correction factors reconstructed form the adopted, smoothed 

data from Burns’ Monte Carlo calculations for NIST FACs. Values for kfl at 

energies below 3.206 keV are not given, as they are not expected to have any 

meaning. The large number of significant figures is for consistency with Table 3.

a. Lamperti chamber.

E/keV kel ksc kfl kbr

2 1.0000000 0.9954059 0.9999979

4 1.0000000 0.9969391 0.9943817 0.9999967

6 1.0000000 0.9976498 0.9956150 0.9999948

8 1.0000000 0.9980605 0.9963734 0.9999921

10 1.0000000 0.9983340 0.9969165 0.9999887

12 1.0000000 0.9985289 0.9973341 0.9999848

14 1.0000000 0.9986697 0.9976620 0.9999808

16 1.0000000 0.9987698 0.9979203 0.9999768

18 1.0000000 0.9988387 0.9981247 0.9999731

20 1.0000000 0.9988842 0.9982890 0.9999699

22 1.0000000 0.9989130 0.9984247 0.9999672

24 1.0000000 0.9989308 0.9985409 0.9999651

26 1.0000000 0.9989417 0.9986442 0.9999638

28 1.0000000 0.9989490 0.9987385 0.9999630

30 1.0000000 0.9989546 0.9988258 0.9999627

32 1.0000000 0.9989599 0.9989075 0.9999629

34 1.0001842 0.9989658 0.9989840 0.9999632

36 1.0018207 0.9989722 0.9990552 0.9999636

38 1.0058194 0.9989797 0.9991215 0.9999640

40 1.0135379 0.9989884 0.9991829 0.9999643

42 1.0262898 0.9989968 0.9992386 0.9999644

44 1.0451052 0.9990013 0.9992863 0.9999640

46 1.0698429 0.9989933 0.9993213 0.9999629

48 1.0983734 0.9989571 0.9993353 0.9999604

50 1.1251489 0.9988627 0.9993131 0.9999550
25

b. Ritz chamber.

E/keV kel ksc kfl kbr

2 1.0000000 0.9916142 0.9999973

4 1.0000000 0.9934071 0.9916391 0.9999956

6 1.0000000 0.9946713 0.9934059 0.9999930

8 1.0000000 0.9955520 0.9945676 0.9999894

10 1.0000000 0.9961639 0.9953799 0.9999849

12 1.0000000 0.9965896 0.9959779 0.9999797

14 1.0000000 0.9968865 0.9964369 0.9999740

16 1.0000000 0.9970941 0.9968014 0.9999682

18 1.0000000 0.9972401 0.9970991 0.9999628

20 1.0000000 0.9973435 0.9973475 0.9999580

22 1.0000000 0.9974186 0.9975589 0.9999540

24 1.0000000 0.9974751 0.9977420 0.9999509

26 1.0000000 0.9975197 0.9979031 0.9999487

28 1.0000000 0.9975573 0.9980472 0.9999473

30 1.0000000 0.9975907 0.9981782 0.9999466

32 1.0000000 0.9976218 0.9982988 0.9999464

34 1.0000000 0.9976513 0.9984115 0.9999467

36 1.0000000 0.9976796 0.9985178 0.9999473

38 1.0000000 0.9977066 0.9986190 0.9999482

40 1.0000000 0.9977323 0.9987157 0.9999493

42 1.0000000 0.9977568 0.9988082 0.9999505

44 1.0000000 0.9977801 0.9988967 0.9999518

46 1.0000000 0.9978027 0.9989810 0.9999532

48 1.0000000 0.9978251 0.9990608 0.9999546

50 1.0001842 0.9978693 0.9991445 0.9999564
26

b. Ritz chamber (cont’d).

E/keV kel ksc kfl kbr

52 1.0003224 0.9978882 0.9992122 0.9999576

54 1.0006910 0.9979065 0.9992744 0.9999588

56 1.0014978 0.9979257 0.9993314 0.9999598

58 1.0031364 0.9979465 0.9993837 0.9999606

60 1.0058425 0.9979695 0.9994315 0.9999614

62 1.0098340 0.9979947 0.9994753 0.9999620

64 1.0151261 0.9980219 0.9995153 0.9999625

66 1.0215274 0.9980505 0.9995521 0.9999628

68 1.0287504 0.9980795 0.9995860 0.9999630

70 1.0363823 0.9981077 0.9996173 0.9999631

72 1.0439026 0.9981340 0.9996463 0.9999631

74 1.0507998 0.9981575 0.9996734 0.9999629

76 1.0566715 0.9981775 0.9996987 0.9999626

78 1.0612800 0.9981938 0.9997224 0.9999623

80 1.0645351 0.9982071 0.9997446 0.9999619

82 1.0665470 0.9982190 0.9997654 0.9999615

84 1.0675789 0.9982316 0.9997847 0.9999611

86 1.0679969 0.9982478 0.9998027 0.9999608

88 1.0681445 0.9982705 0.9998192 0.9999605

90 1.0681937 0.9983018 0.9998343 0.9999605

92 1.0682183 0.9983417 0.9998478 0.9999605

94 1.0679231 0.9983867 0.9998596 0.9999608

96 1.0669646 0.9984280 0.9998697 0.9999611

98 1.0650010 0.9984495 0.9998777 0.9999615

100 1.0623803 0.9984232 0.9998837 0.9999617
27

c. Wyckoff-Attix chamber.

E/keV kel ksc kfl kbr

3.206 1.0000000 0.9867256 0.9917779 0.9999849

5 1.0000000 0.9881827 0.9925562 0.9999820

10 1.0000000 0.9908061 0.9942537 0.9999727

20 1.0000000 0.9930521 0.9963685 0.9999534

30 1.0000000 0.9938706 0.9976026 0.9999399

40 1.0000000 0.9942853 0.9983913 0.9999347

50 1.0000000 0.9946267 0.9989182 0.9999357

60 1.0000000 0.9949880 0.9992746 0.9999392

70 1.0000000 0.9953677 0.9995147 0.9999430

80 1.0000000 0.9957372 0.9996746 0.9999458

90 1.0006910 0.9960689 0.9997799 0.9999472

100 1.0022591 0.9963514 0.9998488 0.9999472

110 1.0040839 0.9965870 0.9998940 0.9999459

120 1.0059584 0.9967829 0.9999237 0.9999436

130 1.0075347 0.9969484 0.9999435 0.9999406

140 1.0086489 0.9970918 0.9999568 0.9999371

150 1.0091832 0.9972195 0.9999659 0.9999334

160 1.0091135 0.9973355 0.9999722 0.9999299

170 1.0085792 0.9974420 0.9999767 0.9999268

180 1.0076971 0.9975401 0.9999799 0.9999243

190 1.0066767 0.9976312 0.9999823 0.9999224

200 1.0057036 0.9977169 0.9999841 0.9999211

210 1.0050785 0.9977993 0.9999856 0.9999205

220 1.0050323 0.9978800 0.9999868 0.9999203

230 1.0059815 0.9979596 0.9999878 0.9999204

240 1.0084399 0.9980361 0.9999887 0.9999207

250 1.0130479 0.9981051 0.9999895 0.9999208

260 1.0206339 0.9981597 0.9999902 0.9999205

270 1.0320720 0.9981945 0.9999908 0.9999196

280 1.0478521 0.9982107 0.9999915 0.9999177

290 1.0677756 0.9982288 0.9999922 0.9999148

300 1.0898080 0.9983084 0.9999931 0.9999110
28

Table 7. Estimated relative standard uncertainties due to smoothing of the Burns data 

adopted for the NIST FACs.

Correction

Factor

Lamperti

(10 kV – 50 kV)

Ritz

(20 kV – 100 kV)

Wyckoff-Attix

(50 kV – 300 kV)

kel 0.02 % 0.06 % 0.04 %

ksc 0.01 % 0.01 % 0.01 %

kfl 0.01 % 0.01 % 0.01 %

Table 8. Estimated relative standard uncertainties inherent in the data adopted for 

calculating correction factors for the NIST FACs (combining results in Tables 2 

and 7). The last row gives the estimate associated with the assumption of kbr/(1-

g ) = 1.

Correction

Factor

Lamperti

(10 kV – 50 kV)

Ritz

(20 kV – 100 kV)

Wyckoff-Attix

(50 kV – 300 kV)

kel 0.05 % 0.08 % 0.10 %

ksc 0.03 % 0.03 % 0.03 %

kfl 0.05 % 0.05 % 0.03 %

kbr/(1-g) 0.02 % 0.02 % 0.03 %
29

Table 9. Adopted correction factors for the NIST free-air chambers: traditional NIST 

beam qualities.

Beam

Code

Lamperti Ritz Wyckoff-Attix

kel ksc kfl kel ksc kfl kel ksc kfl

L10 1.00000 0.99790 0.99608

L15 1.00000 0.99818 0.99662

L20 1.00000 0.99835 0.99698 1.00000 0.99622 0.99549

L30 1.00000 0.99860 0.99758 1.00000 0.99676 0.99635

L40 1.00000 0.99874 0.99798 1.00000 0.99707 0.99694

L50 1.00153 0.99884 0.99831 1.00000 0.99730 0.99740 1.00000 0.99308 0.99656

L80 1.00128 0.99756 0.99810 1.00000 0.99377 0.99750

L100 1.00531 0.99764 0.99838 1.00002 0.99407 0.99792

M20 1.00000 0.99851 0.99732 1.00000 0.99656 0.99598

M30 1.00000 0.99874 0.99790 1.00000 0.99704 0.99681

M40 1.00008 0.99883 0.99823 1.00000 0.99726 0.99729

M50 1.00202 0.99888 0.99844 1.00000 0.99738 0.99760 1.00000 0.99328 0.99681

M60 1.00003 0.99752 0.99796 1.00000 0.99363 0.99730

M80 1.00487 0.99766 0.99844 1.00000 0.99409 0.99796

M100 1.00946 0.99780 0.99885 1.00003 0.99453 0.99855

M120 1.00034 0.99487 0.99889

M150 1.00133 0.99548 0.99937

M200 1.00414 0.99637 0.99975

M250 1.00628 0.99712 0.99993

M300 1.01227 0.99780 0.99998

H10 1.00000 0.99801 0.99629

H15 1.00000 0.99847 0.99720

H20 1.00000 0.99871 0.99777 1.00000 0.99696 0.99661

H30 1.00000 0.99892 0.99849 1.00000 0.99744 0.99766

H40 1.00089 0.99896 0.99889 1.00000 0.99762 0.99828

H50 1.01727 0.99898 0.99909 1.00000 0.99770 0.99859 1.00000 0.99419 0.99820

H60 1.00035 0.99781 0.99899 1.00000 0.99452 0.99873

H100 1.05982 0.99824 0.99976 1.00045 0.99584 0.99970

H150 1.00575 0.99674 0.99991

H200 1.00815 0.99737 0.99997

H250 1.00633 0.99777 0.99998

H300 1.02266 0.99808 0.99999

S60 1.00005 0.99763 0.99835 1.00000 0.99399 0.99784

S75 1.00080 0.99755 0.99810 1.00000 0.99376 0.99750
30

Table 10. Adopted correction factors for the NIST free-air chambers: ISO beam 

qualities. The NS10, NS15, NS20, NS30, and NS40 beam qualities are assumed 

to be the same as that of the NIST H10, H15, H20, H30, and H40 beams, 

respectively.

Beam

Code

Lamperti Ritz Wyckoff-Attix

kel ksc kfl kel ksc kfl kel ksc kfl

HK10 1.00000 0.99790 0.99608

HK20 1.00000 0.99841 0.99712 1.00000 0.99636 0.99568

HK30 1.00000 0.99872 0.99786 1.00000 0.99700 0.99675

HK60 1.00005 0.99760 0.99824 1.00000 0.99389 0.99769

HK100 1.01306 0.99789 0.99910 1.00004 0.99478 0.99888

HK200 1.00414 0.99637 0.99975

HK250 1.00541 0.99687 0.99987

HK280 1.00706 0.99724 0.99994

HK300 1.00854 0.99727 0.99993

WS60 1.00020 0.99776 0.99881 1.00000 0.99438 0.99850

WS80 1.00958 0.99792 0.99923 1.00000 0.99482 0.99904

WS110 1.00058 0.99570 0.99961

WS150 1.00400 0.99646 0.99984

WS200 1.00722 0.99708 0.99994

WS250 1.00716 0.99751 0.99997

WS300 1.01227 0.99780 0.99998

NS10 1.00000 0.99801 0.99629

NS15 1.00000 0.99847 0.99720

NS20 1.00000 0.99871 0.99777 1.00000 0.99696 0.99661

NS25 1.00000 0.99884 0.99815 1.00000 0.99724 0.99715

NS30 1.00000 0.99892 0.99849 1.00000 0.99744 0.99766

NS40 1.00089 0.99896 0.99889 1.00000 0.99762 0.99828

NS60 1.00035 0.99781 0.99899 1.00000 0.99452 0.99873

NS80 1.02295 0.99804 0.99951 1.00000 0.99517 0.99937

NS100 1.05982 0.99824 0.99976 1.00045 0.99584 0.99970

NS120 1.00260 0.99635 0.99984

NS150 1.00569 0.99674 0.99991

NS200 1.00814 0.99739 0.99997

NS250 1.00634 0.99779 0.99998

NS300 1.02266 0.99808 0.99999

LK10 1.00000 0.99810 0.99646

LK20 1.00000 0.99878 0.99795 1.00000 0.99711 0.99685

LK30 1.00000 0.99894 0.99860 1.00000 0.99750 0.99784

LK35 1.00002 0.99895 0.99880 1.00000 0.99758 0.99813

LK55 1.00012 0.99782 0.99901 1.00000 0.99452 0.99876

LK70 1.01031 0.99798 0.99942 1.00000 0.99501 0.99927

LK100 1.06452 0.99828 0.99980 1.00064 0.99596 0.99974

LK125 1.00405 0.99656 0.99989

LK170 1.00868 0.99719 0.99996

LK210 1.00703 0.99758 0.99998

LK240 1.00575 0.99782 0.99999
31

Table 11. Adopted correction factors for the NIST free-air chambers: BIPM/CCRI beam 

qualities. The BIPM10 beam quality is assumed to be the same as that of the ISO 

HK10 beam; the BIPM50b beam quality is assumed to be the same as that of the 

NIST M50 beam. 

Beam

Code

Lamperti Ritz Wyckoff-Attix

kel ksc kfl kel ksc kfl kel ksc kfl

BIPM10 1.00000 0.99790 0.99608 1.00000 0.99523 0.99415

BIPM25 1.00000 0.99858 0.99751 1.00000 0.99672 0.99625

BIPM30 1.00000 0.99790 0.99608 1.00000 0.99523 0.99415

BIPM50A 1.00530 0.99895 0.99883 1.00000 0.99749 0.99788

BIPM50B 1.00202 0.99888 0.99844 1.00000 0.99738 0.99760 1.00000 0.99328 0.99681

BIPM100 1.00709 0.99773 0.99862 1.00002 0.99431 0.99824

BIPM135 1.00068 0.99520 0.99918

BIPM180 1.00281 0.99588 0.99951

BIPM250 1.00556 0.99691 0.99986
32

Figure 1. Schematic of a parallel-plate free-air ionization chamber used by the NIST for 

the realization of air kerma for W-anode x-ray beams. The high-voltage, guard, 

and collecting plates have a width that extends into the paper.
33

Figure 2. Comparison of original Burns data (points) for the Lamperti free-air chamber 

with the results from the smoothed underlying data (curve).

a. Correction factor kel.

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

0 10 20 30 40 50

Correction Factor

Photon Energy, keV

Lamperti kel
34

Figure 2. Comparison of original Burns data (points) for the Lamperti free-air chamber 

with the results from the smoothed underlying data (curve).

b. Correction factor ksc.

0.9955

0.9960

0.9965

0.9970

0.9975

0.9980

0.9985

0.9990

0.9995

0 10 20 30 40 50

Correction Factor

Photon Energy, keV

Lamperti ksc
35

Figure 2. Comparison of original Burns data (points) for the Lamperti free-air chamber 

with the results from the smoothed underlying data (curve).

c. Correction factor kfl.

0.991

0.992

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1.000

0 10 20 30 40 50

Correction Factor

Photon Energy, keV

Lamperti kfl
36

Figure 3. Comparison of original Burns data (points) for the Ritz free-air chamber with 

the results from the smoothed underlying data (curve).

a. Correction factor kel.

1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

0 20 40 60 80 100

Correction Factor

Photon Energy, keV

Ritz kel
37

Figure 3. Comparison of original Burns data (points) for the Ritz free-air chamber with 

the results from the smoothed underlying data (curve).

b. Correction factor ksc.

0.991

0.992

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1.000

0 20 40 60 80 100

Correction Factor

Photon Energy, keV

Ritz ksc
38

Figure 3. Comparison of original Burns data (points) for the Ritz free-air chamber with 

the results from the smoothed underlying data (curve).

c. Correction factor kfl.

0.990

0.991

0.992

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1.000

0 20 40 60 80 100

Correction Factor

Photon Energy, keV

Ritz kfl
39

Figure 4. Comparison of original Burns data (points) for the Wyckoff-Attix free-air 

chamber with the results from the smoothed underlying data (curve).

a. Correction factor kel.

1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

0 50 100 150 200 250 300

Correction Factor

Photon Energy, keV

Wyckoff-Attix kel
40

Figure 4. Comparison of original Burns data (points) for the Wyckoff-Attix free-air 

chamber with the results from the smoothed underlying data (curve).

b. Correction factor ksc.

0.985

0.990

0.995

1.000

0 50 100 150 200 250 300

Correction Factor

Photon Energy, keV

Wyckoff-Attix ksc
41

Figure 4. Comparison of original Burns data (points) for the Wyckoff-Attix free-air 

chamber with the results from the smoothed underlying data (curve).

c. Correction factor kfl.

0.990

0.991

0.992

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1.000

0 50 100 150 200 250 300

Correction Factor

Photon Energy, keV

Wyckoff-Attix kfl