Comparison between theoretical and experimental data sets

Creagh, D. C.; Hubbell, J. H.

doi:10.1107/97809553602060000592

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 229

Section 4.2.4.3. Comparison between theoretical and experimental data sets

D. C. Creagh^b and J. H. Hubbell^d

4.2.4.3. Comparison between theoretical and experimental data sets

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Saloman & Hubbell (1986) and Saloman et al. (1988) have published an extensive comparison of the experimental database with the theoretical values of Scofield (1973, 1986) for photon energies between 0.1 and 100 keV. Some examples taken from Saloman & Hubbell (1986) are shown in Figs. 4.2.4.1 , 4.2.4.2 , and 4.2.4.3 .

Figure 4.2.4.1| top | pdf |

Agreement between theory and experiment for oxygen (Z = 8) in the `soft' X-ray region. The solid line is for the Scofield (1973) values without renormalization and the dotted line is for the semi-empirical data of Henke et al. (1982).

Figure 4.2.4.2| top | pdf |

The total cross section for silicon (Z = 14) compared with the unrenormalized Scofield values. The measured and theoretical attenuation coefficients show systematic differences of several percent for the photon energy range 10 to 100 keV.

Figure 4.2.4.3| top | pdf |

The total cross section for uranium (Z = 92): The theoretical values (solid line) are partially obscured by the high density of available measurements. Deviations of the measured values from the theoretical predictions are mostly of the order of 5%, although a few data sets deviate by more than 30%.

Comparisons between theory and experiment exist for about 80 elements and space does not permit reproduction of all the available information. This information has been summarized in Fig. 4.2.4.4. Superimposed on the Periodic Table of the elements are two sets of data. The upper set corresponds to the average percent deviation between experiment and theory for the photon energy range 10 to 100 keV. The lower set corresponds to the average percent deviation between experiment and theory for the photon energy range 1 to 10 keV. An upwards pointing arrow $[\uparrow]$ means that $[(\sigma _{\exp}- \sigma _{\rm theor}) \,\gt \, 0]$ . No arrow implies that $[(\sigma _{\exp} - \sigma _{\rm theor})=0.]$ A downwards pointing arrow $[\downarrow]$ means that $[(\sigma _{\exp} - \sigma _{\rm theor}) \lt 0.]$ An asterisk means no experimental data set was available.

Figure 4.2.4.4| top | pdf |

Comparison between this tabulation and experimental data contained in Saloman & Hubbell (1986). The upper set corresponds to the average percent deviation between the experimental data and this tabulation for the energy range 10 to 100 keV. The lower set corresponds to the energy range 1 to 10 keV. For explanation of symbols see text.

For example: for tin (Z = 50), the experimental data are on average 5% higher than the theoretical predictions for the range of photon energies from 10 to 100 keV. For the range 1 to 10 keV, the experimental data are on average 7% higher than the theoretical predictions.

Fig. 4.2.4.4 is given as a rapid means of comparing theory and experiment. For more detailed information, see Saloman & Hubbell (1986), Saloman et al. (1988), and Creagh (1990).

References

Creagh, D. C. (1990). Tables of X-ray absorption corrections and dispersion corrections: the new versus the old. Nucl. Instrum. Methods, A295, 417–434.Google Scholar

Henke, B. L., Lee, P., Tanaka, T. J., Shimambukuro, R. L. & Fujikawa, B. K. (1982). Low-energy X-ray interaction coefficients: photoabsorption, scattering and reflection. At. Data Nucl. Data Tables, 27, 1–144.Google Scholar

Saloman, E. B. & Hubbell, J. H. (1986). X-ray attenuation coefficients (total cross sections): comparison of the experimental data base with the recommended values of Henke and the theoretical values of Scofield for energies between 0.1–100 keV. Report NBSIR 86-3431. National Institute of Standards and Technology, Gaithersburg, MD, USA.Google Scholar

Saloman, E. B., Hubbell, J. H. & Scofield, J. H. (1988). At. Data Nucl. Data Tables, 38, 1–197.Google Scholar

Scofield, J. H. (1973). Theoretical photoionization cross sections from 1 to 1500 keV. Report UCRL-51326. Lawrence Livermore National Laboratory, Livermore, CA, USA.Google Scholar

Scofield, J. H. (1986). Personal communication to E. B. Saloman & J. H. Hubbell. Calculated photoeffect values 0.1 to 1.0 keV. [Presented in Saloman & Hubbell (1986)

and Saloman et al. (1988)

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 229