International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. C, ch. 4.2, pp. 191192

The efficiency of the production of characteristic radiation has been calculated by a number of authors (see, for example, Dyson, 1973, Chap. 3). For a particular line, it depends on the fluorescence yield, that is the probability that the decay of an excited state leads to the emission of a photon, on the statistical weights of the Xray levels involved, on the effects of the penetration and slowing down of the bombarding electrons in the target, on the fraction of electrons backscattered out of the target, and on the contribution caused by fluorescent Xrays produced indirectly by the continuous spectrum. The emerging Xray intensity is further affected by the partial absorption of the generated Xrays in the target.
Dyson (1973) has also reviewed calculations and measurements made of the relative intensities of different lines in the K spectrum. The ratio of the to intensities is very close to 0.5 for Z between 23 and 48. The ratio of to rises fairly linearly with Z from 0.2 at Z = 20 to 0.4 at Z = 80 and that of to is near zero at Z = 29 and rises linearly with Z to about 0.1 at Z = 80. Relative intensities of lines in the L spectrum are given by Goldberg (1961).
Green & Cosslett (1968) have made extensive measurements of the efficiency of the production of characteristic radiation for a number of targets and for a range of electron accelerating voltages. Their results can be expressed empirically in the form where is the generated number of Kα photons per steradian per incident electron, N_{0} is a function of the atomic number of the target, E_{0} is the electron energy in keV and is the excitation potential in keV. It should be noted that decreases with increasing Z.
For a copper target, this expression becomes or where is the number of Kα photons per steradian per second per milliampere of tube current.
These expressions are probably accurate to within a factor of 2 up to values of of about 10. Guo & Wu (1985) found a linear relationship for the emerging number of photons with electron energy in the range .
To obtain the number of photons that emerge from the target, the above expressions have to be corrected for absorption of the generated radiation in the target. The number of photons emerging at an angle to the surface, for normal electron incidence, is usually written where (Castaing & Descamps, 1955). Green (1963) gives experimental values of the correction factor f(χ) for a series of targets over a range of electron energies. His curves for a copper target are given in Fig. 4.2.1.1 . It will be noticed that the correction factor increases with increasing electron energy since the effective depth of Xray generation increases with voltage. As a result, curves of as a function of have a broad maximum that is displaced towards lower voltages as decreases, as shown in the experimental curves for copper K radiation due to Metchnik & Tomlin (1963) (Fig. 4.2.1.2 ). For very small takeoff angles, therefore, Xray tubes should be operated at lower than customary voltages. Note that the values in Fig. 4.2.1.2 agree to within ∼40% with those of Green & Cosslett. f(χ) at constant increases with increasing Z, thus partly compensating for the decrease in , especially at small values of . A recent reexamination of the characteristic Xray flux from Cr, Cu, Mo, Ag and W targets has been carried out by Honkimaki, Sleight & Suortti (1990).

f(χ) curves for Cu KL_{3} at a series of different accelerating voltages (in kV). From Green (1963). 
References
Castaing, R. & Descamps, J. (1955). Sur les bases physiques de l'analyse ponctuelle par spectrographie X. J. Phys. Radium, 16, 304–317.Dyson, N. A. (1973). Xrays in atomic and nuclear physics. London: Longman.
Goldberg, M. (1961). Intensités relatives des raies X du spectre L excité par bombardement électronique des éléments lourds. J. Phys. Radium, 22, 743–748.
Green, M. (1963). The target absorption correction in Xray microanalysis. Xray optics and Xray microanalysis, edited by H. Pattee, V. E. Cosslett & A. Engstrom, pp. 361–377. London: Academic Press.
Green, M. & Cosslett, V. E. (1968). Measurement of K, L and M shell Xray production efficiencies. Br. J. Appl. Phys. Ser. 2, 1, 425–436.
Guo, C.L. & Wu, Y.Q. (1985). Empirical relationship between the characteristic Xray intensity and the incident electron energy. Kexue Tongbao, 30, 1621–1627.
Honkimaki, V., Sleight, J. & Suortti, P. (1990). Characteristic Xray flux from sealed Cr, Cu, Mo, Ag and W tubes. J. Appl. Cryst. 23, 412–417.
Metchnik, V. & Tomlin, S. G. (1963). On the absolute intensity of emission of characteristic X radiation. Proc. Phys. Soc. London, 81, 956–964.