Dependence of 50- and 100-keV Bremsstrahlung on Target Thickness, Atomic Numberand Geometric Factors

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JOURNAL OF APPLIED PHYSICS
H. W. Koch and J. W. Motz, Rev. Mod. Phys. 31, 920 (1959). S. T. Stephenson, in Handbuch der Physik., Vol. 30, p. 22. 3 H. A. Kramers, Phil. Mag. 46, 836 (1923). • P. Kirkpatrick and L. Wiedmann, Phys. Rev. 67, 321 (1945). 5A. Sommerfeld, Ann. Physik 11, 257 (1931). 6 M. J. Berger and S. Seltzer, to be published. Preliminary results were published in "Proceedings of the Second Symposium on Protection Against Radiations in Space," Gatlinburg, Tenn. (1964) .
I. INTRODUCTION
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ALTHOUGH a considerable amount of information is available on the bremsstrahlung process,1·2 accurate predictions on thick-target bremsstrahlung production are especially difficult to make in the low energy region where the initial electron kinetic energies are less than a few MeV. This difficulty arises in part from the uncertainties in the bremsstrahlung cross section in this energy region and in part from the complicated calculations required to account for multiple scattering effects in the target. Among the early theoretical thick-target bremsstrahlung studies in the low-energy region, below a few hundred keV, are the calculations by Kramers,3 and by Kirkpatrick and Wiedmann. 4 The Kramers calculations estimate the bremsstrahlung energy spectrum integrated over the photon direction, and are based on a nonrelativistic, semiclassical treatment, while the Kirkpatrick and Wiedmann calculations estimate the efficiency for the total bremsstrahlung production on the basis of the nonrelativistic Sommerfeld5 cross section. However, the calculations by Kramers and by Kirkpatrick and Wiedmann have the following limitations: (1) Electron scattering effects (including backscattering from targets) are neglected and therefore the results apply to the case where electrons lose energy in an infinite medium. (2) No corrections are given for the photon attenuation in the target. Because of these limitations, these calculations cannot be directly compared with experimental results which apply to the bremsstrahlung emitted from a target and which are critically dependent on geometric conditions of the measurement. On the other hand, Berger and Seltzer6 recently have
VOLUME 38, NUMBER 5
APRIL 7
Dependence of 50- and 100-keV Bremsstrahlung on Target Thickness, Atomic Number, and Geometric Factors
R. C. PLACIOUS National Bureau of Standards, Washington, D. C. (Received 28 November 1966; in final form 16 January 1967)
Experimental data have been obtained for the bremsstrahlung spectra produced with 50- and lOO-keV electrons incident on different targets. The spectrum per unit solid angle per incident electron is measured for photon emission angles of 30, 70, and llO deg, for normal and oblique incidence of the electrons on the targets having atomic numbers of 13, 50, and 79, and for four target thicknesses equal to different fractions of the electron range in the given material. Also, results are given for the bremsstrahlung production efficiencies per unit solid angle at a given emission angle. The experimental results at normal incidence show good agreement with the theoretical predictions of Berger and Seltzer, which are based on thin-target bremsstrahlung cross sections and which employ Monte Carlo calculations to account for multiple scattering and energy-loss effects. Similar calculations for other geometries should produce reliable estimates of the emitted bremsstrahlung spectra in this same energy region.
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carried out Monte Carlo calculations which predict the energy and angular distribution of the bremsstrahlung emitted from thick targets and which can be directly compared with experimental results. These calculations, which are based on the Bethe-Heitler7 cross section with an empirical correction factor discussed by Koch and Motz,1 account for energy loss and multiple elastic scattering of the electron and absorption and multiple Compton scattering of the photon in specific slab geometries. References are also available1 •2 on previous experimental low-energy thick-target bremsstrahlung production. Some of these works give data in terms of relative photon intensities8 while others give data in terms of absolute photon intensities9 per incident electron. Most of these papers make comparisons with the predictions of Kramers or Kirkpatrick and Wiedmann, which may not give accurate estimates for the case of targets with finite size. Therefore, the present measurements were undertaken in order to provide more experimental data on thick-target bremsstrahlung production in the low energy region, which can be directly compared to the calculations of Berger and Seltzer, without uncertain correction factors for geometry and photon attenuation. These measurements are made with initial electron kinetic energies of SO and 100 keV. For each electron energy, the photon energy spectrum per unit solid angle per incident electron is obtained as a function of the photon emission angle, the target thickness, and the target atomic number. Also, these spectra are integrated over the photon energies and estimates are made for the bremsstrahlung production efficiency per unit solid angle for a given photon emission angle and a given electron angle of incidence, as defined in Sec. III.2.