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Bremsstrahlung cross-section measurements at the short-wavelength limit
Volume 39A, number 2
PHYSICS LETTERS
24 April 1972
BREMSSTRAHLUNG CROSS-SECTION MEASUREMENTS AT THE SHORT-WAVELENGTH LIMIT B. STAREK, H. AIGINGER and E. UNFRIED Atominstitut der Osterreichischen Hochschulen, Wien, Austria
Received 21 February 1972 Very precise (± 2-3%) measurements of the electron-bremsstrahlungcross-sectionsd2a/dkdf~k at the shortwavelength limit for an incident electron energy of 1.84 MeV and targets of Li, AI, Cu, Ag, Au and Pb show that the theoretical results of Elwert-Haug, Scherzer and Sauter-Fano do not agree with the experiment. The available results for the cross-section near the short-wavelength limit [I -5] have been obtained by extrapolation of bremsstrahlung spectra measured with NaI '(Tl)-spectrometers. Due to the low energy resolution of such spectrometers and due to the necessary application of appropriate corrections to take into account for the response function of the respective spectrometer, the accuracy of these experimental results is rather poor. In this investigation a true coaxial Ge(Li)-detector with an active volume of 37.4 cm 3 and a resolution of 3.34 keV (FWHM) was used as a spectrometer. Fig. 1 shows the principal arrangement of the beam defining system, the scattering chamber and the spectrometer with collimators which allows measurements at different angles. The beam defining system consists of two deflecting magnets and two apertures and supplies an electron beam with an energy
spread of + 2 keY. The response function of the Ge(Li)-spectrometer was determined with an 8 Sy standard (E = 1.836 MeW) at the site of the target. The background of the measured spectra was carefully reduced by means of analytical expressions for the spectrometer response function and the background. The targets were made by evaporation in the scattering chamber in order to avoid contamination of the targets by vapor or oxygen. This procedure is essential especially in the case of Li. For the targetthickness measurements the frequency shift of a quartz crystal oscillator was used. For this purpose ~vo quartz crystals were mounted close to the evaporation position of the target. To avoid problems due to different condensation coefficients both crystals were coated with a thin film of the backing material prior to evaporation. Nevertheless a substance de-
Van de @raaff
Fig. I. Schematic of overall experimental arrangement Al ,*A2 beam defining apertures, MI, Ms deflecting magnets, CI, C2 collimators. 151
Volume 39A, number 2 k d(3" (mb/sr) Z=dkd~k
PHYSICS LETTERS
/
To,"1.84 MeV k ,, 1.84 MeV el " I 0 °
/ Sauter- /
Z 0
I
I
I
I
t I
13
29
47
79 82
Fig. 2. Z-dependence of the electron bremsstrahlung crosssection at the short-wavelengthlimit.
24 April 1972
the bremsstrahlung cross-sections in the high-frequency limit gives correct values for Z = 13 (A1) only and a crude qualitative description of the Z-dependence only in the region below Z = 13. The theory of Elwert-Haug which uses Sommerfeld-lVl'aue wavefunctions disagrees with the experiment even for those values of aZ (0.00219 for Li) which satisfy the condition aZ ,~ 1 (a = 1/137, Sommerfelds fine structure constant). The same happens for the earlier theory of Scherzer [8] which can be derived from the recently developed Elwert-Haug theory by apt plying of some simplifying assumptions. Both theories fail to describe the Z-dependence of the crosssection. The fact that existing theories show considerable discrepancies even for low aZ and give a completely inadequate Z-dependence of the cross-section indicates clearly that these theories are rather inadequate for the description of the physical process at the short-wavelength limit.
References pendence of the method could be observed. Therefore calibrating measurements for all target materials were carried out. In this way an overall precision of -+2-3% could be obtained. Fig. 2 shows the experimental results obtained for ® = 10°. These results are compared with theoretical results of Sauter-Fano [6], Elwert-Haug [7] and Scherzer [8]. The Sauter-Fano theory which relates photoelectric cross-sections to
152
[1] J.W.Motz, Phys. Rev. 100 (1955) 1560. [2] H.Aigingerand H. Zinke, Acta Physica Austriaca 23 (1966) 76. [3] H. Aiginger, Z. f. Physik 197 (1966) 8. [4] H. Aiginger, Habilitationsschrift TH-Wien 1969. [5] D.H. Rester and W.E. Dance, Phys. Rev. 161 (1967) 85. [6] U. Fano, Phys. Rev. 116 (1959) 1156. [7] G. Elwert and E. Haug, Phys. Rev. 183 (1969) 90. [8] O. Scherzer, Ann. Physik 13 (1932) 137.
PHYSICS LETTERS
24 April 1972
BREMSSTRAHLUNG CROSS-SECTION MEASUREMENTS AT THE SHORT-WAVELENGTH LIMIT B. STAREK, H. AIGINGER and E. UNFRIED Atominstitut der Osterreichischen Hochschulen, Wien, Austria
Received 21 February 1972 Very precise (± 2-3%) measurements of the electron-bremsstrahlungcross-sectionsd2a/dkdf~k at the shortwavelength limit for an incident electron energy of 1.84 MeV and targets of Li, AI, Cu, Ag, Au and Pb show that the theoretical results of Elwert-Haug, Scherzer and Sauter-Fano do not agree with the experiment. The available results for the cross-section near the short-wavelength limit [I -5] have been obtained by extrapolation of bremsstrahlung spectra measured with NaI '(Tl)-spectrometers. Due to the low energy resolution of such spectrometers and due to the necessary application of appropriate corrections to take into account for the response function of the respective spectrometer, the accuracy of these experimental results is rather poor. In this investigation a true coaxial Ge(Li)-detector with an active volume of 37.4 cm 3 and a resolution of 3.34 keV (FWHM) was used as a spectrometer. Fig. 1 shows the principal arrangement of the beam defining system, the scattering chamber and the spectrometer with collimators which allows measurements at different angles. The beam defining system consists of two deflecting magnets and two apertures and supplies an electron beam with an energy
spread of + 2 keY. The response function of the Ge(Li)-spectrometer was determined with an 8 Sy standard (E = 1.836 MeW) at the site of the target. The background of the measured spectra was carefully reduced by means of analytical expressions for the spectrometer response function and the background. The targets were made by evaporation in the scattering chamber in order to avoid contamination of the targets by vapor or oxygen. This procedure is essential especially in the case of Li. For the targetthickness measurements the frequency shift of a quartz crystal oscillator was used. For this purpose ~vo quartz crystals were mounted close to the evaporation position of the target. To avoid problems due to different condensation coefficients both crystals were coated with a thin film of the backing material prior to evaporation. Nevertheless a substance de-
Van de @raaff
Fig. I. Schematic of overall experimental arrangement Al ,*A2 beam defining apertures, MI, Ms deflecting magnets, CI, C2 collimators. 151
Volume 39A, number 2 k d(3" (mb/sr) Z=dkd~k
PHYSICS LETTERS
/
To,"1.84 MeV k ,, 1.84 MeV el " I 0 °
/ Sauter- /
Z 0
I
I
I
I
t I
13
29
47
79 82
Fig. 2. Z-dependence of the electron bremsstrahlung crosssection at the short-wavelengthlimit.
24 April 1972
the bremsstrahlung cross-sections in the high-frequency limit gives correct values for Z = 13 (A1) only and a crude qualitative description of the Z-dependence only in the region below Z = 13. The theory of Elwert-Haug which uses Sommerfeld-lVl'aue wavefunctions disagrees with the experiment even for those values of aZ (0.00219 for Li) which satisfy the condition aZ ,~ 1 (a = 1/137, Sommerfelds fine structure constant). The same happens for the earlier theory of Scherzer [8] which can be derived from the recently developed Elwert-Haug theory by apt plying of some simplifying assumptions. Both theories fail to describe the Z-dependence of the crosssection. The fact that existing theories show considerable discrepancies even for low aZ and give a completely inadequate Z-dependence of the cross-section indicates clearly that these theories are rather inadequate for the description of the physical process at the short-wavelength limit.
References pendence of the method could be observed. Therefore calibrating measurements for all target materials were carried out. In this way an overall precision of -+2-3% could be obtained. Fig. 2 shows the experimental results obtained for ® = 10°. These results are compared with theoretical results of Sauter-Fano [6], Elwert-Haug [7] and Scherzer [8]. The Sauter-Fano theory which relates photoelectric cross-sections to
152
[1] J.W.Motz, Phys. Rev. 100 (1955) 1560. [2] H.Aigingerand H. Zinke, Acta Physica Austriaca 23 (1966) 76. [3] H. Aiginger, Z. f. Physik 197 (1966) 8. [4] H. Aiginger, Habilitationsschrift TH-Wien 1969. [5] D.H. Rester and W.E. Dance, Phys. Rev. 161 (1967) 85. [6] U. Fano, Phys. Rev. 116 (1959) 1156. [7] G. Elwert and E. Haug, Phys. Rev. 183 (1969) 90. [8] O. Scherzer, Ann. Physik 13 (1932) 137.