Energy dependence of the bremsstrahlung cross section at the short wavelength limit

Volume 51A, number 4

PHYSICS LETFERS

10 March 1975

ENERGY DEPENDENCE OF THE BREMSSTRAHLUNG CROSS SECTION AT THE SHORT WAVELENGTH LiMIT A. AEHLIG, M. SCHEER, F. ZILKER Physikalisches Institut der Universitit, D-87 Wilrzburg, Federal Republic of Germany Received 11 November 1974 We have measured the bremsstrahlung cross section at the short wavelength limit for copper. The incident energy of the electrons ranged between 100 key and 250 keV. The Elwert-Haug calculationsare found to be valid within 20%.

Starek, Aiginger and Unfried were the first to use a Ge(Li)-detector lnstead of a NaJ(Tl)-spectrometer to measure bremsstrahlung cross sections at the short wavelength limit [1,2]. Because of the good energy resolution of this detector and other features of their experiment they claimed an overall precision of their

experiment. The electrons were accelerated in an eight-stage tube. The negative high-tension was delivered by an electrostatic generator which has an electronic stabilization (±100 V). After being focussed the beam was adjusted by 2 sets of He]mholtz coils (H1, H2) in such a way that it passed the two control

measurements of ±2—3%.This paper was a stimulus of theoretical work concerning the tip region of the bremsstrahlung spectrum. Dautrey, Dugne and Proriol did exact ealculations using point Coulomb potentials [3,4]. Haug discussed the use of Sommerfeld-Mau~wave functions for calculations of the tip region [5]. Tseng and Pratt did exact calculations for screened potentials and described the present theoretical status [6]. According to these considerations the Elwert-Haug calculation should be a good approximation for small atomic numbers Z in spite of the discrepancies found by Starek, Aiginger and Unfried. To test the validity of Elwert-Haug calculations for medium Z we used copper target. Fig. 1 shows, in principle, the aarrangement of the

apertures (CA1, CA2) without touching. In this way the direction of the primary electrons in the scattering chamber (diameter 485 mm) was defined within 2 X i0~ rad. A conically drilled collimator of lead defines the solid angle of the detected photons (1.43 X l0~sr). One important feature of our experimental procedure is the use of elastic electron scattering as a reference. Simultaneously with the detected photons we counted the elastic scattered electrons in a surface barrier detector (OR = 120 degrees; ~~E1 = 1.66 X l0~ sr). By this method the bremsstrahlung cross section can be determined from 2a dtJESS ~E1 ~1E1 N~ d d~2dk d&2 0R

Fig. 1. Experimental arrangement. FC Focussing coil; H 1, H2 two sets of Helmholtz coils; CA1, CA2 control apertures; HT negative high tension from an electrostatic generator; R1, R2 ... R8 potential divider for the stages ofthe accelerator tube.

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Volume 5lA,number 4

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ergies using calibrated radioactive sources. To get the efficiency for other energies a semi-empirical formula was fitted to these experimental values [9]. The tar-

gets were made by evaporation of copper onto thin plastic films. The thicknesses of the foils were 10 and 20 ~tg/cm2. Within the experimental error multiple scattering did not influence the results. Fig. 2 thows the measured cross sections for two photon emission angles (25 and 50 degrees). The solid line represents the Elwert-Haug formula [10]. The dashed line represents where Nm is the number of the detected photons in the energy interval ~k, NE 1 is the the de2Ph~~2E1 are number the solidofangles tected electrons,~ of the photon and the electron detector, ~ ~ the efficiency of the photon and the electron detector. The cross section for the elastic electron scattering was calculated using the partial wave method [7]. In a former experiment we made sure that these calculations describe elastic scattering within an accuracy of a few percent [8]. The advantages of this reference method is the fact that the result does not depend on the thickness of the target foils. The efficiency of the Ge(Li)-detector was determined for 13 different en-

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the Elwert-Haug formula with a correction in second order of aZ [11]. In the average the experimental data are somewhat higher than Elwert-Haug values, the discrepency never exceeds 20%. The authors want to thank Dr. H.K. Tseng and Dr. R.H. Pratt for sending a preprint of their paper prior to its publication.

References

[1] 39A B. Starek, Aiginger and E. Unfried, Phys. Lett. (1972)H.151. [2] (1972) H. Aiginger 331. and E. Unfried, Acta Phys. Austr. 35 [3] H. Dautrey, J. Dugne and J. Proriol, Phys. Lett. 47A (1974) 107. [4] J. Proriol, Nuovo Cnn. B19 (1974) 211. [5] E. Haug, Phys. Lett. 49A (1974) 68. [6] Tseng and Rev. R.H. 133, Pratt,A965 to be(1964). published. [7] H.K. S.R. Lin,Phys. [8] A. Aehlig, E. Hdrber, D. Kuscheck and M. Scheer, z. Phys. 253 (1972) 421. [9] R.S. Mowatt, Nuci. Instr. Meth. 70 (1969) 237. [10] G. Elwert and E. Haug, Phys. Rev. 183 (1969) 90. [11] E. Haug, thesis Tubingen (1966).