Statistics of energy losses of fast electrons

ORAL

Abstract

Electrons deflected by the field of a nucleus will emit photons (``Bremsstrahlung, BMS"), resulting in energy losses $E$. The differential cross section for this effect is of the form $\sigma_b(E)=\chi/E$. For Si, $\chi \sim~2\cdot 10^{-24}$~cm$^2$/nucleus. For collisions with atomic electrons the differential cross section is $\sigma_R(E,\beta)=\xi/E^2$, $\xi=1.3\cdot 10^{-19}$~eV/cm$^2$ for fast electrons ($\beta=v/c\sim1$). We use the {\it moments } $M_0(T) \equiv N \int_{E_l}^{T} \sigma_{\mathrm{rad}} (E;T) dE $ to get the mean number of collisions per cm and $M_1(T) \equiv N \int E~ \sigma_{\mathrm{rad}} (E;T) dE $ to get the mean energy loss per cm for electrons with energy $T$, giving $_b M_0(T)=\chi~\ln (T/E_l)$ and $_R M_0(T)=\xi~ (1/T~-~1/E_l)$. Also $_bM_1(T)~=~\chi \cdot T$, $_R M_1(T)=\xi~\ln (T/E_l)$. Assuming $E_l=20$ eV, $M_0$ depends little on $T$, and the {\it average energy loss per collision} $=M_1/M_0$ depends little on $T$ for electron collisions, but is almost proportional to $T$ for BMS collisions. The ratio $_R M_0(T)/_b M_0(T)$ is of the order of 10,000, while $_b M_0(T)~\sim 1.6$ col/cm for Si. In a thick absorber this causes great variances in the distributions of the number of BMS collisions, the practical range of the primary electrons and its electronic energy loss. These effects have been simulated with Monte Carlo calculations and will be described.

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Authors

  • Anthony Colaprete

    Triumf, Texas A\&M University, Tel Aviv University, TRIUMF, Simon Fraser University, Dept. of Physics, SFU, BC, Canada, Department of Physics and Astronomy, University of British Columbia, Cavendish Laboratory, University of Cambridge, Department of Physics, Simon Fraser University, University of British Columbia, University of Wisconsin-Madison, Brookhaven National Laboratory, Los Alamos National Laboratory, Department of Molecular Science and Technology, Ajou University, Suwon 443-749, Korea, Department of Physics, Oregon State University, Corvallis, OR 97331-6507, Imago Scientific Instruments Corp., Department of Physics, Simon Fraser University, 8888 University Dr., Burnaby, BC, V5A 1S6 Canada, Linfield College, PNNL, University of Washington, University of Victoria, IUPUI1, Wabash, IUPUI2, Environmental Biotechnology Institute, University of Idaho, Moscow ID 83843, Physics Department, University of Idaho, Moscow ID 83843, Environmental Biotechnology Institute, University of Idaho, Moscow, ID 83844, Physics Department, University of Idaho, Moscow, Idaho 83844, TRIUMF / UBC, 5CSNSM-IN2P3-CNRS, Universit\'e Paris 11, University of Manitoba, Texas A\&M, U. Manitoba, Tel Aviv U., U. British Columbia, Universidad de Pa\'is Vasco, Department of Physics, University of Idaho, Moscow, Idaho 83844-0903, University of Idaho, Boise State University, Idaho State University, NASA Ames Research Center