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24. PHOTON and ELECTRON INTERACTIONS with MATTER Photon Attenuation Length Photon Pair Conversion Probability

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24. PHOTON and ELECTRON INTERACTIONS with MATTER Photon Attenuation Length Photon Pair Conversion Probability 152 24. Photon and electron interactions with matter 24. PHOTON AND ELECTRON INTERACTIONS WITH MATTER Revised April 1998 by D.E. Groom (LBNL). Photon Attenuation Length 100 10 ) Sn 2 1 Fe Pb cm / Si (g 0.1 λ H C 0.01 0.001 Absorption length –4 10 –5 10 –6 10 10 eV 100 eV 1 keV 10 keV 100 keV 1 MeV 10 MeV 100 MeV 1 GeV 10 GeV 100 GeV Photon energy Figure 24.1: The photon mass attenuation length (or mean free path) λ =1/(µ/ρ) for various elemental absorbers as a function of photon energy. The mass attenuation coefficient is µ/ρ,whereρis the density. The intensity I remaining after traversal of thicknessP t (in mass/unit − ≈ area) is given by I = I0 exp( t/λ). The accuracy is a few percent. For a chemical compound or mixture, 1/λeff elements wZ /λZ,where wZ is the proportion by weight of the element with atomic number Z. The processes responsible for attenuation are given in Fig. 24.4. Since coherent processes are included, not all these processes result in energy deposition. The data for 30 eV <E<1 keV are obtained from http://www-cxro.lbl.gov/optical constants (courtesy of Eric M. Gullikson, LBNL). Thedatafor1keV<E<100 GeV are from http://physics.nist.gov/PhysRefData, through the courtesy of John H. Hubbell (NIST). Photon Pair Conversion Probability 1.0 0.9 Figure 24.2: Probability P that a photon interaction will result in conversion to an e+e− 0.8 NaI pair. Except for a few-percent contribution from photonuclear absorption around 10 or 20 0.7 Ar C MeV, essentially all other interactions in this Pb energy range result in Compton scattering off 0.6 H2O an atomic electron. For a photon attenuation H P 0.5 Fe length λ (Fig. 24.1), the probability that a given photon will produce an electron pair 0.4 (without first Compton scattering) in thickness t of absorber is P [1 − exp(−t/λ)]. 0.3 0.2 0.1 0.0 1 2 5 10 20 50 100 200 500 1000 Photon energy (MeV) 24. Photon and electron interactions with matter 153 Contributions to Photon Cross Section in Carbon and Lead Carbon (Z = 6) Lead (Z = 82) − σ − σ 1 Mb experimental tot experimental tot 1 Mb σ p.e. σ p.e. σ 1 kb coherent 1 kb σ coherent κ σ N Cross section, barns/atom Cross section, barns/atom incoh 1 b 1 b κ κ e N σ σ σ κ nuc incoh nuc e 10 mb 10 mb 10 eV 1 keV 1 MeV 1 GeV 100 GeV 10 eV 1 keV 1 MeV 1 GeV 100 GeV Photon Energy Photon Energy Figure 24.3: Photon total cross sections as a function of energy in carbon and lead, showing the contributions of different processes: σp.e. = Atomic photo-effect (electron ejection, photon absorption) σcoherent = Coherent scattering (Rayleigh scattering—atom neither ionized nor excited) σincoherent = Incoherent scattering (Compton scattering off an electron) κn = Pair production, nuclear field κe = Pair production, electron field σnuc = Photonuclear absorption (nuclear absorption, usually followed by emission of a neutron or other particle) From Hubbell, Gimm, and Øverbø, J. Phys. Chem. Ref. Data 9, 1023 (80). Data for these and other elements, compounds, and mixtures may be obtained from http://physics.nist.gov/PhysRefData. The photon total cross section is assumed approximately flat for at least two decades beyond the energy range shown. Figures courtesy J.H. Hubbell (NIST). Fractional Energy Loss for Electrons and Positrons in Lead 0.20 Positrons Lead (Z = 82) Figure 24.4: Fractional energy loss per radiation length in lead as a function of electron or positron Electrons energy. Electron (positron) scattering is considered ) 1.0 ) 1 0.15 as ionization when the energy loss per collision is 1 − 0 − below 0.255 MeV, and as Moller (Bhabha) scattering g X Bremsstrahlung ( 2 when it is above. Adapted from Fig. 3.2 from Messel dx dE (cm and Crawford, Electron-Photon Shower Distribution 0.10 1 E Ionization Function Tables for Lead, Copper, and Air Absorbers, − − Pergamon Press, 1970. Messel and Crawford use 0.5 Møller (e ) X (Pb) = 5.82 g/cm2, but we have modified the + 0 Bhabha (e ) 0.05 figures to reflect the value given in the Table of Atomic and Nuclear Properties of Materials, namely X0(Pb) 2 Positron = 6.4 g/cm . The development of electron-photon annihilation cascades is approximately independent of absorber 0 1 10 100 1000 when the results are expressed in terms of inverse E (MeV) radiation lengths (i.e., scale on left of plot)..
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