30. Passage of particles through matter 1 - Particle Data Group

More documents

Recommendations

Info

20 30. Passage of particles through matter At very high energies and except at the high-energy tip of the bremsstrahlung spectrum, the cross section can be approximated in the “complete screening case” as [40] dσ/dk = (1/k)4αr 2 e{( 4 4 3 − 3y + y2 )[Z2 (Lrad − f(Z)) + Z L ′ rad ] + 1 9 (1 − y)(Z2 + Z)} , (30.27) where y = k/E is the fraction of the electron’s energy transfered to the radiated photon. At small y (the “infrared limit”) the term on the second line ranges from 1.7% (low Z) to 2.5% (high Z) of the total. If it is ignored and the first line simplified with the definition of X0 given in Eq. (30.24), we have dσ dk = A X0NAk � 4 4 3 − 3y + y2� . (30.28) This cross section (times k) is shown by the top curve in Fig. 30.12. (X 0 N A /A) ydσ LPM /dy 1.2 0.8 0.4 0 100 GeV 10 GeV 1 TeV 10 TeV 100 TeV Bremsstrahlung 1 PeV 10 PeV 0 0.25 0.5 0.75 1 y = k/E Figure 30.12: The normalized bremsstrahlung cross section k dσLPM/dk in lead versus the fractional photon energy y = k/E. The vertical axis has units of photons per radiation length. This formula is accurate except in near y = 1, where screening may become incomplete, and near y = 0, where the infrared divergence is removed by the interference of bremsstrahlung amplitudes from nearby scattering centers (the LPM effect) [42,43] and dielectric suppression [44,45]. These and other suppression effects in bulk media are discussed in Sec. 30.4.5. With decreasing energy (E < ∼ 10 GeV) the high-y cross section drops and the curves become rounded as y → 1. Curves of this familar shape can be seen in Rossi [2] (Figs. 2.11.2,3); see also the review by Koch & Motz [46]. Except at these extremes, and still in the complete-screening approximation, the number of photons with energies between kmin and kmax emitted by an electron June 18, 2012 16:19
dE/dx × X 0 (MeV) 200 100 70 50 40 30 20 30. Passage of particles through matter 21 Copper X 0 = 12.86 g cm −2 E c = 19.63 MeV Rossi: Ionization per X 0 = electron energy Brems ≈ E Total Ionization Exact bremsstrahlung Brems = ionization 10 2 5 10 20 50 100 200 Electron energy (MeV) Figure 30.13: Two definitions of the critical energy Ec. E c (MeV) 400 200 100 50 20 10 5 610 ________ MeV Z + 1.24 Solids Gases 710 MeV ________ Z + 0.92 H He Li Be B CNO Ne Fe Sn 1 2 5 10 Z 20 50 100 Figure 30.14: Electron critical energy for the chemical elements, using Rossi’s definition [2]. The fits shown are for solids and liquids (solid line) and gases (dashed line). The rms deviation is 2.2% for the solids and 4.0% for the gases. (Computed with code supplied by A. Fassó.) travelling a distance d ≪ X0 is Nγ = d � 4 3 ln � � kmax X0 kmin − 4(kmax − kmin) 3E June 18, 2012 16:19 + k2 max − k2 min 2E2 � . (30.29)
Page 1 and 2: 30. Passage of particles through ma
Page 15 and 16: (Δp/x) / dE/dxmin 1.00 0.95 0.90 0
Page 19: 30. Passage of particles through ma
Page 23 and 24: Cross section (barns/atom) 1 Mb 1 k
Page 31 and 32: 30.6. Muon energy loss at high ener
Page 33 and 34: E μc (GeV) 4000 2000 1000 700 400
Page 37 and 38: dS/d( ω), differential yield per i

30. Passage of particles through matter 1 - Particle Data Group

Create successful ePaper yourself

Delete template?

Save as template?