rpp2010-rev-passage-particles-matter

rpp2010-rev-passage-particles-matter - 27 Passage of...

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27. Passage of particles through matter 1 Revised January 2010 by H. Bichsel (University of Washington), D.E. Groom (LBNL), and S.R. Klein (LBNL). 27. PASSAGE OF PARTICLES THROUGH MATTER. .................... 2 2 7 . 1 .N o t a t i o n ................... 2 27.2. Electronic energy loss by heavy parti- c l e s ...................... 3 27.2.1. Moments and cross sections . . . . . . . . 3 27.2.2. Stopping power at intermediate e n e r g i e s ................... 4 27.2.3. Energy loss at low energies . . . . . . . . . 8 2 7 . 2 . 4 .D e n s i t ye ± e c t............... 1 0 27.2.5. Energetic knock-on electrons ( δ r a y s )..................... 1 1 27.2.6. Restricted energy loss rates for relativistic ionizing particles . . . . . . . . . . 11 27.2.7. Fluctuations in energy loss . . . . . . . . . 12 27.2.8. Energy loss in mixtures and com- pounds . . . . . . . . . . . . . . . . . . . . 13 2 7 . 2 . 9 .I o n i z a t i o ny i e l d s.............. 1 4 27.3. Multiple scattering through small a n g l e s ..................... 1 5 27.4. Photon and electron interactions in m a t t e r ..................... 1 7 27.4.1. Radiation length . . . . . . . . . . . . . 17 27.4.2. Energy loss by electrons . . . . . . . . . . 18 2 7 . 4 . 3 .C r i t i c a le n e r g y .............. 2 2 27.4.4. Energy loss by photons . . . . . . . . . . 24 27.4.5. Bremsstrahlung and pair produc- t i o na tv e r yh i g he n e r g i e s........... 2 4 27.4.6. Photonuclear and electronuclear interactions at still higher energies . . . . . . . 27 27.5. Electromagnetic cascades . . . . . . . . . . . 27 27.6. Muon energy loss at high energy . . . . . . . . 30 27.7. Cherenkov and transition radiation . . . . . . . 32 K. Nakamura et al. ,JPG 37 , 075021 (2010) (http://pdg.lbl.gov) July 30, 2010 14:36
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2 27. Passage of particles through matter 27. PASSAGE OF PARTICLES THROUGH MATTER 27.1. Notation Table 27.1: Summary of variables used in this section. The kinematic variables β and γ have their usual meanings. Symbol DeFnition Units or Value α ±ine structure constant 1 / 137 . 035 999 11(46) ( e 2 / 4 π± 0 ~ c ) M Incident particle mass MeV/ c 2 E Incident part. energy γMc 2 MeV T Kinetic energy MeV m e c 2 Electron mass × c 2 0 . 510 998 918(44) MeV r e Classical electron radius 2 . 817 940 325(28) fm e 2 / 4 0 m e c 2 N A Avogadro’s number 6 . 022 1415(10) × 10 23 mol 1 ze Charge of incident particle Z Atomic number of absorber A Atomic mass of absorber g mol 1 K/A 4 πN A r 2 e m e c 2 /A 0 . 307 075 MeV g 1 cm 2 for A = 1 g mol 1 I Mean excitation energy eV ( Nota bene! ) δ ( βγ ) Density e²ect correction to ionization energy loss ~ ω p Plasma energy p ρ ± Z/A ²× 28 . 816 eV ( p 4 e r 3 e m e c 2 )( ρ in g cm 3 ) N e Electron density (units of r e ) 3 w j Weight fraction of the j th element in a compound or mixture n j number of j th kind of atoms in a compound or mixture —4 αr 2 e N A (716.408 g cm 2 ) 1 for A =1gmo l 1 X 0 Radiation length g cm 2 E c Critical energy for electrons MeV E μc Critical energy for muons GeV E s Scale energy p 4 π/α m e c 2 21.2052 MeV R M Moli` ere radius g cm 2 July 30, 2010 14:36
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27. Passage of particles through matter 3 27.2. Electronic energy loss by heavy particles [1–32] 27.2.1. Moments and cross sections : The electronic interactions of fast charged particles with speed v = βc occur in single collisions with energy losses E [1], leading to ionization, atomic, or collective excitation. Most frequently the energy losses are small (for 90% of all collisions the energy losses are less than 100 eV). In thin absorbers few collisions will take place and the total energy loss will show a large variance [1]; also see Sec. 27.2.7 below. For particles with charge
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