Interactions of Particles and Radiation with Matter

Abstract

Main types of interactions of charged particles and photons are briefly described. For charged particles, we present basic formulas for energy losses by ionization and excitation, fluctuations of ionization losses, δ electrons, channeling, multiple scattering, and bremsstrahlung. We consider photoelectric effect, Compton effect, and electron–positron pair production for photons. Also discussed are nuclear interactions of hadrons with matter as well as neutrino interactions.  Introduction A knowledge of phenomena, which occur when particles and radiation interact with matter, is necessary for development and usage of particle detectors, radiation protection,material studies with the help of ionizing radiation, etc. In this chapter main types of interactions of charged particles, photons, and neutrinos are briefly described. There is an extensive literature devoted to interactions of particles and radiation with matter. A brief review and further references are given in Amsler et al. (), while the detailed consideration of the main relevant issues can be found in the classical book of Rossi ().  Penetration of Charged Particles ThroughMatter The common phenomenon for all charged particles, which causes a change of their energy and direction in matter, is the electromagnetic interactions with electrons and nuclei. Electromagnetic interactions are responsible for particle scattering, ionization and excitation of atoms, bremsstrahlung, Cherenkov and transition radiations. It should be noted that Cherenkov and transition radiations result in a negligible energy loss and do not change a direction of particle motion. The main contribution to the energy loss comes from ionization and bremsstrahlung while the change of the particle trajectory is mostly caused by collisions with nuclei. . Energy and Angular Spectra of Delta Electrons When an incident charged particle collides with an electron at rest, a maximum energy transfer is emax = me P M +me + Eme/c , () whereM, P, and E are the mass, momentum, and total energy of the incident particle whileme is the electron mass. The following approximations are useful in particular cases: γ ∼  emax [MeV] ≈ (γ − )  ≪ γ ≪ M/(me) emax [MeV] ≈ γ () γ ≫ M/(me) emax [MeV] ≈ E , where γ = E/Mc. Interactions of Particles and Radiation with Matter   Recoil electrons are usually referred to as δ electrons. The recoil angle, θδ , is related to the δ-electron kinetic energy (i.e., equivalent to the energy loss of the incident particle): cos θδ = E +mec P √ e e + mec . () The collision of the heavy incident particle with a free electron can be approximately described by the well-known Rutherford formula dσ dΩ = zr e  ( mec βcpc )   sin(θc/) , () where βc, pc, and θc are the electron velocity, momentum, and scattering angle in the centerof-mass system, z is the charge of the incident particle in units of the electron charge, and re – classical electron radius.The quantities pc and θc can be easily related to the δ-electron kinetic energy e: e = pc( − cos θc) me ; de = − pc me d cos θc; pc = meemax  . () Taking into account these relations, we obtain the differential cross section dσ/de: dσ = πzr emec βe de . () When the incident particle is much heavier than the electron, we can take the electron velocity βc equal to the velocity of the incident particle β in the laboratory frame. Then the energy distribution of δ electrons is dn de dx = NA Z A dσ de = . Z A  βe , () where Z and A are the atomic number and atomic mass, respectively.The thickness of material is measured in units of g/cm. To take into account the electron spin, we have to use the formula for the Mott cross section (Mott ) instead of > Eq. : dσ dΩ = zr e  ( mec βcpc )   sin(θc/) ( − β c sin  (θc/)) . () This modifies the energy distribution to dn de dx = . Z A  βe ( − β e emax ) . () The formulas for the δ-electron energy distributions in the case of the incident electron, positron, and heavy spin-/ particle are given in Rossi (). . Energy Loss by Ionization and Excitation The total energy transferred by the initial particle to δ electrons with the kinetic energy e, exceeding a certain emin, can be found by integrating > Eq. . However, emin cannot approach  since electrons are assumed to be free in this expression.The accurate calculations in the Born   Interactions of Particles and Radiation with Matter approximation result in the Bethe–Bloch equation (Bethe , ; Bloch ) for the specific energy loss by a heavy spinless particle: