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Stopping Power. The linear stopping power S for charged particles in a given absorber is simply defined as the differential energy loss for that particle within the material divided by the corresponding differential path length: S = – dE / dx ………………………. (1.3)
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Stopping Power • The linear stopping power S for charged particles in a given absorber is simply defined as the differential energy loss for that particle within the material divided by the corresponding differential path length: • S = – dE / dx………………………. (1.3) • The value of – dE / dx along a particle track is also called specific energy lossor rate of energy loss. For particles with a given charge state, S increases as the particle velocity is decreased
Stopping Time • The time required to stop a charged particle in an absorber can be deduced from its range and average velocity. For nonrelativistic particles of mass m and kinetic energy E, the velocity is, • ... (1.6) • Where mA is the particle mass in atomic mass units and E is particle energy in MeV. If we assume that the average particle velocity as it slow down is v = Kv, where v = • and evaluated at initial energy, then the stopping time T can be calculated from the range R as • …(1.7)
Energy Loss in Thin Absorbers • For thin absorbers or detectors that are penetrated by a given charged particle, the energy deposited within the absorber can be calculated from • ∆E = (- dE/dx)avg. t ……………(1.8) • Where t is the absorber thickness and (- dE/dx)avg is the average linear stopping power. If the energy loss is small, the stopping power does not change much and it can be approximated to its value at the incident particle energy.
Photons, also called X-rays or rays are electromagnetic radiation, are considered as particles that travel with the speed of light c and they have zero rest mass and charge. • There is no clear destination between X-rays and γ–rays. The term X-rays is applied generally to photons with E < 1 MeV. Gammas are the photons with E > 1 MeV. X-rays are generally produced by atomic transitions such as excitation and ionizations. Gamma rays are emitted in nuclear transitions. Photons are also produced in bremsstrahlung, by accelerating or decelerating charged particles. X-rays and γ-rays emitted by atoms and nuclei are monoenergetic; bremsstrahlung has a continuous energy spectrum. • There are several possible interactions of photons, but the three most important ones are: the photoelectric effect, Compton scattering and pair production.
A) The Photoelectric Effect • The energy of the gamma-ray photon is completely transferred to an orbital electron which is ejected from its atom (figure 1.2). The gamma-ray no longer exists after the collision. The ejected electron then causes ionization until it loses its energy, and is captured by an atom. The photoelectric effect is more likely to occur when the photon energy is low, i.e. below 0.5 MeV and the absorber is a heavy material
B) Compton Scattering • Higher energy photons may lose only part of their energy to the atomic electron which is again ejected from its atom (figure 1.3). This electron goes on to create ionization. The remaining energy is taken up by another photon of reduced energy which is scattered in a new direction. The new photon will either be absorbed by a photoelectric effect, or if the energy is still high by further Compton scattering. • Compton scattering occurs in all materials and predominantly with photons of medium energy, i.e. about 0.5 to 3.5 MeV.
C) Pair Production • Gamma-ray photons with energy greater than 1.02 MeV may interact with a nucleus to form an electron-positron pair. This amount of energy is just sufficient to provide the rest masses of the electron and positron (0.51 MeV each). Excess energy will be carried away equally by these two particles which produce ionization as they travel in the material. The positron is eventually captured by an electron and annihilation of the two particles occurs. This results in the release of two photons each of 0.51 MeV known as annihilation radiation. These two photons then lose energy by Compton scattering or the photoelectric effect. Pair production is illustrated in Figure 1.4
D) Coherent scattering • In addition to Compton scattering, another type of scattering can occur in which the gamma-ray photon interacts coherently with all the electrons of an absorber atom. This coherent scattering or Raleigh scattering process neither excites nor ionizes the atom, and the gamma-ray photon retains its original energy after the scattering event. Because virtually no energy is transferred, this process is often neglected in basic discussions of gamma-ray interactions. However, the direction of the photon is changed in coherent scattering. The probability of coherent scattering is significant only for low photon energies (typically below a few hundred keV for common materials) and is most prominent high-Z absorbers.
Gamma-ray attenuation • If monoenergetic gamma-rays are collimated into a narrow beam and allowed to strike a detector after passing through an absorber of variable thickness, the result should be simple exponential attenuation of the gamma rays. Each of the interaction processes removes the gamma-rays photon from the beam either by absorption or by scattering away from the detector direction and can be characterized by a fixed probability of occurrence per unit path length in the absorber. The sum of these probabilities is simply the probability per unit path length that the gamma-ray photon is removed from the beam. • µ = Ί (photoelectric) + σ (Compton) + ĸ (pair) [1.3] • And is called the linear attenuation coefficient. The number of transmitted photons I is then given in terms of the number without an absorber I0 as • The gamma-ray photon can also be characterized by their mean free path λ, defined as the average distance traveled in the absorber before an interaction takes place.
Directly ionizing and indirectly ionizing radiations • Ionizing radiations can be divided into two major groups, the first consists of charged particles such as electrons, protons, alpha particles and heavy ions, which have sufficient energy to cause ionization on collision and do so by coulomb interactions with electrons in the absorbing material. Such radiations are directly ionizing. This situation may be contrasted with indirectly ionizing radiations, which are uncharged. Incident photons (X-rays and γ-rays) release secondary electrons, while incident neutrons release secondary charged recoil nuclei, which in turn produce most of the excitations and ionizations in the absorber. The major difference between the interactions of directly ionizing and indirectly ionizing radiations is that the latter experience relatively few collisions, each involving a large energy loss, whereas the former undergo a very large number of interactions, with little loss of energy each time. Indeed, charged particles are often considered to lose energy and so slow down in a continuous manner.
