Radiation Physics PHYS /251. Prof. Gocha Khelashvili

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1 Radiation Physics PHYS /251 Prof. Gocha Khelashvili

3 Interaction of Radiation with Matter: Heavy Charged Particles Directly and Indirectly Ionizing Radiation Classification of Indirectly Ionizing Radiation Radiation Quantities and Units Dose in Water for Various Radiation Beams Concept of Interaction Cross-Section Interaction of Charged Particles with Matter

4 Directly Ionizing Radiation Light charged particles (electrons and positrons) Heavy charged particles (protons, deutrons and alpha particles) Heavier charged particles (e.g. carbon-14)

5 Types and Sources of Directly Ionizing Radiation Heavy charged particles are produced for use in radiotherapy through acceleration of nuclei or ions in cyclotrons, synchrotrons or heavy particle linacs 3 4 Proton: H; Deuteron: H; Triton: H; Helium-3: He; α-particle: He Heavier Charged Particles: Heavier charged particles are nuclei or ions of heavier atoms such as carbon-12: C, nitrogen-14: N, or neon-20: Ne Pions Pions ( π -mesons) are produced in nuclear reactions of energetic electrons or protons striking nuclei.

6 Types and Sources of Directly Ionizing Radiation Electrons released in the medium by photoelectric effect are referred to as photoelectrons. Electrons released in the medium by Compton effect are referred to as Compton or recoil electrons. Electrons produced in the medium by pair production interaction in the field of the nucleus or in the field of an orbital are referred to as pair production electrons. β Electrons emitted from nuclei by radioactive decay are referred to as beta particles. Electrons produced by linear accelerators (linacs), betatrons or microtrons for use in radiotherapy with kinetic energies typically in the range from 4 MeV to 30 MeV are referred to as megavoltage electrons. Electrons produced through Auger effect are referred to as Auger electrons, Coster-Kronig electrons or super Coster-Kronig electrons. Electrons produced by charged particle collisions are of interest in radiation dosimetry and referred to as δ -rays.

7 Classification of Indirectly Ionizing Radiation Characteristic (fluorescent) X-rays - result from electron transitions between atomic shells Bremsstrahlung photons - result from electron-nucleus Coulomb interactions Gamma ray s - result from nuclear transitions Annihilation quanta - result from positron-electron annihilation

8 Absorption of Energy

9 Dose in Water for Various Radiation Beams

10 Radiation Quantities and Units

11 Energy Loss Mechanisms

12 Interactions of Charged Particles "Soft" Collisions - b(impact parameter) a(atomic radius): Particle ineracts with whole atom atom disturbed, excited or valence electron ejected

13 Interactions of Charged Particles Hard "Knock-On" Collision - b a: Particle interacts with single atomic electron Electron ejected as a δ -ray, when inner-shell electron is ejected characteristic x-rays or Auger electron can be emitted

14 Interactions of Charged Particles Coulomb-Force Interaction with External Nuclear Field b a

15 General Aspects of Stopping Power Kinetic Energy of Charged Particle Transferred to Medium Transferred to Photons Collision Losses Radiation Losses Each is characterized by σ - Cross Section (Probability of Interaction)

16 General Aspects of Stopping Power The rate of energy loss (MeV) per path length (cm) expressed as de - - Linear Stopping Power dx de N E σ - = i ni ni dx i n Quantum Mechanics - expectation value of energy loss rate per unit path length σ ni E N i ni - cross section of given energy loss - energy loss incement for interaction - number density of atoms n

17 Mass Stopping Power Mass Stopping Power (Tabulated) de de S = - = - ρdx ρdx YZE,, SI system unit for mass stopping power: J m kg 2 1 Common unit for mass stopping power: MeV cm g 2 1

18 Mass Stopping Power

19 Radiation (Nuclear) Stopping Power

20 Radiation (Nuclear) Stopping Power

21 Radiation (Nuclear) Stopping Power

22 Radiation (Nuclear) Stopping Power

23 Radiation (Nuclear) Stopping Power

24 Collision Stopping Power for Heavy Charged Particles

25 Collision Stopping Power for Heavy Charged Particles

26 Bohr s Semiclassical Stopping Power Coulomb interation between the heavy charged particle and orbital electron M m e

27 Collision Stopping Power for Heavy Charged Particles

28 Collision Stopping Power for Heavy Charged Particles

29 Collision Stopping Power for Heavy Charged Particles

30 Collision Stopping Power for Heavy Charged Particles

31 Minimum Energy Transfer

32 Mean Ionization / Excitation Potential

33 Mean Ionization / Excitation Potential 19.0 ev, Z = 1 (Hydrogen) I = Z ev, 2 Z Z ev, Z > 13 For compound mixture: nln I= NZ ln I n - total # of electrons in cm N - # of atoms with Z and excitation energy I in cm -3 i i i i i i i -3

34 Mean Ionization / Excitation Potential

35 Maximum Energy Transfer in a Single Collision Energy Conservation: MV = MV1 + mυ Momentum Conservation: MV = MV + mυ 1 Goal is to find: 1 1 E = MV MV max 1

36 Maximum Energy Transfer in a Single Collision Momentum Conservation M υ = V m ( V ) 1 Energy Conservation max 1 υ ( 1 ) 1 M M m E = MV MV = m = m V V V = V m M + m M m 2 4mM 1 Ema x Emax = MV MV = MV M V = M + m + ( M m) E

37 Maximum Energy Transfer in a Single Collision Nonrelativistic expression for energy loss: E = 4mM ( M + m) max 2 E If m= M (electron or positron is incident) E = E max 4m( 207m) ( ) E = = E m m max For muon M 207 m % 2 Relativistic expression for energy loss: 2 2 2γ mv E = 1 + 2γ mm + m M max 2 2 γ m Ultra-relativistic 1 expression for energy loss: Emax = 2γ mv = 2γ mc β M where 1 γ = and β = 2 1 β V c

38 Maximum Energy Transfer in a Single Collision Emax MeV 100 Emax / E

39 Maximum Energy Transfer

40 Bohr Semiclassical Stopping Power

41 Bohr Semiclassical Stopping Power

42 Bohr Semiclassical Stopping Power

43 Bohr Semiclassical Stopping Power

Units and Definition

RADIATION SOURCES Units and Definition Activity (Radioactivity) Definition Activity: Rate of decay (transformation or disintegration) is described by its activity Activity = number of atoms that decay