PHYS 571 Radiation Physics

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1 PHYS 571 Radiation Physics Prof. Gocha Khelashvili login

2 Interaction of Electrons with Matter

3 The Plan Interactions of Electrons with Matter Energy-Loss Mechanism Collisional Stopping Power Restricted Stopping Power Linear Energy Transfer Specific Ionization Multiple Coulomb Scattering Angular Scattering Power Energy Loss by Radiation - Bremsstralung Radiative Stopping Power Range of Electrons Bremsstralung Yield Slowing Down Time Energy Straggling Range Straggling

4 Energy Loss Mechanism Similarity with heavy charged particles: Beta particles (electrons or positrons) can also excite and ionize atoms through Coulomb force interactions with atomic electrons. Difference from heavy charged particles: Beta particles are much lighter (about 2000 times) and thus same magnitude of Coulomb force can result in very different outcome. Main differences are: 1. Relativistic effects become important at relatively low kinetic energies. 2. Collisions with orbital electrons may result in large energy transfers (up to 50% of the incident for electrons and up to 100% of the incident energy for positrons. 3. They may also result in elastic and inelastic scattering. 4. Collisions of electrons with nuclei of the absorber may result is radiative loss of energy (bremsstrahlung production). Depending on the light charged particle incident energy, radiation loss may actually exceed the collision loss.

5 Collision and Radiative Stopping Powers Radiative Stopping Power results from charged particle Coulomb interaction with the nuclei of the absorber. Only light particles (electrons and positions) experience appreciable energy losses through these interactions, referred as bremsstrahlung interactions Collision Stopping Power results from charged particle Coulomb interaction with orbital electrons of the absorber. Interaction results in energy transfer from charged particle to orbital electrons, i.e. excitation and ionization of absorber atom E = E + E tot rad col S = S + S tot rad col

6 Soft and Hard Collisons Soft (distant) energy transfers E to an orbital electron E < η Hard (close) energy transfers E to an orbital electron E η

7 Collision Stopping Power E max 1 E = 2 E K K - Electrons - Positrons dσ col Moller Scattering - ee ee d( E) Bhabha Scattering - ee ee + +

8 Collision Stopping Power Moller Scattering - ee ee + Bhabha Scattering - ee ee + + +

9 Collision Stopping Power

10 Collision Linear Stopping Power ± de 4πk0 z en mc e τ τ + 2 ± = ln F ( β ) dx col mec β 2I with τ = K mc e β τ Electrons - F ( β) = 1 + ( 2τ + 1) ln β Positrons - F ( β ) = ln τ + 2 τ + 2 τ + 2 ( ) ( ) 2 3

11 Collision, Radiative and Total Stopping Powers Stot = Srad + Scol

12 Collision Stopping Power Dependence on Stopping Medium ± Z 1 ± Scol F 2 ( τ) 2ln I δ A υ ± 1. The factor Z A makes S dependent on the number of electrons per unit mass of the absorber. Z A= 1 col for hydrogen; 0.5 for low Z absorbers; then drops to 0.4 for high Z absorbers. ± 2. The ln I term decreases S with increasing Z, since I increases almost linearly with increasing Z. col

13 Radiative Stopping Power N S = Nσ E or S = αrz B E A N = N A - number of atoms per unit mass σ a rad A 2 2 A rad a rad i rad e rad i - total bremsstrahlung production cross section 2 i = K + e - total kinetic energy of light charged particle E E mc E K - initial kinetic energy of the light charged particle α - fine structure constant

14 Radiative Stopping Power Dependence on Stopping Medium 2 2 N A 1/3 Srad αrz e + Z + A ( τ 1) ln ( 183 1/18) Z A S Z 2 1. The factor causes an increase in rad for higher of absorber.

15 Total Stopping Power Dependence on Stopping Medium Stot = Srad + Scol 1. The crossover between radiative and collision stopping powers occures at a critical kinetic energy ( ) E where the two stopping powers are equal, i.e. S = S K crit rad col number Z. for a given absorber with atomic 800 MeV ( EK ) crit Z 2. For high Z absorbers the dominance of radiative losses over collision losses starts at lower kinetic energ Z Z E K crit is at 10 MeV, well in the relativistic region. 3. The ratio of collision to radiative power at a given electron kinetic energy can be estimated as follows: ies than in low absorbers. However, even in higher media such as lead and uranium ( ) Srad 800 MeV 1600mc e = = S ZE ZE col K K 2

16 Concept of Restricted Stopping Power

17 Concept of Restricted Stopping Power The choice of energy threshold at hand depends on the problem In dosimetry typical measurements involve air-filled ionization chamber with typical electrod separation of 2 mm. Since range of 10 kev electrons in air is about 2 mm 10 kev

18 Concept of Restricted Stopping Power 2 2 2γ mv E = 1 + 2γ mm + m M max For heavy charged particles 1 E - For electrons and E for positrons 2 K K

19 Concept of Restricted Stopping Power

20

21

22 Concept of Restricted Stopping Power 1 ρ F S max de Z d col Q Q min max 2 e 2 τ τ 2 τ 2 2 ( β) F( τ, ) = 1 β + ln 4 ( τ ) τ ( 2τ + 1) ln 1 ( τ + 1) col σ = N A Q dq Q dx A = = dq m c 1 dl L = ρ dx - Restricted Collision Stopping Power 2 δ - ray E δ > e ±

23 From Cosmic Rays to Treatment Room Cosmic rays come from outside solar system but generally from within our Milky Way galaxy. Atomic nuclei stipped away of their electrons during their high-speed passage through the galaxy. They have been accelerated nearly to the speed of light probably by blast waves of supernova remnants. Discovered in 1912 by Victor Hess (1936 Nobel Prize). 90% Protons 9% α-particles 1% electrons

24 From Cosmic Rays to Treatment Room

25 Differential Scattering Cross Section for Single Scattering

26 Total Scattering Cross Section for Single Scattering

27 Mean Square Scattering Angle

28 Mollière Multiple Scattering

29 Mollière Multiple Scattering

30 Mollière Multiple Scattering Heavy Charged Particles Electrons

31 Mass Angular Scattering Power

32 Mass Angular Scattering Power

33 Bragg Peak

34 Range and Bremsstrahlung Yield B = E 0 1 Srad ( E) de E S ( E) 0 0 tot R = E 0 0 de S ( E) tot - Range - Bremss. Yield - fraction of radiated energy

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