Interaction Between Ionizing Radiation And Matter, Part 2 Charged-Particles Audun Sanderud

1. Department of PhysicsUniversity of Oslo Interaction Between Ionizing Radiation And Matter, Part 2 Charged-ParticlesAudun Sanderud

2. Department of PhysicsUniversity of Oslo Ionization Excitation Excitation / ionization • Incoming charged particle interact with atom/molecule: • Ion pair created from ionization

3. m2, v2 c Department of PhysicsUniversity of Oslo q m1, v m2 m1, v1 Elastic collision • Interaction between two particles with conservation of kinetic energy ( and momentum): • Classic mechanics give:

4. Department of PhysicsUniversity of Oslo Elastic collision(2) • These equations gives the maximum transferred energy:

5. Department of PhysicsUniversity of Oslo Elastic collisions(3) • Proton(#1)-electron(#2):qmax=0.03o, Emax=0.2 % T0 • Electron(#1)-electron(#2):qmax=90o, Emax=100 % T0

6. Department of PhysicsUniversity of Oslo Elastic collisions-cross section • Rutherford proved that the cross section of elastic scattering is:  Small scattering angels most probable • Differentiated by the energy  Small energy transferred most probable

7. Department of PhysicsUniversity of Oslo dx T0 T0-dT nv targets per volume unit Stopping power • Stopping power, (dT/dx): the expectation value of the rate of energy loss per unit of pathlength. Dependent on: -type of charged particle -its kinetic energy -the atomic number of the medium

8. Department of PhysicsUniversity of Oslo Impact parameter • The charged particle collision is a Coulomb-force interaction • Most important: the interaction with electrons • The impact parameter b useful versus the classic atomic radius a

9. Department of PhysicsUniversity of Oslo Soft collisions • b>>a: particle passes an atom in a large distance • Small energy transitions to the atom • The result is excitations (dominant) and ionization;amount energy transferred range from Emin to a certain energy H • Hans Bethe did quantum mechanical calculations on the stopping power of soft collision in the 1930 • We shall look at the results from particles with much larger mass then the electron

10. Department of PhysicsUniversity of Oslo Soft collisions(2) r0: classic electron radius = e2/4pe0mec2I: mean excitation potentialb: v/c z: charge of the incoming particler: Density of the medium NAZ/A: Number of electrons per gram in medium H: Maximum transferred energy at soft collision

11. Department of PhysicsUniversity of Oslo Soft collisions(3) • The quantum mechanic effects are specially seen in the excitation potential I Mean excitation potential, I/Z [eV] Atomic number, Z • High Z – small transferred energy less likely

12. Department of PhysicsUniversity of Oslo Hard collisions • b<<a: particle passes trough the atom • Large (but few) energy transactions to single electron • Amount energy transferred range from H to Emax • Can be seen as an elastic collision between free particles (bonding energy nelectable)

13. Department of PhysicsUniversity of Oslo Collisions stopping power • The total collision stopping power is then (soft + hard): • Important: increase with z2, decrease with v2, not dependent on particle mass

14. Department of PhysicsUniversity of Oslo Sc/r in different media • I and electron density (ZNA/A) gives the variation

15. Department of PhysicsUniversity of Oslo SC for electrons/positrons • Electron-electron scattering more complicated;interaction between identical particles • Sc,soft/r: Bethe’s soft coll. formula • Sc,hard/r: electron-elektron; Møller cross section positron-electron; Bhabha cross section The characteristics similar to that of heavy particles

16. Department of PhysicsUniversity of Oslo Shell correction • The approximation used in the calculations of SC assume v>>vatomic electron • When v~vatomic electron no ionizations will occur • Occur first in the K-shell - highest atomic electron speed • Shell correction C/Z handles this, and reduce SC/r • C/Z depend on particle velocity and medium

17. Department of PhysicsUniversity of Oslo Density-effect correction • Charged particles polarizes the medium Charged (+z) particle • Weaker interaction with distant atoms because of the reduction of the Coulomb force field • • Polarization increase with (relativistic) speed • But: polarization not important at low r • Most important for electrons / positrons

18. Department of PhysicsUniversity of Oslo Density-effect correction(2) • Density-effect correction dreduces Sc/r in solid and liquid elements • Sc/r (water vapor) > Sc/r (water) Dashed curves: Sc without d

19. Department of PhysicsUniversity of Oslo Charged particle atomic electron Radiative stopping power • When charged particles are accelerated by the Coulomb force from atomic electrons or nucleus photons can be emitted; Bremsstrahlung • The Lamor equation (classic el.mag.) denote the radiation power from an acceleration, a, of a charged particle:e0: Permittivity of a vacuum

20. Department of PhysicsUniversity of Oslo Radiative stopping power(2) • The case of a particle accelerated in nucleus field: • Comparison of proton and electron as incoming: • Bremsstrahlung not important for heavy charged particles

21. Department of PhysicsUniversity of Oslo Radiative stopping power(3) • The maximum energy loss to bremsstrahlung is the total kinetic energy of the electron • Energy transferred to radiation per pathlength unit: radiative stopping power: •Br(T,Z) weak dependence of T and Z • Radiative energy loss increase with T and Z

22. Department of PhysicsUniversity of Oslo Total stopping power, electrons • Total stopping power, electrons: • Comparison:

23. Department of PhysicsUniversity of Oslo Radiation yield • Estimated fraction of the electron energy that is emitted as bremsstrahlung: Radiation yield, Y(T) Water Tungsten Kinetic energy, T (MeV)

24. Department of PhysicsUniversity of Oslo Comparison of Sc Electrons, total Electrons, collision Electrons, radiative Protons, total Kinetic energy, T [MeV]

25. Department of PhysicsUniversity of Oslo Other interactions •Cerenkov effect: very high energetic electrons (v>c/n) polarize a medium (water) of refractive index n and bluish light is emitted (+UV) • Little energy is emitted

26. Department of PhysicsUniversity of Oslo Other interactions(2) •Nuclear interactions: Inelastic process in which the charged particle cause an excitation of the nucleus. Result: - Scattering of charged particle - Emission of neutron, g-quant, a-particleNot important below ~10 MeV (proton) •Positron annihilation: Positron interact with atomic electron, and a photon pair of energy ≥ 2x0.511MeV is created. The two photons are emitted 180o apart.Probability decrease by ~1/v

27. Department of PhysicsUniversity of Oslo Braggs rule • Braggs rule for mixtures of n-atoms/elements:

28. Department of PhysicsUniversity of Oslo d-electron as a result of ionization Trace of charged particle d-electrons living the volume → energy transferred > D Linear Energy Transfer • LETD; also known as restricted stopping power •D, cutoff value; LETD includes all the soft and the fraction of the hard collision d-rays with energy<D • Sc includes energy transitions from Emin to Emax • LETD the amount of energy disposed in a volume defined by the range of an electron with energy D

29. Department of PhysicsUniversity of Oslo Linear Energy Transfer(2) • The energy loss per length unit by transitions of energy between Emin < E < D: • If D = Emax then L= Sc ; unrestricted LET • LETD given in keV/mm • 30 MeV protons in water: LET100eV/L  = 0.53

30. Department of PhysicsUniversity of Oslo Range •The range  of a charge particle in a medium is the expectation value of the pathlength p • The projected range <t>is the expectation value of the farthest depth of penetration tf in its initial direction Electrons:<t> <  Heavy particles:<t> ≈ 

31. Department of PhysicsUniversity of Oslo T0 Dx Range(2) • Range can by approximated by the Continuous Slowing Down Approximation, CSDA • Energy loss per unit length is given by dT/dx – gives an indirect measure of the range:

32. Department of PhysicsUniversity of Oslo Range(3) • Range is often given multiplied by density • Unit is then [cm][g/cm3]=[g/cm2] • Range of a charge particle depend on:- Charge and kinetic energy- Density, electron density and average excitation potential of absorbent

33. Department of PhysicsUniversity of Oslo Range(4)

34. Department of PhysicsUniversity of Oslo Straggling and multiple scattering • In a radiation field of charged particles there is:- variations in rate of energy loss- variations in scattering The initial beam of particle at same speed and direction, are spread as they penetrate a medium

35. Department of PhysicsUniversity of Oslo Multiple scattering • Electrons experience most scattering – characteristic of initially close to monoenergetic beam: Initial beam Beam at small depth in absorbent Beam at large depth in absorbent Number Energy [MeV]

36. Department of PhysicsUniversity of Oslo Projected range <t> • Characteristic of different type of particles penetrating a medium:

37. Department of PhysicsUniversity of Oslo Energy disposal • Protons energy disposal at a given depth:

38. Department of PhysicsUniversity of Oslo Energy disposal(2) • Electrons energy disposal at a given depth; multiple scattering decrease with kinetic energy:

39. Department of PhysicsUniversity of Oslo Monte Carlo simulations • Monte Carlo simulations of the trace after an electron (0.5 MeV) and an a-particle (4 MeV) in water • Notice: e- most scattered a has highest S

40. Department of PhysicsUniversity of Oslo Hadron therapy • Heavy charged particles can be used in radiation therapy – gives better dose distribution to tumor than photons/electrons

41. Department of PhysicsUniversity of Oslo Tables on the web • Stopping powerhttp://physics.nist.gov/PhysRefData/Star/Text/ • Attenuation coefficients http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html

42. Summary