Radiation and radiation dosimetry Spring 2006 Introduction Audun Sanderud Department of Physics University of Oslo

Contents Interaction between ionizing radiation and matter Radioactive and non-radioactive radiation sources Calculations and measurement of radiation doses (dosimetry) The effect of radiation on relevant substances like water and important biological molecules The understanding of:  the biological effects of ionizing radiation  measurement principles and methods  the principles of radiation protection

Department of Physics University of Oslo Learning objectives To understand primary and secondary effects of ionizing radiation How radiation doses are calculated and measured The understanding of the principles of radiation protection, their origin and applications This will provide a tool for evaluating possible dangers in the use of ionizing radiation

AtomsMatter Department of Physics University of Oslo Overview Ionizing radiation Radiation scours Interactions Effects H 2 O DNA MoleculesCellsHumans Radiation protection § Dosimetry -Photons -Charged particles -Neutrons -Photons CalculationMeasurement

Interaction Between Ionizing Radiation And Matter, Part 1 Photons Audun Sanderud Department of Physics University of Oslo

Five interaction processes between photons and matter:  Rayleigh scattering  Compton scattering  Photoelectric effect  Pair- and triplet -production  Photon-nuclear reactions Probability of interaction described by cross section Scattering and energy transfer described kinematics Joint gives the possibility to calculate radiation doses Department of Physics University of Oslo Photon Interaction Scattering Absorption

Department of Physics University of Oslo Rayleigh/Coherent scattering Scattering of photons without loss of energy Photons absorbed by the atom, then emitted with a small angel Depend on photon energy, hν, and atomic structure The atomic cross section of coherent scattering: Special case hν → 0 : Thomson scattering

Department of Physics University of Oslo Photon attenuation Probability of a photon interaction: μdx Number of photons interacting : Nμdx MatterPhotons N dx N-dN

Department of Physics University of Oslo Average pathlength The probability of a photon not interacting: e -  x Normalized probability:

Department of Physics University of Oslo Attenuation - Cross section µ: Denote the number of photons with a single energy E and direction which interacts per length unit µ=p/dx, probability of per length unit; macroscopic σ: Cross section target area; surface proportional with the probability of interaction σ=p/n v dx, σ: cross section, probability per atom density n v, and length unit; microscopic µ=  (N A /A)  : mass density, (N A /A): number of atoms per mass unit

Look at two spheres:  equals total area:  (r 1 +r 2 ) 2 Cross section Department of Physics University of Oslo Atom, radius r 2 Incoming particle, radius r 1 (direction normal to the surface)

N particles move towards an area S with n atomsProbability of interaction: p=S cs /S = n  /SNumber of interacting particles: Np= Nn  /S Cross section (2) Department of Physics University of Oslo Atom cross section,  S missedhit Incoming particle

The cross section of an interaction depend on: -Type of target (nucleus, electron,..) -Type of incoming particle -Energy of the incoming particle -Distance between target and particleCross section calculated with quantum mechanics - visualized in a classical window Cross section (3) Department of Physics University of Oslo

A wave beam interacts with a weak potential The Hamiltonian is: Free particle wave function:Initial: Final: What is the probability of elastic scattering by an angel θ of a photon of energy hν? Department of Physics University of Oslo Calculating Rayleigh Cross section

The photon energy loss due to the interaction is significantThe interaction is a photon-electron scattering, assuming the electron being free (binding energy neglect able)Also called Compton scattering Incoherent scattering Department of Physics University of Oslo h e -   h ’ T

Kinematics: Solution: Compton scattering(1) Department of Physics University of Oslo

Compton scattering(2) Department of Physics University of Oslo

Klein and Nishina derived the cross section of the Compton scatteringThe differential cross section for photon scattering at angel , per unit solid angel and per electron, may be written as. r 0: classic electron radius; distance between two electrons with potential energy equal electron rest mass energy; m e c 2 = e 2 /4  0 r 0 Compton scattering-Cross section Department of Physics University of Oslo   z x y dd (The incoming photon direction along the z-axis)

The cylinder symmetry gives: Compton scattering-Cross section(2) Department of Physics University of Oslo Denotes the probability of finding a scattered photon inside the angel interval [  +d  ] after the interaction with the electronThe total cross section per electron e  is: Atomic C. scat. cross section is then: a  e 

Scattered photons are more forward directed as initial energy increase Compton scattering-Cross section(3) Department of Physics University of Oslo The differential cross section, d e  /d  [cm 2 /radian] Photon scatter angel, q

The photon spectra of the scattered photons: Compton scattering-Cross section(4) Department of Physics University of Oslo

The cylinder symmetry gives: Compton scattering-Cross section(5) Department of Physics University of Oslo The photon energy, hv’ [MeV] d e  /d(hv’) [cm 2 /MeV]

More correct treatment of the cross section gives a small atom number dependence: Compton scattering-Cross section(6) Department of Physics University of Oslo The photon energy, hv’ [MeV] Incoherent atomic cross section per atom number a  /Z [cm 2 ]

The energy transferred to the electron in a Compton process: Energy transferred Department of Physics University of Oslo The energy-transfer cross section: The average fraction of transferred energy:

Mean fraction of energy transferred to the electron: Energy transferred(2) Department of Physics University of Oslo

Photon is absorbed by an atom/molecule; resulting in an excitation or ionization Photoelectric effect Department of Physics University of Oslo The vacancy is filled by an electron from an outer orbit and characteristic radiation is emitted TaTa  e-e-

The binding energy of the electron E b most be accounted for: Photoelectric effect (2) Department of Physics University of Oslo The atomic cross section  is approximately when E b =0 assumed:  : Fine structure constant  : Points to the emitted electron

Photoelectric cross section (d  /d  )/  Photoelectron – distribution angle Department of Physics University of Oslo

The energy of characteristic radiation depend on the electron structure- and transitionsThe K- and L-shell vacancies: photons with energy h K and h L are emitted after de-excitationEmitted photons are isotropic distributedThe fraction of events that occur in the K- or L- shell: P K [h  b ) K ] and  P L [h  b ) L ]The probability of c.r. being emitted: Y K and Y LThe energy transport away from the atom by c.r.: P K Y K h   P L Y L h L Characteristic radiation Department of Physics University of Oslo

Alternative path which the ionized atom dispose energyShallow outer-shell vacancies are emitted from the atom with kinetic energy corresponding to its excess energyLow Z: most AugerHigh Z: most characteristic radiationAuger electrons are low-energetic Auger effect Department of Physics University of Oslo

It is observed: Photoelectric cross section Department of Physics University of Oslo The fraction of energy transferred to the photoelectron But: Auger electrons are also given energyThe energy-transfer cross section of the electron:

Photon absorption when an electron-positron pair iscreated Pair production Department of Physics University of Oslo Occurs in a Coulomb force field from an atom nucleus or atomic electron (triplet production)

Conservation of energy: Pair production (2) Department of Physics University of Oslo Average kinetic energy after absorption: Estimate of scatter angle of electron/positron: Total cross section:

An electron-positron pair is created in a field from an electron – conservation of energy: Triplet production Department of Physics University of Oslo Note that the atomic electron can gain significant kinetic energy Threshold photon energy: hv = 4m 0 c 2 Average kinetic energy after absorption:

Pair production most important: Pair- and triplet production Department of Physics University of Oslo The photon energy, hv’ [MeV] Atomic cross section a  /Z 2 [cm2] C (Z=6) Al (Z=13) Cu (Z=29) Pb (Z=82) Triplet production a  tp /Z 2

Photon (energy above a few MeV) excites a nucleusProton or neutron is emitted( , n) interactions may lead to radiation protection problemsExample: Tungsten W ( , n)Not important in dosimetry Photonuclear interactions Department of Physics University of Oslo

Total coefficient of photon interaction: Attenuation coefficients Department of Physics University of Oslo Coefficient of energy transfer to electrons: Braggs rule for mixtures of n-atoms/elements:

Attenuation coefficients (2) Department of Physics University of Oslo

Photon Interaction Summary µ tr /ρ Photon interaction Processes Kinematics Cross section Mean energy transferred ComptonRayleigh Photo el.eff.Pair/triplet T=0 T= hn-E b -T a = hn-E b hn= 2m 0 c 2 + T ˉ + T ⁺ Photon- nuclear reactions

Summary Department of Physics University of Oslo