Interaction of Radiation with Matter I

Particle interactions

• Energetic charged particles interact with matter by electrical forces and lose kinetic energy via:– Excitation– Ionization– Radiative losses

• ~ 70% of charged particle energy deposition leads to nonionizing excitation

Specific Ionization

• Number of primary and secondary ion pairs produced per unit length of charged particle’s path is called specific ionization– Expressed in ion pairs (IP)/mm

• Increases with electrical charge of particle

• Decreases with incident particle velocity

Specific ionization for 7.69 MeV alpha particle from polonium 214

Charged Particle Tracks

• Electrons follow tortuous paths in matter as the result of multiple scattering events– Ionization track is sparse and nonuniform

• Larger mass of heavy charged particle results in dense and usually linear ionization track

• Path length is actual distance particle travels; range is actual depth of penetration in matter

Path lengths vs. ranges

Linear Energy Transfer

• Amount of energy deposited per unit path length is called the linear energy transfer (LET)

• Expressed in units of eV/cm• LET of a charged particle is proportional to the

square of the charge and inversely proportional to its kinetic energy

• High LET radiations (alpha particles, protons, etc.) are more damaging to tissue than low LET radiations (electrons, gamma and x-rays)

Bremsstrahlung

Bremsstrahlung

• Probability of bremsstrahlung production per atom is proportional to the square of Z of the absorber

• Energy emission via bremsstrahlung varies inversely with the square of the mass of the incident particle– Protons and alpha particles produce less than

one-millionth the amount of bremsstrahlung radiation as electrons of the same energy

Bremsstrahlung

• Ratio of electron energy loss by bremsstrahlung production to that lost by excitation and ionization = EZ/820– E = kinetic energy of incident electron in MeV

– Z = atomic number of the absorber

• Bremsstrahlung x-ray production accounts for ~1% of energy loss when 100 keV electrons collide with a tungsten (Z = 74) target in an x-ray tube

Neutron interactions

• Neutrons are uncharged particles• They do not interact with electrons

– Do not directly cause excitation or ionization

• They do interact with atomic nuclei, sometimes liberating charged particles or nuclear fragments that can directly cause excitation or ionization

• Neutrons may also be captured by atomic nuclei– Retention of the neutron converts the atom to a

different nuclide (stable or radioactive)

Neutron interaction

X- and Gamma-Ray Interactions

• Rayleigh scattering

• Compton scattering

• Photoelectric absorption

• Pair production

Rayleigh Scattering

• Incident photon interacts with and excites the total atom as opposed to individual electrons

• Occurs mainly with very low energy diagnostic x-rays, as used in mammography (15 to 30 keV)

• Less than 5% of interactions in soft tissue above 70 keV; at most only 12% at ~30 keV

Rayleigh Scattering

Compton Scattering

• Predominant interaction in the diagnostic energy range with soft tissue

• Most likely to occur between photons and outer (“valence”) shell electrons

• Electron ejected from the atom; photon scattered with reduction in energy

• Binding energy comparatively small and can be ignored

Compton Scattering

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Compton scatter probabilities

• As incident photon energy increases, scattered photons and electrons are scattered more toward the forward direction

• These photons are much more likely to be detected by the image receptor, reducing image contrast

• Probability of interaction increases as incident photon energy increases; probability also depends on electron density– Number of electrons/gram fairly constant in tissue;

probability of Compton scatter/unit mass independent of Z

Relative Compton scatter probabilities

Compton Scattering

• Laws of conservation of energy and momentum place limits on both scattering angle and energy transfer

• Maximal energy transfer to the Compton electron occurs with a 180-degree photon backscatter

• Scattering angle for ejected electron cannot exceed 90 degrees

• Energy of the scattered electron is usually absorbed near the scattering site

Compton Scattering

• Incident photon energy must be substantially greater than the electron’s binding energy before a Compton interaction is likely to take place

• Probability of a Compton interaction increases with increasing incident photon energy

• Probability also depends on electron density (number of electrons/g density)– With exception of hydrogen, total number of electrons/g

fairly constant in tissue– Probability of Compton scatter per unit mass nearly

independent of Z

Photoelectric absorption

• All of the incident photon energy is transferred to an electron, which is ejected from the atom

• Kinetic energy of ejected photoelectron (Ec) is equal to incident photon energy (E0) minus the binding energy of the orbital electron (Eb)

Ec = Eo - Eb

Photoelectric absorption (I-131)

Photoelectric absorption

• Incident photon energy must be greater than or equal to the binding energy of the ejected photon

• Atom is ionized, with an inner shell vacancy• Electron cascade from outer to inner shells

– Characteristic x-rays or Auger electrons

• Probability of characteristic x-ray emission decreases as Z decreases– Does not occur frequently for diagnostic energy photon

interactions in soft tissue

Photoelectric absorption (I-131)

Photoelectric absorption

• Probability of photoelectric absorption per unit mass is approximately proportional to

• No additional nonprimary photons to degrade the image

• Energy dependence explains, in part, why image contrast decreases with higher x-ray energies

33 / EZ

Photoelectric absorption

• Although probability of photoelectric effect decreases with increasing photon energy, there is an exception

• Graph of probability of photoelectric effect, as a function of photon energy, exhibits sharp discontinuities called absorption edges

• Photon energy corresponding to an absorption edge is the binding energy of electrons in a particular shell or subshell

Photoelectric mass attenuation coefficients

Photoelectric absorption

• At photon energies below 50 keV, photoelectric effect plays an important role in imaging soft tissue

• Process can be used to amplify differences in attenuation between tissues with slightly different atomic numbers, improving image contrast

• Photoelectric process predominates when lower energy photons interact with high Z materials (screen phosphors, radiographic constrast agents, bone)

Percentage of Compton and photoelectric contributions

Pair production

• Can only occur when the energy of the photon exceeds 1.02 MeV

• Photon interacts with electric field of the nucleus; energy transformed into an electron-positron pair

• Of no consequence in diagnostic x-ray imaging because of high energies required

Pair Production