Interaction of X and gamma rays

with matterDr. Varun Babu MD

Al Sabah HospitalKuwait

Possible outcomes3 possible fates of individual photons when they encounter matter

1. Transmitted: pass through unaffected, as primary or direct radiation

2. Absorbed: transferring to the matter all of their energy (photon disappears

completely)

3. Scattered: diverted in new direction; with or without loss of energy

transferring to matter; secondary radiation

Outcomes

Absorption and scattering are stochastic processes - impossible to predict which of the individual photons in beam will be transmitted by 1mm of a material.

The fraction of photons that will traverse can be precisely predicted.

X ray image formed by transmitted photons.

Absorbed/scattered represent attenuation by matter

AttenuationNarrow, monoenergetic X ray beam

● For a monoenergetic beam, equal thicknesses of an absorber transmit equal fractions of the radiation entering them.

● Half-value layer is the thickness of stated material that will reduce intensity of Xray beam to one half of its original value.

● HVL - measure of penetrating power/effective energy of the beam● Linear attenuation coefficient

○ μ = 0.693/HVL

○ measures probability that a photon interacts per unit length of the path it travels in a specified material

HVL decreases and LAC increases as:

1. density of material increases2. atomic number of material increases3. photon energy of radiation decreases

Mass attenuation coefficient (μ/⍴) = LAC/density of material

● Independent of density ● Depends on atomic number and photon energy

Exponential graphHowever thick the absorber, never possible to absorb an X ray beam completely

I = I0e-μd

I - intensity transmitted through materialI0 - intensity of incident X ray on absorberμ - LACd - thickness of absorber

Attenuation of wide beamMeasured percentage transmission depends on width of beam

● narrow beam - small amount of scatter is produced ● wide beam - amount of scatter produced and thus detected, is greater,

hence measured HVL would be increased

Attenuation of a heterogeneous beamX ray tube beams are heterogeneous (polyenergetic)

● lower energy photons attenuated proportionately● higher energy photons less attenuated

HVL of typical diagnostic beam

● 30mm in tissue● 12mm in bone● 0.15mm in lead

Beam hardeningAs beam penetrates material, it becomes progressively more homogeneous

Proportion of higher energy photons in beam increases - beam hardening.

Beam becomes more penetrating

1st HVL - reduces beam intensity from 100 to 50%2nd HVL - 50 to 25% - greater than first HVL

X ray beams in practice are usually wide and heterogeneous, do not strictly adhere to exponential law

Beam hardening

Interaction processes3 processes

1. Compton effect - interaction with a loosely bound or free electron (inelastic

or non-coherent scattering)

2. Photoelectric absorption - interaction with an inner shell or ‘bound’

electron; photon is totally absorbed

3. Elastic scatter - interaction with bound electron

Compton effect Photon passing through material bounces off free electron which recoils and takes away some energy of photon as kinetic energy

Photon is diverted in new direction with reduced energy

Angle = angle between scattered and incident ray

Electrons projected in sideways or forward direction

Compton scattering

Effect of angle of scattering Greater the angle of scatter

● greater the energy and range of recoil of electron● greater the loss of energy (& increase of wavelength) of scattered photon

Effect of initial photon energyHigher the initial photon energy

● greater the remaining photon energy of scattered radiation & more penetrating it is

● greater the energy carried off by recoil electron and greater it’s range

In diagnostic energy, no more than 20% is absorbed, rest is scattered.

Electron densityProbability of Compton effect occurring depends on number of electrons per unit volume (independent of atomic number)

Mass per unit volume x No. of electrons per unit mass (physical density x electron density)

Electron density = Z/A ; hydrogenated materials have more electrons per gram

Hence, compton attenuation is proportional to physical density

Compton effect = /E and independent of Z

Photoelectric effectWhen X ray photon collides with electron say in K-shell, if its energy is more than the EK then it ejects the electron and the energy is completely absorbed - part of it expended in removing electron from atom, remaining transferred as kinetic energy to electron

Kinetic energy of electron = Photon energy - EK

Ejected electrons are called photoelectrons

Holes in the atomic shell are filled by electrons falling from outer shells with emission of characteristic radiation such as photon

Photoelectric absorption

Photoelectric linear attenuation coefficient μ = + �

Photoelectric effect � Z3/E3

Probability of photoelectric absorption

● decreases as photon energy increases● increases as atomic number of material increases● proportional to density of material

Effective atomic numberWeighted average of the atomic numbers of the constituted elements.

Defined as the cube root of weighted sum of cubes of atomic numbers of the constituents.

Fat 6.4Air 7.6Water, muscle 7.4Bone 13.3

Absorption edgesWhen photon energy reaches EK, the probability of photoelectric absorptions jumps to a higher value. As energy increased further, probability decreases

The higher the atomic number, larger the EK and hence greater the photon energy at which edge absorption occurs.

Iodine k-edge

Importance of Compton/Photoelectric effects● Photoelectric absorption is more important

○ High Z materials○ Low energy photons

● Compton process is more important○ Low Z materials○ High energy photons

Photon energy at which both equally important

● 30keV - air, water, tissue 300keV - iodine, barium● 50keV - aluminium, bone 500keV - lead

Compton process predominates for air, water and soft tissues

Photoelectric absorption for contrast media, lead and materials used in films

Both important for bone

Elastic scatterPhoton bounces off electron firmly bound to its atom.

No electron is released, no ionization

Small angle of scatter

No role in radiology

aka coherent, classical, unmodified or Rayleigh scattering

Secondary electrons and ionizationRefers to the recoil electrons and photoelectrons set moving by Compton and Photoelectric effect.

When the electron has lost whole of it’s initial energy, the electron comes to the end of its range

The excitations and ionizations produced by secondary electrons - account for various properties of X and gamma rays

Ionization of air and gases - makes them electrically conducting - enables measurement of x and gamma rays

Ionization in living cells - biological damage - hazards of radiation exposure - necessitates protection against radiation

Excitation of atoms of certain materials - luminescence, fluorescence - used in measurement of X and gamma rays - as basis of radiological imaging

Effects on atoms of silver & bromine - photographic film blackening - measuring X and gamma rays - basis of conventional radiography

Greater part of energy converted to increased molecular motion -> extremely small rise in temperature

X rays and gamma rays are indirectly ionizing - through secondary electrons