Photon - interaction with matter

dr rahul ts Jr

dpt of radiotherapy

gmch tsr

MATTER

• Matter > elements > atoms• Atomic structure

– An atom consists of a positively charged nucleus surrounded by a cloud of negatively charged electrons.

– radius of atom ~10-10 m, radius of nucleus ~10-15 m.

– An atom is specified by the formula AZX,

• A is the mass number (number of protons + neutrons), • Z is the atomic number (number of protons).

• Atomic energy levels – The binding energy of electrons in various orbits

depends on the magnitude of the Coulomb force of attraction between the positively charged nucleus and the negatively charged electrons.

• The closer the orbit is to the nucleus, the greater is the binding energy.

– maximum possible number of electrons in any orbit is given by 2n2

• Nuclear stability – High n/p ratio gives rise to β- decay and a low n/p ratio

can result in electron capture and β+ decay

PHOTONS

• Electromagnetic radiation

– Electromagnetic radiations are characterized by oscillating electric and magnetic fields, always perpendicular to each other and to the direction of their energy propagation.

– Wavelength (λ), frequency (n), and velocity (c) of electromagnetic waves are related by c = nl.

– If λ is given in meters, the photon energy in electron volts (eV) is given by E = (1.24 × 10-6)/λ.

• When an X-ray or γ ray beam passes through a medium , interactions between photons & matter can take place with transfer of energy to the medium

• The initial step in the energy transfer involves the ejection of electrons from the atoms of the absorbing medium

Outer electron ionization,

retunes to normal state + infrared (low energy)

Inner electron excitation + free outer electron takes its place + characteristic x-rays

– Characteristic x-rays produces Auger electron

• These high speed electrons transfer

their energy by producing IONIZATION and EXCITATION of the atoms along their path

• If the absorbing medium consists of body tissues sufficient energy may be deposited with in the cells destroying their reproductive capacity

• Photons are INDIRECTLY ionizing radiations

• Interact with the atoms of a material or absorber to produce high speed electrons by 3 major processes

♣ Photoelectric effect ♣ Compton effect ♣ Pair production

Types of interaction

1. Coherent scattering

2. Compton effect

3. photoelectric effect

4. pair production

5. photodisintegration.

4 possible types of fate awaits the photon when it passes through matter

1.May be deflected from its original path & proceed in a new direction, but with UNCHANGED energy

2.May be deflected as before, but also LOSE some energy

3.Disappear altogether

4.May be transmitted unchanged

4 possible types of fate awaits the photon when it passes through matter

1. May be deflected from its original path & proceed in a new direction, but with UNCHANGED energy

2. May be deflected as before, but also LOSE some energy

3. Disappear altogether

4. May be transmitted unchanged

scatter

Photoelectric effect

Pair production

incoherent

coherent

Attenuation processes

Divided into 2 sets

• Photon scattering (elastic scattering, inelastic scattering)

• Disappearance phenomenon (photo-electric effect, pair production)

‘Bound’ and ‘free’ electrons

• Strictly speaking there are normally no ‘free’ electrons in matter

• Each electron is bound in the atom by the electrostatic attraction between itself and the positive charge on the nucleus

• It can only be ‘free’ if it receives enough energy to overcome this binding force

• For the outer electrons of any atom, the binding energy is only a few electron volts , which is small when compared to the inner electrons and very small when compared to the energy of X-ray photons

• This leads to the concept that , an electron may be considered to be ‘free’ when its binding energy is small compared to the energy of the photons with which it interacts

Elastic scattering (coherent, classical, unmodified, Thomson, Rayleigh)

• More easily described by considering the radiation as waves rather than photons

• Interaction is with bound electrons

• Radiation is deflected with out losing any energy

• The electric field of the incident wave accelerates the particle, causing it to in turn emit radiation at the same frequency as the incident wave, and thus, the wave is scattered

Elastic scattering

• No energy is permanently taken up by the irradiated material

• The process is of ATTENUATION WITH OUT ABSORPTION

• Since the process involves bound electrons, it occurs more in high atomic number materials and also more with low energy radiations

• The mass attenuation coefficient for elastic scattering is

α Z² α 1/ E

Elastic scattering…

• Contributes nothing to energy absorption

• Contributes never more than a few percent to the total attenuation

• This makes it UNIMPORTANT in radiography and radiotherapy

Elastic scattering…

• Low energy photons

• High atomic number material.

• Scattering of photons at small angles

• No energy absorption

• No much clinical significance

Compton effect (inelastic, incoherent )

• Interaction is with free electrons

• In this interaction , the electron receives some energy from the photon and is emitted at an angle θ

• The photon with reduced energy is scattered at an angle Ф

Compton effect

• The angle through which the photon is scattered,

the energy lost by the photon and the energy handed on to the electron are all interconnected

By applying the laws of conservation of energy and momentum, following relationships can be derived

E = hvo α ( 1- cos Ф) 1+ α (1-cos Ф)

hv’ = hvo 1 1 + α (1-cos Ф)

hvo = energy of incident photon hv’ = energy of scattered photon E = energy of electron α = hvo/µoc² where µoc² is the rest mass

energy of electron

( 0.511 Mev)

• If the angle Ф, through which the photon is scattered is small , a very small share of the energy is given to the electron, and the photon loses very little energy

If Ф= 0˚, then E = 0, hv΄ = hvo

• In a head on collision , in which the photon is turned back along its original track (180˚) ,the maximum energy is transferred to the recoil electron

Emax = hvo 2α

1+ 2α

and the scattered photon will be left with minimum energy

hv΄min = hvo 1

1+2α

• Most collisions will lie somewhere between these 2 extremes

Dependence on energy and atomic number

• As the energy increases the relative importance of scattering as an attenuation process increases , but the absolute amount of scattering steadily decreases with increase in energy

• Independent of atomic number Z, depends only on the number of electrons per gram

• With the exception of hydrogen, most materials have approximately the same number of electrons/gram

• Compton mass attenuation coefficient ( σ/ρ ) is nearly the same for all materials

Direction of scattering and recoil electrons

• Although any photon can be scattered in any direction , the general pattern of scattered radiation in space changes with photon energy

• For low energy photons there is roughly an equal chance of being scattered in any direction

As the photon energy increases the scattered photon is more and more likely to be travelling in forward direction

• Compton interaction probability in water increases with photon energy from 10 to 150 keV. It then decreases with further increase in energy.

• Maximum energy of a photon scattered at 90 degrees is 0.511 MeV, and at 180 degrees it is 0.255 MeV

Disappearance phenomena

• Photoelectric effect

• Pair production

Photoelectric effect

• Photon interacts with an atom and ejects one of the orbital electrons from the atom

• Entire energy of the photon is absorbed by the electron

• The kinetic energy of the ejected electron (photoelectron) is equal to hv – EB(binding energy)

Photoelectric effect

• After the electron is ejected from the atom, a vacancy is created in the shell, thus leaving the atom in an excited state

• The vacancy can be filled by an outer orbital electron with the emission of characteristic X-rays

• There is also possibility of emission of Auger electrons which are mono energetic electrons produced by the absorption of characteristic X-rays internally by the atom

Dependence on energy and atomic number

τ/ρ α Z³ E³

τ/ρ = photoelectric mass attenuation coefficient

Photoelectric effect in water (or soft tissue) is predominant for photon energies of 10 to 25 keV

• The relationship with atomic number forms the basis of many applications in diagnostic radiology

• The difference in Z of various tissues such as bone, muscle, fat amplifies differences in X-ray absorption, provided the primary mode of interaction is photoelectric

Basis of: •Diagnostic x-rays

•Use of contrast, eg. barium

•Use of lead as radiation protector.

Pair production

• If the energy of the photon is greater than 1.02 Mev

• Photon strongly interacts with the electromagnetic field of atomic nucleus and gives up all its energy in the process of creating a pair consisting of a negative electron (e-) and a positive electron(e+)

• As the rest mass energy of electron is equal to 0.51 Mev , a minimum energy of 1.02 Mev is required to create the pair of electrons

• Thus the threshold energy for pair production is 1.02 Mev

Pair production

The photon energy in excess of 1.02 Mev is shared between the particles as kinetic energy

The particles tend to be emitted in the forward direction relative to the incident photon

The positron created as a result of pair production process lose its energy as it traverses the matter

Near the end of its range the slowly moving positron combines with one of the free electrons in its vicinity to give rise to 2 annihilation photons each having

0.51 Mev energy

2 photons are ejected in opposite directions

Dependence on energy and atomic number

• Since the pair production is caused by the nuclear field , the chance of its occurrence increases with the magnitude of that field , and hence with the nuclear charge , or the atomic number of the irradiated material

• In marked contrast with other attenuation processes described , pair production increases with energy

• Mass attenuation coefficient for pair production (П/ρ) α Z

α E

Photodisintegration

High energy photon + atomic nucleus

Nuclear reaction

Emission of nucleons.

•10 -15 Mev

•Neutron is ejected commonly

•Neutron + KE

•Very rare

Relative importance of various types of interactions

• The total mass attenuation coefficient µ/ρ is the sum of 4 individual coefficients

• µ/ρ = σ /ρ + σ/ρ + τ/ρ + П/ρ

• Coherent scattering is only important for very low energy (< 10 kev) and at therapeutic energies it is often omitted from the sum

Coherent Compton PE effect pair production

The µ/ρ decreases rapidly with energy until the photon energy far exceeds the electron binding energies and the Compton effect becomes the predominant mode of interaction

In the Compton range of energies µ/ρ of lead & water do not differgreatly since this type of interaction is independent of atomic number

The coefficient however decreases with energy until pair production becomes important . The dominance of pair production occurs atenergies much greater than the threshold energy of 1.02 Mev

Thank you…