2. EXCITATION, IONIZATION & RADIATIVE LOSSES
• Energetic charged particles interact with matter by electrical
(columbic) forces and lose energy via:
• A) excitation
• B) ionization
• C) radiative losses.
• Excitation and ionization occur when charged lose energy by
interacting with orbital electrons in the medium.
3. Excitation:
• Excitation is the transfer of some of the incident particle’s energy to
electron in the absorbing material .
• Excitation promotes electron to higher energy level.
• Excitation is followed by de-excitation i.e. electron returns to lower
energy level.
• De- excitation causes the liberation of energy in the form of E.M
radiation or Auger electron
• In excitation process the transferred energy does not exceeds the
binding energy of absorbing electron.
4. Ionization :
• IF the transferred energy exceeds the binding energy of absorbing
electron , ionization occurs.
• Electron is ejected out of the Atom.
• Sometime , the ejected electrons posses the sufficient energy to cause
further ionization called secondary ionization.
• These electrons are called as delta rays
5. Specific Ionization:
• The average number of primary and secondary ion pairs produced per
unit length of the charged particle’s path is called as Specific
Ionization.
• SI increases with the square of the electric charge (Q) and decreases
with the square of incident particle velocity (v)
• E.g – Alpha particle.
• As alpha particle slows down the SI is maximum called the Bragg peak
Used in Radiotherapy.
6. Linear Energy Transfer.
• LET is a measure of the average amount of energy deposited locally in the
absorber per unit path length.
• LET is expressed in units of Kev or eV per μm.
• LET ∝ Q2 / EK
• Q= charge of particle X-ray LET in soft tissue approx. 3 Kev/ μm
Alpha LET in soft tissue approx. 100Kev/ μm
• EK = KEof particle
High LET – alpha ray and protons
Low LET – beta rays , x-rays, gamma rays.
7. Scattering :
• Scattering refers to an interaction that deflects a particle or photon
from its original trajectory.
• A scattering event in which the total K.E of the colliding particles is
unchanged is called elastic/ billiard ball collision.
• The process of ionization is elastic collision if the binding energy of
electron is negligible compared to the K.E of incident electron.(i.e. the
K.E of ejected electron is equal to the K.E lost by incident electron.)
• If the binding energy that must be overcome to ionize the atom is
significant compared to the K.E of the incident electron (i.e. the K.E of
ejected electron is less than the K.E lost by incident electron.) , the
process is said to be inelastic .
8. Radiative Interaction - Bremsstrahlung
• The radiation emission accompanying electron deceleration is called
as bremsstrahlung / breaking radiation .
• The deceleration of high speed electron in an x-ray tube produces
breaking radiation used in diagnostic radio imaging .
9. X-ray and Gamma-ray Interactions.
• There are Four major types of interaction of x-ray and gamma ray
photons with matter which are useful in diagnostic imaging and
nuclear medicine :
• A) Rayleigh/ coherent/ classical / unmodified or elastic scattering
• B) Compton scattering
• C) Photoelectric absorption
• D) pair production (nuclear medicine)
• E) Photodisintegration / Photo fission
10. Rayleigh/ coherent/ classical / unmodified or
elastic scattering
• In Rayleigh scattering , the incident photon interacts with and excites the
total atom.
• This interaction occurs mainly with very low energy x-ray, such of those
used in mammography (15 keV to 30 keV).
• The incident photos deposits energy in an atom ,causing all the electrons in
the scattering atom to oscillate in phase.
• The atom’s electron cloud immediately radiates this energy, emitting
photon of the same energy but in opposite direction.
• In this interaction the electrons are not ejected so ionization doesn’t
happen.
• This scattering account for less than 5% of x-ray interaction above 70 Kev
and mostly 10% at 30 Kev.
• Low probability of occurring in diagnostic energy range.
11.
12. Compton Scattering / inelastic / nonclassical :
• This is predominant interaction of x-ray and gamma ray photons in
the diagnostic range with soft tissue.
• Compton scattering predominates from the diagnostic range of 26Kev
to out of diagnostic range approx. 30 Mev
• This interaction is most likely to happen between photon and
valence/outer shell electron.
• The electron is ejected from an atom and the scatter photon is
emitted with some reduction in energy relative to incident photon.
• As in all type of interaction both energy and momentum must be
conserved , the energy of incident photon Eo is equal to the sum of
the energy of scattered photon E sc and K.E. of ejected electron E e-.
• Eo = E sc + E e-
13. Cont..
• Compton scattering results in the ionization of the atom and a division of
the incident photon’s energy between the scattered photon and the
ejected electron.
• The ejected/recoiled electron will lose its k.E via excitation and ionization
of atoms in the surrounding material.
• Compton scattered photon may travers the medium without interaction or
may undergo subsequent interaction.
• The energy of scattered photon can be calculated from the energy of the
incident photon and the angle of the scattered photon.
• Esc = Eo / 1+ Eo / 511 KeV * (1-cos θ)
• The scattering angle of the ejected electron can not exceed 90 degree
,whereas that of the scattered photon photon can be of any value including
180 degree back scatter.
• Energy of ejected electron is usually absorbed near the scattering site.
14. Cont..
• Compton scattering depends upon density of material.
• Hydrogenous material have higher probability of Compton scattering
compared to an hydrogenous materials.
• Lack of proton in Hydrogenous material results in approx. doubling
electron cloud .
15. Photoelectric effect /Absorption:
• In the photoelectric effect, all of the incident photon energy is transferred
to an electron, which is ejected from the atom.
• The K.E of the ejected photoelectron (E pe ) is equal to the incident photon
energy (E 0 ) minus the binding energy of the orbital electron (E b ).
• E pe = E 0 - E b
• In order for photoelectric effect to occur , the incident photon energy must
be greater or equal to the binding energy of the electron that is ejected.
• Following a photoelectric interaction , the atom is ionized , with an inner
shell electron vacancy. Vacancy is filled with another electron from lower
energy shell during this process characteristic radiation is emitted.
16. cont..
• The probability of characteristic X-ray emission decreases as the atomic
number of the absorber decreases.(No ch. X-ray emission in soft tissue in
diagnostic range).
• The probability of photoelectric absorption per unit mass is approx.
proportional to Z^3/E^3.
• PE interaction probability in iodine (Z=53) is (53/20)^3 i.e. 18.6 times
greater than in calcium (z= 20).
• The benefit of photoelectric absorption in X-ray transmission imaging is
that there are no scattered photon to degrade the image.
• If the photon energy is doubled the probability of PEI is decreased by 8
times. (1/2)^3 = 1/8.
• But… every elements have different absorption edge. The probability of
interaction for photons of energy just above the absorption edge is mush
greater than that of photon energy below the edge.
17. Cont..
• For eg: a 33.2 Kev x-ray photon is about six times as likely to have
photoelectric interaction with iodine atom as a 33.1 Kev photon.
• A photon can not undergo a PEI with an electron in a particular atom
shell or subshell if the photon’s energy is less than the binding energy
of that shell or subshell.
• The photon energy corresponding to an absorption edge increases
with the atomic number (Z) of the element.
• For eg: the primary elements comprising soft tissue (H,C,N and O)
have absorption edge below 1 Kev.
• The element iodine (z=53) commonly used contrast media has a K-
absorption edge of 33.2 Kev. Tungsten has 69.5 , phosphorus has
2.1542 kev, calcium has 1.530 etc
18. Take away..
• The photoelectric process predominates when lower energy photon
interact with high Z materials.
• In fact photoelectric absorption is the primary mode of interaction of
diagnostic X-ray with image receptors, radiographic contrast material ,
bone and radiation shielding, all of which have much higher atomic
number than soft tissue.
• Compton scattering predominates at most diagnostic and therapeutic
photon energies in material of lower atomic number such as soft
tissue and air.
• At photon energies below 50 KeV, PEI in soft tissue play an important
role in medical imaging.
• The photoelectric absorption process can be used to amplify
difference in attenuation between tissue with slightly different atomic
number.
19.
20. Pair Production :
• Pair production can only occur when the energies of x-rays and gamma
rays exceed 1.02 Mev.
• In pair production, an x-ray or gamma ray interacts with the electric field
of the nucleus of an atom.
• The photon’s energy is transformed into an electron- positron pair.
• The rest mass energy equivalent of each electron is 0.511 Mev /
511Kev.This is why the threshold energy for this reaction is 1.02 Mev.
• The electron and positron loss energy via excitation,ionization,radiative
loss.
• When Positron comes into rest and interacts with electron , result in
annihilation process i.e. formation of two oppositely directed 0.511Mev
annihilation photons. (gamma rays).
21.
22. Attenuation of x-ray and Gamma ray:
• Attenuation is the removal of photons from a beam of x-ray or
gamma rays as it passes through matter.
• Attenuation is caused by both absorption and scattering of the
primary photons.
23. Linear Attenuation coefficient:
• The fraction of photons removed from a monoenergetic beam of x-ray or
gamma rays per unit thickness of material is called as linear attenuation
coefficient (μ). Typically expressed in units of inverse centimeter (cm^-1).
• The number of photons removed from the beam traversing a very small
thickness Δx can be expressed as :
n = μ N Δx
• n= number of photon removed from the beam.
• N= number of photons incident on the material
• Δx = thickness of material .
• The above equation would only be true in tissue with thickness 1-mm.
• For tissue more than 1 mm thickness different equation must be used.
24. Cont..
•N=N0e-μx
• Thus using the above equation , the fraction of 100 keV photons
transmitted through 6 cm of slice is:
• N/N
0 = e -(0.16 cm -1) (6cm) = 0.38
• This results indicates that on average , 380 of the 1,000 incident
photons (i.e. 38% ) would be transmitted through the 6-cm slab
without interacting.
25. Cont..
• In diagnostic energy range, the LAC decreases with increasing energy
except at absorption edge. The LAC for soft tissue ranges from
approx. 0.35 to 0.16 cm ^-1 for photon energy ranging from 30 to 100
Kev.
• For given thickness of material, the probability of interaction depends
on the number of atom the x-ray or gamma ray encounters per unit
distance. i.e. density of material (ρ, in g/cm^3).
• So, if density is doubled , the photons will encounter twice as many
atoms per unit distance through the material.
• LAC is proportional to the density of material.
• μ water > μ ice > μ water vapour.
26. Mass Attenuation Coefficient:
• For a given material and thickness , the probability of interaction is
proportional to the number of atoms per volume.
• This dependency can be overcome by normalizing the linear
attenuation coefficient for the density of material.
• The linear attenuation coefficient, normalized to unit density, is called
the mass attenuation coefficient.
• Mass attenuation coefficient (μ / ρ ) [cm^2 / g ].
= Linear Attenuation Coefficient (μ) cm^-1 / density of material (ρ)
[g/cm^3].
Unit of MAC is cm^2/g.
Mass attenuation coefficient is independent of density.
27. Cont..
• To calculate the linear attenuation coefficient for a density other than
1 g/cm^3, the density ρ of the material is multiplied by the mass
attenuation coefficient to yield the linear attenuation coefficient.
• To use the mass attenuation coefficient to compute attenuation,
equation can be written as :
N= No e -(μ/ρ) ρx
ρx= mass per unit area.
