Chapter 5Interactions of Ionizing Radiation

Ionization• The process by which a neutral atom acquires a

positive or a negative charge• Directly ionizing radiation

– electrons, protons, and particles– sufficient kinetic energy to produce ionization ray• excitation

• Indirectly ionizing radiation– neutrons and photons– to release directly ionizing particles from matter when

they interact with matter

Photon beam description

• Fluence ()

• Fluence rate or flux density ()

• Energy fluence ()

• Energy fluence rate, energy flux density, or intensity ()

da

dN

dtda

dN

dt

d

da

dE fl

dtda

dE

dt

d fl

Photon beam attenuation

• x–the absorber thickness (cm) –linear attenuation coefficient (cm-1)

• I–intensity

dxNdN

dxNdN

xeIxI

dxIdI

0)(

Half-value layer (HVL)

• x=HVL I/I0=1/2 6930.

HVL

A mono-energetic beam A practical beam produced by an x-ray generator

Coefficients (1)

• Linear attenuation coefficient (, cm-1) – Depend on the energy of the photons

the nature of the material

• Mass attenuation coefficient (/, cm2/g)– Independent of density of material– Depend on the atomic composition

Coefficients (2)

• Electronic attenuation coefficient (e, cm2/electron)

• Atomic attenuation coefficient (a, cm2/atom)0

1

Ne

0N

Za

w

A

A

ZNN

0

Z the atomic number

N0 the number of electrons per gram

NA Avogradro’s number

AW the atomic weight

Coefficients (3)

• Energy transfer coefficient (tr)

– When a photon interacts with the electrons in the material, a part or all of its energy is converted into kinetic energy of charged particles.

h

E trtr

The average energy transferred into kinetic energy of charged particles per interaction

trE

Coefficients (4)

• Energy absorption coefficient (en)

– Energy loss of electrons• Inelastic collisions lossesionization and excitation

• Radiation lossesbremsstrahlung

en= tr(1-g)

– g fraction energy loss to bremsstrahlung• increses with Z of the absorber

the kinetic energies of the secondary particles

Etr = ? Een=?

1 MeV

(Initial Energy ofCompton Electron, Ee) (Bremsstrahlung)

(Scattered Photon)0.3 MeV

0.7 MeV

0.2 MeV

(Incident Photon, h)

Energy imparted of photon

Interactions of photons with matter

• Photo disintegration (>10 MeV)

• Coherent scattering (coh) Photoelectric effect ()

• Compton effect (c)

• Pair production ()

nXX AZ

AZ

10

1

Coherent scattering

• Classical scattering or Rayleigh scattering– No energy is changed into electronic motion– No energy is absorbed in the medium– The only effect is the scattering of the photon at

small angles.

• In high Z materials and with photons of low energy

K

LM

Photoelectric effect (1)

• A photon interacts with an atom and ejects one of the orbital electrons.

h-EB

Photoelectric effect (2)

/ Z3/E3

• The angular distribution of electrons depends on the photon energy.

15 keV

L absorption edge

88 keV

K absorption edge

Compton effect (1)

• The photon interacts with an atomic electron as though it were a “free” electron.– The law of conservation of energy

– The law of conservation of momentum

1

1

122

200

cvcmhh

/'

sin/

sin'

cos/

cos'

22

0

22

0

1

1

cv

vm

c

hcv

vm

c

h

c

h

K

LM

h

h’

Free electron

Compton electron

…………(1)

………(2)

…...…………(3)

Compton effect (2)

= h0/m0c2 = h0/0.511

)cos()cos(

11

10hE

)cos('

11

10hh

h0

h’

Free electron

E

By (1), (2), (3)

Special cases of Compton effect

• The radiation scattered at right angles (=90°) is independent of incident energy and has a maximum value of 0.511 MeV.

• The radiation scattered backwards is independent of incident energy and has a maximum energy of 0.255 MeV.

Dependence of Compton effect on energy

• As the photon energy increase, the photoelectric effect decreases rapidly and Compton effect becomes more and more important.

• The Compton effect also decreases with increasing photon energy.

Dependence of Compton effect on Z

• Independent of Z• Dependence only on the number of electrons per

gramelectrons/g

Pair production

• The photon interacts with the electromagnetic field of an atomic nucleus.

• The threshold energy is 1.02 MeV.

• The total kinetic energy for the electron-positron pair is (h-1.02) MeV.

h

E-

E+

+-

0.51 MeV

0.51 MeV

Positron annihilation

The probability of pair production

Z2/atom

PE effect

Compton effect

PP production

h

h

h

Ee

E+

E-

tr

h

hh

h

Etr

'

h

h

h

EEtr

021.

The relationships between and tr

PE effect

Compton effect

PP production

h

h

h

Ee

E+

E-

)1( gtren

)1( gtren

)1( gtren

The relationships between tr and en

The comparison between and en

Interactions of charged particles

• Coulomb force– Collisions between the particle and the atomic electrons

result in ionization and excitation.

– Collisions between the particle and the nucleus result in radiative loss of energy or bremsstrahlung.

• Nuclear reactions• Stopping power (S) =

• Mass stopping power (S/, MeV cm2/g)

lengthpath

lossenergykinetic

Heavy charged particles

• The particle slows down

energy loss ionization or absorbed

dose

2

2

(velocity)

charge)particle(theS

Bragg peak

Electrons

• Multiple changes in direction during the slowing down process smears out the Bragg peak.

Ionization

Excitation

Bremsstrahlung

Interactions of neutrons

• Recoiling protons from hydrogen and recoiling heavy nuclei from other elements– A billiard-ball collision

– The most efficient absorbers of a neutron beam are the hydrogenous materials.

• Nuclear disintegrations– The emission of heavy charged particles, neutrons,and rays

– About 30% of the tissue dose

Comparative beam characteristics (1)

• Neutron beams nBBeH 10

105

94

21

Comparative beam characteristics (2)

• Heavy charged particle beams

Comparative beam characteristics (3)

• Electron beams & protons

Thank you…Thank you…