Interacti ons of P h otons with Mat t er

 Photons are el ectro magnetic radiation with zero mas s , zero charge , and a velocity that is alway s c, the speed of light.

 Because they are el ectr ically neutral, they do not ste a dily lose energy via coulom bic interactions with atom ic el ectrons, as do charged particles.

 Photons travel som e considerable distance before undergoing a m o re “catastrophic” interaction leading to partial or total transfer of the phot on energy to electron energy .

 These electrons will ultim ately de posit the i r energy in the m e dium .

 Photons are far more penetrating than charged particles of similar energy.

Energy Loss Mech anisms

 phot oelectric effect

 Com p ton scattering

 pair production

Interaction probability

 linear attenuation coefficient ,  ,

The probability of an interacti on per unit distance traveled Dim e nsions of inverse length (eg. cm -1 ).

N  N e   x

 The coefficient  depends on photon energy and on the material being traversed .



 mass attenuation coefficient , 

The probability of an interaction per g cm -2 of material traversed. Units of cm 2 g -1

      x 

N  N 0 e  

Mechanisms of Energy Loss: Photoelectric Effect

 In the phot oelectric absorption proce ss, a phot on undergoes an interaction with an ab sorber atom in which the photon completely disappears .

 In its place, an en ergetic photoelectron is ejected from one of the bound shells of the ato m .

 For gamm a rays of sufficient energy, the m o st probable origin of the phot oelectron is the m o st tightly bound or K shell of the ato m .

 The photoelectron appears with an energy given by

E e- = hv – E b

(E b represents the binding energy of the p hotoelectron in its original shell)

Thus for gamma-ray energies of m o re than a few hundred keV, the photoelectron carries off the m a jority of the original phot on energy.

Filling of the inner shell vacancy can produce fluorescen ce ra diation , or x ray phot on(s).

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The photoelectric process is the predominant mode of photon interaction at

o relatively lo w photon energies

o high atomic number Z

The probability of photoelectric absorption, sym bolized  (tau), is roughly proporti onal to

  Z n

( h  ) 3

where the exponent n varies between 3 and 4 over the gamma-ray energy region of interest.

This severe dependence of the photoelect ric absorption probability on the atom ic num ber of the absorber is a primary reason for the preponderance of high-Z materials (such as lead) in gamma-ray shields .

The photoelectric interaction is m o st likely to occur if the energy of the incident phot on is just greater than the binding energy of the electron with which it interacts.

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Compton Scattering

 Com p ton scattering takes place betw een the incident gamma-ray phot on and an electron in the absorbing material.

 It is m o st often the predom inan t interaction mechanism for gamma-ray energies typical of radioisotope sources.

 It is the most dominant interaction mechanism in tissue .

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In Com p ton scattering, the incom i ng gamma-ray photon is deflected through an angle  with respect to its or i g i n al direction.

The photon transfers a portion of its energy to the electron (assumed to be initially at rest), which is then known as a recoil electron, or a Compton electron .

 All angles of scattering are possible.

 The energy transferred to the electron can vary from zero to a large fraction of the gamma-ray energy.

 The Co mp ton process is most important for energy absorption for soft tissues in t h e range from 100 keV to 10MeV.

 The Co m p ton scattering probability is is sym bolized  (sigm a ):

 al most independent of atomic number Z ;

 decreases as the photon energy increases;

 directly proport i onal to the number of electrons per gram , which only varies by 20% from the lightest to th e heaviest el ements (except for hydrogen).

Compton Scattering Energetics

The energies of the scattered photon

h  ' and the Co mpt on electron E e, are given by

h  '  h 

1

1   ( 1  cos  )

E e = h 

 ( 1  cos  ) 1   ( 1  cos  )

h 

w h e r e  =

m c 2

[ m c 2

is the electron rest energy, 0.511 MeV,

h  is the incom i ng photon energy]

Limits of Energy Loss

Maximum en ergy transfer to recoil el ectron:

 angle of el ectron recoil is forward at 0  ,  = 0  ,

 the scattered photon will be scattered straight back,  = 180 

 With  = 180  , cos  = -1 the expressions above simplify t o :

2 

E e(m a x) = hv 1  2 

and

'

min

= hv

1

1  2 

The Table below illustrates how the am o unt of energy transferred to the electron varies with photon energy. Energy transfer is not large until the incident photon is in excess of approxi m ately 100 keV.

For low - energy photons , when the scatt e ring interaction takes place, little energy is transferred , regardless of the probabili ty of such an interaction.

As the energy increases, the fractional tr ansfer increases, approaching 1.0 for phot ons at energies above 10 to 20 MeV.

Pair Production

If a photon enters matter with an energy in excess of 1.022 MeV , it may interact by a process called p a ir production .

The photon, passing near the nucleus of an at om , is subjected to strong fi eld effects from the n u cleus and may disappear as a photon and reapp ear as a p o sitive and negative electron pair .

The two el ectrons produced, e- and e+, ar e not scattered orbital electrons , but are creat ed, de novo , in the energy/mass conversion of t h e disappearing phot on.

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Pair Production Energetics

The kinetic en ergy of the electrons produ ced will be the difference between the energy of the incom i ng photon and the energy equivalent of two electron masses (2 x 0.511, or 1.022 MeV).

E e+ + E e- = h  - 1.022 (MeV)

Pair production probability, sym bolized  (kappa),

 Increases with increasing photon energ y

 Increases with ato m i c nu m b er approxim a tely as Z 2

(a) Com p ton scattering

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(b) Photoelectric effect

(c) Pair production

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 Photoelectric effect: produces a scatte red phot on and an electron, varies as ~ Z 4 /E 3

 Co mpton effect: produces an electron, varies as ~ Z

 Pair production: produces an elec tron and a positron, varies as ~Z 2

Bulk Behavi or of Phot on s in an Absorb er

Attenuation Coefficients

Linear attenuation coefficient  :

The probability of an interacti on per unit distance traveled.  has the dimensions of inverse length (eg. cm -1 ).

N  N e   x

The coefficient  depends on photon energy and on the material being traversed .

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The mass attenuation coefficient,  /  , is obtained by dividing  by the density  of the material, u s ually expressed in cm 2 g -1 .