VISIPLAN - Basics physics principles

Radiation basics
The dose to the workers assessed with VISIPLAN covers the external exposure with gamma and x-ray radiation. In the following, we describe the origin of this radiation and the way in which shielding and doses to the workers are calculated.

Gamma radiation, X-ray radiation

Gamma radiation and X-ray radiation are both forms of electromagnetic radiation with energies above 10 keV. This kind of radiation is characterised by its high penetrability through matter.

Gamma Radiation Gamma radiation originates from unstable isotopes (natural or artificial) which after disintegration through α-decay or β-decay remain in an excited state.
The isotope can reduce its excess energy by emitting a photon of gamma (γ)-radiation (see fig.1. below).

Fig.1. : Sources of gamma-radiation
 
X-ray radiation X-ray radiation is produced when the electrons around the nucleus of an atom are rearranged. This rearrangement can be caused by collision of a particle with the atom or through interaction with radiation.
X-ray radiation is also produced through the energy loss of an electron moving in the electrical field of a heavy nucleus (see fig.2.)

Fig.2. : Sources of X-ray radiation
 

Interaction of radiation with matter

Different interactions between radiation and matter are possible, s.a. the photo-electric effect, the Compton-effect and pair production.

Photoelectric
effect
In the photoelectric effect the incoming photon collides with an electron of the atom. The photon is absorbed and the electron is ejected from the atom. The energy of the photon is completely transferred to the electron. Part of the energy is spent to compensate the binding energy of the electron, the remaining part is taken up as kinetic energy of the electron. This type of interaction is predominant for low energy photons.
Compton Scattering The Compton effect occurs when a photon colliding with an electron of the atom loses only a fraction of its energy. The photon survives the collision but is deviated from its trajectory. Compton scattering is predominant in the energy range from 1 MeV to 10 MeV for elements of low and intermediate atomic number.
Pair production Pair production is the most likely process for photons of high energy. During this interaction the photon creates an electron positron pair. This process only occurs when the energy of the photon is greater then 1.02 MeV.

All these effects can be seen on the following figure (3.).
  Fig.3. : Photoelectric effect and pair production

 

Gamma-ray attenuation

In order to describe the attenuation of radiation through shielding matter we introduce the quantity called fluence rate.

Fluence rate The fluence rate Φ gives the intensity of the radiation at a certain point i.e. the number of photons passing a unit surface per unit time (cm-2.s-1).

Narrow beam attenuation

Consider a narrow collimated beam of photons passing through matter. Part of the incoming photons will be removed from the beam, in a distance dx, due to processes s.a. the photoelectric effect, Compton scattering and pair production.

The fluence rate reduction is found to be proportional to dx, the distance travelled through the matter and can be written as :
  (formula 1.)
Linear attenuation The linear attenuation coefficient µ is determined by the above mentioned interaction processes, and is a function of the material composition and photon energy.
The photon fluence rate after passing a distance t through a homogeneous medium can thus be written as :
  (formula 2.)
With Φ0 the photon fluence rate of the incoming beam.
This equation determines the number of uncollided photons that arrive at the dose point.
 
Fig.4. : Narrow beam attenuation

 


Broad beam attenuation

The narrow beam attenuation, described above, determines as mentioned only the number of uncollided photons that arrive at the dose point after travelling a distance t through the material. However photons that were scattered in the medium or subsidiary photons locally released can also arrive at the dose point (see fig.5.).

Build-up factor To adjust the result of the uncollided photons to include contributions from the scattered and subsidiary radiation a dimensionless correction factor B called build-up factor is introduced.
The photon fluence rate after passing a distance t through a homogeneous medium can thus be written as :
(formula 3.)
The build-up factor is a function of the energy of the gamma radiation and is also function of the distance travelled through the absorbing material.
The build-up increases with the distance travelled through the absorbing medium. The build-up factors are determined for different materials and are tabulated in ANSI/ANS-6.4.3.-1991 "American National Standards for Gamma-Ray Attenuation Coefficients and Buildup Factors for Engineering Materials".
 
Fig.5. : Broad beam attenuation

 

Photon fluence rate calculation

Point source The photon fluence rate at a dose point which is a distance &ro; from a point source is given as :
  (formula 4.)
Source strength With S (n.s-1), the source strength representing the number of photons emitted by the source per unit time.
   
Main free paths b represents the main free paths.
It is a dimensionless term which represents the attenuation effectiveness of a shield. The higher the value the higher the radiation attenuation. The value of b is found using :
  (formula 5.)
With µi the attenuation coefficient of material i and Σi the distance travelled following the source-dose point line-of-sight through the material i.
   
Volume source The photon fluence rate at a dose point near a volume source can be determined by considering the volume source as consisting of a number of point sources.
By Adding the contribution of every point source to the dose at the dose point we find the photon fluence rate at the dose point from the entire source.
  (formula 6.)
Where S represents the source strength per unit volume.
   
Point kernel Each small source is called a kernel and the process of integration, where the contribution to the dose of each point is added up, is called "point kernel" integration.
This is the method used in the VISIPLAN software.
 
Fig.6. : Point kernel integration