610 Chapter 11. Dosimetry and Radiation Protection
beam has an energy spectrum with a range that could be very narrow or very wide.
If the energy spectrum is well defined, in most instances we can assign an average
energyE ̄pto all the particles and still use the above formulas to compute the energy
flux. However a better thing to do would be to compute theenergy flux spectrum
through the relation
dΨr=EspdN
dtda, (11.2.9)
wheredΨ represents the energy flux at the energyEsp. A practical but very basic
way to do this would be to increment the discriminator windows in a single channel
analyzer in small steps and counting the particles for a certain time. This procedure
when carried out for the whole range of particle energies would yield the energy
flux spectrum. Of course a better way would be to use a multi channel analyzer,
which generates the spectrum without the need to change the discriminator level
repeatedly.
11.2.CIntegratedFluxorFluence
Sometimes it is desired to compute the flux and fluence rates integrated over a
certain time period. This could, for example, be required to determine the radiation
dose received by a patient undergoing radiation therapy.
The flux integrated over a period of time is calledintegrated fluxorfluence.
Mathematically, it is given by
Φ=dN
da, (11.2.10)
where,dNrepresents the number of particles passing through the areada.Since
this relation does not explicitly contain time, it can also be interpreted to represent
the number of particles incident on a surface areadaat any instant. However this
definition is somewhat misleading, since practically speaking, it is unmeasurable. We
have repeatedly seen in the previous chapters that performing a counting experiment
always involves time during which the counting is performed. This time can be
made very small but its width is still limited by the timing resolution of the readout
circuitry. It is therefore preferable to see the particle fluence as representing the
particle flux integrated over a time period.
Just like the particle fluence we can also define theenergy fluenceorintegrated
energy fluxas the amount of energy incident on a surface area within a certain time
period. Mathematically speaking, this can be written as
Ψ=
E ̄pdN
da, (11.2.11)
where, as before,E ̄prepresents the average particle energy.
Example:
1. 5 × 104 photons having an average wavelength of 0.12nmpass through a
surface of area 1.8cm^2 per second. Determine the energy fluence rate and
the integrated particle flux for 1 second of irradiation.