334 Chapter 6. Scintillation Detectors and Photodetectors
know that the number of charge pairs produced can be characterized by the so called
W-value, that is, the energy needed to create a charge pair. Hence the number of
charge pairs created by the radiation can be written as
Nep=Ei
W. (6.1.8)
The energy lost by the radiation is gained by the ions. Now, the ions thus produced
attract other ions to produce excited molecular ions, which in turn attract electrons
to again dissociate into their constituents. This process can be visualized as the
transfer of energy from the excited ions to the luminous centers. Unfortunately
this is not a very efficient process since the ions can also loose energy through non-
radiative processes, such as by collision with impurity molecules. Let us represent
the efficiency of this process byξ. The number of luminous centers activated by the
ions can then be estimated from
Nlum = ξNep= ξEi
W. (6.1.9)
The luminous centers are now ready to emit scintillation light. However there are
also other non-radiative processes possible through which they can loose energy. The
efficiency of scintillation emission by the luminous centers is generally represented
byqand most authors prefer to call it thequantum efficiencyof luminous emission.
Mathematically it is equal to the ratio of number of scintillation photonsNsto the
number of luminous centersNlum,thatis
q=Ns
Nlum. (6.1.10)
The number of scintillation photons emitted can be determined by substitutingNlum
from equation 6.1.9 into the above equation.
Ns = qNlum= qξEi
W(6.1.11)
The scintillation photons thus emitted are not monochromatic but their spectrum
has a well defined peak. The energy corresponding to this peak is themost probable
energy. We will represent it byEmax. To simplify the computations we can assume
that each of the scintillation photon carries this much energy. Hence the total energy
of the scintillation light can be written as
Es = NsEmax= Nshc
λmax(6.1.12)
whereλmaxis the wavelength of the photons corresponding to the peak of the
scintillation spectrum. SubstitutingNsfrom equation 6.1.11 into the above equation
gives
Es = qξEmax
Ei
W
= qξEi
Whc
λmax