Physics and Engineering of Radiation Detection

6.1. Scintillation Mechanism and Scintillator Properties 335

Using this and the equation 6.1.6 we can write the expression for the scintillation
efficiency as

η = qξ

Emax

W

(6.1.14)

= qξ

hc

Wλmax

. (6.1.15)

Although this expression does not take into account the energy dependence of
different parameters involved, still it gives a good estimation of the efficiency for
most scintillators. When the efficienciesqandξare not known, one can estimate
the maximum scintillation efficiency by substitutingq=1andξ=1intheabove
expression.

ηmax=

hc

Wλmax

(6.1.16)

This expression is most suitable for estimating the physical limit on the scintillator
efficiency. For crystalline scintillators it can be transformed into a more convenient
form by noting that theWvalues for such a material is about 3 times its band gap
energy. In general, one can write

W=γEg, (6.1.17)

whereEgis the band gap energy andγis a factor that depends on the material.
For most crystals its value is around 3 but can be as high as 8 for certain materials.
The maximum efficiency of crystalline scintillators can therefore also be written as

ηmax=

hc

γEgλmax

. (6.1.18)

Since the light output of a scintillator is directly related to its scintillation effi-
ciency therefore one strives to maximize the efficiency by adding impurities to the
material or by operating it at a different temperature. Unfortunately the scintilla-
tion efficiency for most scintillators is quite poor and can range from a few percents
to about 30%. The low efficiency points to the fact that most of the energy delivered
by the incident radiation goes into increasing the thermal agitations and non radia-
tive transitions. However even with such low efficiencies, scintillators can be very
effectively used for precision measurements. The reason is that the light output is
generally sufficient to obtain good signal-to-noise ratio. for example the light output
of thallium activatedNaIcrystal is about 40,000 photons perMeVof energy deliv-
ered. If a photomultiplier tube is used to detect these photons, even with a modest
20% efficiency of the photocathode, the tube will see enough photons to produce a
pulse that is large enough to be measured.

Example:

Determine the maximum efficiency of thallium activated NaI and CsI

scintillators. The wavelength of maximum emission forNaI:Tlis 410nm

and that ofCsI:Tlis 550nmwhile their band gaps are approximately 5.9

eV and 6.2eV respectively.