6.2. Organic Scintillators 341
The reader should note that not all the disadvantages listed here are typical
of only plastic scintillators. As we will see later, other types of scintillators also
suffer from one or more of such performance related issues. The decision to use
a particular type of scintillator is highly application specific. That is why, even
with these disadvantages, plastic scintillators are still extensively used in a variety
of applications ranging from medical dosimetry to high energy physics.
Before we start our discussion on the details of plastic scintillators, let us first
spend some time understanding the Birk’s formula as presented above and given by
dL
dx=
AdE/dx
1+kdE/dx.
This formula is extensively used to characterize response of plastic scintillators and
therefore deserves some attention. The left hand side of the formula represents the
light yield per unit length of the particle track. On the right hand side there are three
parameters: A,k,anddE/dx. The constantAis called theabsolute scintillation
efficiencyof the material. It is a function of the scintillator material and is generally
available in literature for most of the scintillators. The constantkon the other
hand, which is sometimes referred to as thesaturation parameter, is unfortunately
available only for a few materials. The practice is, therefore, to use the available
value for a material that closely resembles the material under consideration. In
general the value ofkis of the order of 0.01gMeV−^1 cm−^2. The third parameter
is thestopping powerof the material for the type of incident particle. It depends
not only on the type of the material but also on the type of incident radiation. In
Chapter 2 we discussed the stopping power at length and saw that it can be fairly
accurately determined from the Beth-Bloch formula.
Some authors prefer to write the Birk’s formula for the total light yield Lin
terms of the total energy lost by the particle E,thatis
L=
A E
1+kdE/dx. (6.2.3)
The reader can readily verify that this representation is equivalent to the formula
6.2.2.
Let us now try to understand what the Birk’s formula physically represents.
When particles pass through a scintillator they loose energy with a rate that can
be determined by the Bethe-Bloch formula. The energy lost by the particles goes
not only into exciting molecules but a part of it also increases the lattice vibrations.
The de-excitation of the molecules leads to the emission of scintillation photons
with a high probability. Now, if we increase the stopping power (for example by
increasing the energy of the incident particles), more molecules will get excited per
unit track length, thus producing more scintillation light. But this behavior can not
persist indefinitely since the sample has a finite number of molecules that can be
excited. This implies that the number of molecules available for scintillation actually
decreases with increase in the total energy delivered by the radiation. Taking this
argument a step further we can conclude that there must be a value of stopping
power at which all the molecules have been excited. The sample in this state will
be said to have reached a state of saturation. After reaching this state, delivering
more energy to the material would not increase the light output. This statement is
actually what is referred to as theBirk’s lawand is mathematically represented by