Subatomic Physics

4.1. Scintillation Counters 55
The efficiency of these inorganic crystals for gamma rays is high, but the decay of
each pulse is slow, about 0.25µs. Moreover, NaI(Tl) is hygroscopic and large crystals
are very expensive. Plastic scintillators, for instance polystyrene with terphenyl
added, are cheap; they can be bought in large sheets and can be machined in nearly
any desired shape. The decay time is only a few ns, but the efficiency for photons
is low. They are therefore mainly used for the detection of charged particles.
A few remarks are in order concerning the mechanism of observation of gamma
rays in NaI(Tl) crystals. For a gamma ray of less than 1 MeV, only photoeffect
and Compton effect have to be considered. Photoeffect results in an electron with
an energy Ee = Eγ − Eb, whereEb is the binding energy of the electron before it
was ejected by the photon. The electron will usually be completely absorbed in the
crystal. The energy deposited in the crystal produces a number of light quanta that
are then detected by the photomultiplier. In turn, these photons result in a pulse
of electric charge proportional to Ee andwithacertainwidth∆E. This photo
or full-energy peak is shown in Fig. 4.3. The energy of the electrons produced by
the Compton effect depends on the angle at which the photons are scattered. The
Compton effect therefore gives rise to a spectrum, as indicated in Fig. 4.3. The
width of the full-energy peak, measured at half-height, depends on the number of
light quanta produced by the incident gamma ray; typically ∆E/Eγ is of the order of
20% at Eγ = 100 keV and 6–8% at 1 MeV. At energies above 1 MeV, the incident
gamma ray can produce an electron–positron pair; the electron is absorbed, and
the positron annihilates into two 0.51 MeV photons. These two photons can escape
from the crystal. The energy deposited is Eγ if no photon escapes, Eγ − mec 2 if
one escapes, and Eγ − 2mec 2 if both annihilation photons escape.
The energy resolution ∆E/E deserves some additional consideration. Is a resolution
of about 10% sufficient to study the gamma rays emitted by nuclei? In
some cases, it is. In many instances, however, gamma rays have energies so close
together that a scintillation counter cannot separate them. Before discussing a
counter with better resolution, it is necessary to understand the sources contributing
to the width. The chain of events in a scintillation counter is as follows: The
incident gamma ray produces a photoelectron with energy Ee ≈ Eγ. The photoelectron,
via excitation and ionization, produces n1q light quanta, each with an energy
of E1q ≈ 3eV(λ ≈ 400nm). (For clarity we call the incident photon the gamma ray
and the optical photon the light quantum.) The number of light quanta is given by
n1q ≈ Eγ
ɛlight,
E1q
where ɛlight is the efficiency for the conversion of the excitation energy into light
quanta. Of the n1q light quanta, only a fraction ɛcoll are collected at the cathode
of the photomultiplier. Each light quantum hitting the cathode has a probability
ɛcathode of ejecting an electron. The number ne of electrons produced at the input