Physics and Radiobiology of Nuclear Medicine

from a radionuclide. Considering these factors, the overall counting effi-
ciency of a counter for a radiation is given by the following expression:

Efficiency =fi×fp×fg×Ni (8.2)

where fi is the intrinsic efficiency; fp is the photopeak efficiency, or
photofraction;fgis the geometric efficiency; and Niis the abundance of the
radiation in question.Niis available in literature on Tables of Isotopes.

Intrinsic Efficiency

The fraction of all radiations of a given type and energy impinging on the
detector that interacts with it to produce pulses is called the intrinsic effi-
ciency,fi, of the detector:

(8.3)

It includes all photons undergoing both photoelectric absorption and
Compton scattering. Intrinsic efficiency depends on the type and energy of
the radiation and the linear attenuation coefficient (m) and thickness of the
detector. The dependence of intrinsic efficiency on the photon energy and
the detector thickness is illustrated in Figure 8.8. The value of fiis almost 1
for low-energy g-rays and thicker detectors. The fitends to 0 for high-energy
g-rays and thinner detectors. These conditions apply to all solid scintillation
detectors. The intrinsic efficiency of gas detectors is almost unity for a- and
b-particles but is about 0.01 (1%) for g- and x-rays.

Photopeak Efficiency or Photofraction

The fraction of all detected g-rays that contributes only to the photopeak
is called the photopeak efficiency, or photofraction(fp). It is given as the
total photopeak area divided by the total area under the entire spectrum:

(8.4)

This value is affected by all factors that influence photoelectric effect, such
as the size and composition of the detector and g-ray energy, but is primarily
determined by the discriminator settings on the PHA. The fpincreases with
increasing window width of the PHA.

Geometric Efficiency

Radiations from a source are emitted uniformly with equal intensity in all
directions. If a source of radiation is placed at a distance from a detector,

fp=

All counts under the photopeak

All photons detected by the detector

=

All counts under the entire spectrum

No. of radiations impinging on the detector

fi=

No. of radiations detected by the detector

No. of radiations impinging on the detector

Characteristics of Counting Systems 97