Physics and Radiobiology of Nuclear Medicine

then only a fraction of all radiations emitted from the source will be
detected by the detector. This fraction is determined by the solid angle sub-
tended by the detector on the source. The geometric efficiency,fg, is equal
to the number of radiations striking the detector divided by the total
number of radiations emitted by the source. Thus,

(8.5)

For a circular detector with radius r, it is equal to the area pr^2 of the detec-
tor divided by the total spherical area 4pR^2 , where Ris the distance between
a point source Sand the detector D(Fig. 8.9).

(8.6)

As the distance Rbetween the source and the detector increases, the fg
decreases, according to the inverse square law, that is,fg∝1/R^2 (Fig. 8.9A).
Thus the fgat 2Ris one fourth of the fgat R. The value of fgincreases with
the size of the detector. Also, the finite size of the radiation source affects
the fgvalues.

f

r

R

g=

p

p

2

4 2

fg=

No. of radiations striking the detector

Total number of radiations emitted by the source

98 8. Scintillation and Semiconductor Detectors

70 140 210 280

100

75

50

25

1.3 cm

0.6 cm

Intrinsic efficiency (%)

Gamma ray energy (keV)

NaI(Tl)

thickness

Fig. 8.8. Dependence of intrinsic efficiency on photon energy and detector
thickness.