Nuclear Spectroscopy

mentally from a measurement of the counting rate of
a source with known activity (a calibrated standard),
or from an interpolation between measurements of
calibrated sources at energies bracketing those being
studied. For the 3.8 cm x 2.5 cm NaI(Tl) detector, the
effective detector efficiency (πr 2 ε/4πd 2 ) as a function
of gamma energy is shown in Figure 10.1.
The source distance used for the data in Figure 10.1
is the distance from the detector face to a commercially
encapsulated source placed on the eighth shelf.
Obtaining ε requires the knowledge of the solid
angle, Ω/4π,
2
Ω πr
10.2 =
2
4π
4πd
For source to detector distances that are much larger
than the largest dimension of the detector, this Ω/4π
calculation is straight forward. The shelf eight position
is not far enough from the detector to meet this
requirement. Calculations suggest that Ω/4π is about
1.54 x 10 -2 . See the 1977 paper by E. M. Wray.
Another technique for determining the absolute activity
of a few special sources, such as 22 Na and 60 Co, is
to utilize the sum peak in the detector spectrum,
shown in Figure 1.1 for 22 Na. This peak occurs when
two gammas arrive at the detector at about the same
time (within the resolving time of the detection system).
The pulses produced by each gamma interacting
with the crystal combine to produce an event that
the computer interprets as a gamma energy equal to
the sum of the energies of the individual gammas,
hence the name “sum” peak. The measured activity of
the sum peak, A sum
, depends upon the product of the
absolute activity of the source and the individual
probabilities for detecting each gamma, resulting in
10.3
A A r 2
2
π
=
d f π
ε
rd f
2 γ B 2
4π
4π
sum B γ A A
In equation 10.3 the subscripts A and B refer to the
two gammas that are coincident in the detector. For
an isotope like 22 Na, one of the annihilation gammas
(511 keV) and the 1,274 keV gamma from the nuclear
state transition can be naturally coincident with each
ε
Effective Detection Efficiency
0.01
0.001
J J
J J
J
Figure 10.1 NaI(Tl) detector efficiency curve for a 3.8 cm x
2.5 cm cylindrical crystal with a source on the eighth shelf.
Larger crystals will have greater detection efficiencies. The
effective detector efficiency is the product (πr 2 ε/4πd 2 ).
J
J
J
J
J J J
0.0001
100 1000 4000
Gamma Energy (keV)
J
Data
linear fit
other to form a sum peak. The reason they are
coincident can be seen from the 22 Na decay scheme in
Appendix D. In the decay of a single 22 Na nucleus, the
1,274 keV gamma and the positron are emitted within
picoseconds of each other. The positron annihilation
occurs quickly after its emission, producing two
oppositely-directed, 511 keV gammas. The direction
of the 1,274 keV gamma emission is not correlated
with the direction of emission of either 511 keV
gamma. This results in a small probability that one
511 keV gamma and the 1,274 keV gamma will arrive
at the detector at the same time, due to the detector’s
geometry. This probability is expressed as the product
of the individual probabilities for the detection of
each gamma, included in equation 10.3.
Using equation 10.1 for the A and the B gammas to
get A A
and A B
, you can obtain the absolute activity of
the source, A, from equation 10.3 as
10.4
A
AA A
=
A
sum
B
This will work for sources where two gammas are
emitted within the resolving time of the detector and
there is no correlated direction between the two
29