Biomedical Engineering Reference
In-Depth Information
Table 2.1:
Properties of some commonly used positron-emitting isotopes
β +
E max
Half-life
Range
(MeV) a
(mm) b
Radionuclide
Production
fraction
(min)
Carbon-11 ( 11 C)
Cyclotron
0.99
0.96
20.4
0.28
Fluorine-18 ( 18 F)
Cyclotron
0.97
0.64
109.7
0.22
Nitrogen-13 ( 13 N)
Cyclotron
1.00
1.19
9.96
0.45
Oxygen-15 ( 15 O)
Cyclotron
1.00
1.72
2.07
1.04
Gallium-68 ( 68 Ga)
Cyclotron
0.89
1.90
68.3
1.35
Rubidium-82 ( 82 Rb)
Generator
0.96
3.35
1.25
2.6
a
E max = maximal positron energy.
b Approximated distance that a positron traveled before annihilation, expressed in full width at half
maximum (FWHM).
For positron emission to be energetically feasible, the total energy difference
between the parent and the daughter states should be at least 1.022 MeV, which
is the energy equivalent of a positron and an electron, according to Einstein's
energy-mass equivalence: E = mc 2 . The energy difference between the parent
and the daughter states is shared between the positron and the neutrino. In other
words, the emitted positrons have a spectrum of energies, whose maximum is
given by
E max = E ( Z X ) E (
A
Z 1 Y ) 1.022 MeV .
(2.3)
Typically, the likelihood of positron emission is higher for elements with lower
atomic number, but for proton-rich nuclei with intermediate atomic number both
decay modes are competing with each other. Table 2.1 lists some commonly
used positron-emitting isotopes and their properties. Positron emitters are of
special interest in medicine because the main elements (e.g. carbon, oxygen and
nitrogen) that constitute living organisms have isotopes that emit positrons. The
only exception is hydrogen for which fluorine-18 is an analogue.
2.4 Positron Annihilation
The positron will have some initial energy after emission from the parent nu-
cleus. It travels a short distance from the nucleus, scatters and collides with
loosely bound electrons nearby before fusing with one of them to form positro-
nium (which has a very short half-life, 10 7
s) and then annihilates. Their
 
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