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Positron emitters and 511 keV shielding

Positron emitters and 511 keV shielding

A positron emitter is, for shielding purposes, a source of 511 keV photons, and it behaves quite differently from the gamma emitters that most radiation work is organised around. The photons do not come from the nucleus. Their energy is fixed by the electron mass rather than by nuclear structure, so every positron emitter shares the same principal line. And the nuclides used in medicine have half-lives measured in minutes, so the source changes during the time it takes to handle it. This note goes through each of those with figures computed from the nuclide table.

Annihilation radiation

In positron decay a proton in the nucleus becomes a neutron and the nucleus emits a positron and a neutrino. The positron slows down in the surrounding material, combines with an electron, and the pair annihilates. Almost always the result is two photons of 511 keV each — the rest energy of the electron — travelling in nearly opposite directions. The photons therefore originate where the positron stopped, a short distance from the decaying atom, and the source of the radiation is in effect the vial wall, the syringe, or the tissue around the injection site.

Positron emission always competes with electron capture, which leads to the same daughter without emitting a positron, and positron emission is only possible when the decay energy exceeds twice the electron rest energy. The share of decays that go by positron emission is a property of each nuclide, and it can be read straight from the decay data.

Reading the 511 keV line in decay data

Decay data record annihilation radiation as a line at 511 keV with an intensity per hundred decays. Because each positron gives two photons, the intensity can approach 200%, and half of it is the number of positrons per hundred decays. The nuclides in this table with a recorded 511 keV line are below.

NuclideHalf-life511 keV photons per 100 decays Positrons per 100 decays
F-18 109.77 minutes 193 96.7
Na-22 2.6018 years 180 90.0
Ga-68 67.71 minutes 178 88.9
Zn-65 243.93 days 2.84 1.42
Y-88 106.626 days 0.420 0.210
Cl-36 3.013 × 10⁵ years 0.0280 0.0140
Eu-152m1 9.3116 hours 0.0142 0.00710
K-40 1.248 × 10⁹ years 0.00200 0.00100

Positrons per hundred decays are half the recorded 511 keV intensity. The last column is the most intense other photon line above 20 keV, where there is one.

F-18, Na-22, Ga-68 are positron emitters in the practical sense: most of their decays produce a positron. F-18 emits nothing else above 20 keV, so its photon field is annihilation radiation and nothing more. Ga-68 adds a weak line at 1077 keV. Na-22 adds a 1275 keV photon in almost every decay, which is why Na-22 is a long-lived reference for 511 keV and also a source of true-coincidence summing when the two photons arrive together in a detector close to the source. For Zn-65, Y-88, Cl-36, Eu-152m1, K-40 the positron branch is minor, and their 511 keV line is a small feature beside their other emissions.

Lead, tungsten and concrete at 511 keV

F-18 has a single line, so the half-value layers computed for its spectrum are the half-value layers of 511 keV photons themselves: 3.90 mm of lead, 2.68 mm of tungsten and 34.1 mm of concrete, with a tenth-value layer in lead of 13.0 mm. Compared with the sources nuclear medicine was built around, that is a different order of shielding. The lead half-value layer for Tc-99m is 0.23 mm, so each halving costs 17 times as much lead at 511 keV, and F-18 has an air kerma rate constant 8.8 times that of Tc-99m per becquerel. Even Cs-137, at 5.34 mm, is not far above it.

Two practical consequences follow. Syringe and vial shields for positron emitters are made of tungsten and are much thicker than their Tc-99m counterparts, because tungsten's higher density achieves the same attenuation in a size that can still be handled. And protective aprons designed for diagnostic X-rays do little at this energy: a layer of 0.5 mm of lead, a common lead-equivalence rating for such aprons, transmits 92% of a narrow 511 keV beam on the half-value layer above. Lead-equivalence is in any case specified at X-ray tube energies, and aprons made from lead-free composites can do worse at 511 keV than their rating suggests.

The figures here are narrow-beam values. For room shielding, where scattered photons reach the point of interest around and through the barrier, broad-beam transmission data apply; the AAPM Task Group 108 report on PET and PET/CT shielding gives them for lead, concrete and iron, and also takes account of the attenuation of the photons in a patient's own body. The gamma shielding calculator here includes a buildup factor for a point source and is a first estimate, not a room design.

Decay through a working day

With half-lives of 109.77 minutes for F-18 and 67.71 minutes for Ga-68, the activity in hand changes noticeably between dispensing and use. For F-18:

This works in both directions. A dose ordered for a time of injection has to be dispensed with more activity than will be given, by a factor that grows exponentially with the delay, and a delay in the schedule raises the activity needed from the dispensing laboratory accordingly. On the other side, F-18 waste only needs to be held: after 24 hours 0.0112% of the activity remains, so storage for decay disposes of it within days. The decay calculator gives the exact factor for any interval.

The Ge-68/Ga-68 generator

Ga-68 is usually obtained from a generator in which its parent, Ge-68 (270.93 days), is held on a column. Ge-68 has no photon line in this table; the radiation from a generator is the annihilation radiation of the Ga-68 growing on it. After an elution removes the Ga-68, it grows back to 46% of its equilibrium activity in one hour, 71% in two and 91% in four, and is fully back within 11.3 hours. The parent sets the generator's working life: after one year a generator retains 39% of its Ge-68, and the Ga-68 it can deliver falls in proportion. The same parent–daughter pair is used in sealed form, as Ge-68 phantoms for PET calibration, where the daughter is permanently in equilibrium.

A 511 keV peak is not an identification

In gamma spectrometry a peak at 511 keV does not by itself show that a positron emitter is present. Any photon above twice the electron rest energy can create an electron–positron pair in the detector or in the material around it, and the positron's annihilation then produces 511 keV photons. High-energy gamma emitters, cosmic radiation and the shielding of the spectrometer all contribute a 511 keV peak in this way, and it is present in most background spectra. The annihilation peak is also visibly wider than neighbouring gamma peaks, because the motion of the electrons involved spreads the photon energies slightly. A positron emitter is identified by its other lines where it has them, by the decay of the 511 keV peak with the right half-life, or by coincidence between the two back-to-back photons — the principle on which positron emission tomography is built.

Limits of these figures

The positron itself is not modelled here. This table carries no positron spectrum for these nuclides, so nothing on this site gives positron ranges, and the point-source figures assume all annihilation happens at the source. Bremsstrahlung from positrons, three-photon annihilation and the attenuation of the photons in the source container are also outside these figures.

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