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Nuclides for check and calibration sources

Nuclides for check and calibration sources

A laboratory that measures radiation keeps two kinds of source. One kind tells it whether an instrument still reads what it read yesterday. The other, fewer and more carefully kept, tells it what the instrument should read in the first place. The nuclide chosen for either job is decided almost entirely by three properties: the half-life, the energies emitted, and what the nuclide decays into. All three are in the table this site calculates from, so the reasons behind the conventional choices can be checked here rather than inherited.

Check sources and reference sources

A check source confirms constancy. Its activity does not need to be known well; what matters is that it changes only by decay and that it can be placed in the same position every time. The record that goes with it is the instrument's own reading on the day the source was put into service, and later readings are compared with that figure after correcting for decay.

A reference source carries a certificate. The certificate states an activity, or an emission rate, at a reference date, with an uncertainty and a statement of how the value is traceable to a national standard. Contamination monitors are the case where the distinction matters most: the certified quantity is usually the surface emission rate — particles leaving the active face per second — because backscatter from the backing and absorption in the deposit separate it from the activity by an amount that depends on the source's construction. ISO 8769 describes reference sources of this kind. The same nuclide often serves both purposes; the difference is the certificate and the care taken over handling, not the physics.

Half-life and the working life of a source

The half-life sets two things at once: how long a source stays useful, and how much a mistake in the reference date costs. The table gives both, shortest-lived first.

NuclideHalf-lifeLost per year Lost in one month
Y-88 106.626 days 90.7% 17.95%
Co-57 271.74 days 60.6% 7.47%
Mn-54 312.20 days 55.6% 6.53%
Cd-109 461.9 days 42.2% 4.46%
Na-22 2.6018 years 23.4% 2.20%
Co-60 1925.28 days 12.3% 1.09%
Ba-133 10.551 years 6.4% 0.55%
Eu-152 13.517 years 5.0% 0.43%
Sr-90 28.91 years 2.4% 0.20%
Cs-137 30.08 years 2.3% 0.19%
Am-241 432.6 years 0.2% 0.01%

Computed from the recorded half-life alone: the fraction lost is 1 − 2−t/T½.

The last column is the one that is easy to overlook. A reference date read wrongly by one month costs 0.19% for Cs-137, which disappears inside any realistic uncertainty, and 7.47% for Co-57, which does not. Co-57 keeps only 0.9% of its activity after five years, so sources of it are replaced on a schedule measured in months rather than years. Cs-137 loses 2.28% a year and is the usual long-term constancy source for that reason: a decay correction is still required, but a careless one does little damage. Am-241 loses 0.16% a year, which over the life of an instrument is close to no change at all.

Short half-lives are not a defect in themselves. Na-22 and Y-88 are chosen for their photon energies, and the price is a source that loses 23.4% and 90.7% of its activity a year. A laboratory using them has to apply the decay correction every time, and has to budget for replacement.

Photon energy and what it tests

A detector's response depends on photon energy, and a source tests the response only at the energies it emits. The table lists the line that carries the largest share of each nuclide's air kerma rate, the number of lines needed to account for nine-tenths of that kerma, the air kerma rate constant itself, and the half-value layer in lead for the whole spectrum.

NuclideMain line (keV) Lines for 90%
Cd-109 22.2 4
Am-241 59.5 2
Co-57 122.1 2
Ba-133 356.0 7
Cs-137 661.7 1
Mn-54 834.8 1
Na-22 1274.5 2
Co-60 1332.5 2
Eu-152 1408.0 15
Y-88 1836.1 2

Kerma shares and constants are summed over recorded lines above 20 keV. Lines below that cutoff, such as the neptunium L X-rays from Am-241, are emitted but not counted here.

Read down the table and the conventional uses follow. Cs-137 puts 98% of its kerma into a single line, which is why it serves as a reference radiation for dose-rate meters; ISO 4037-1 lists it, with Co-60, among the gamma reference radiations. Co-60 gives a constant 4.0 times larger from two lines of almost equal yield at the high end of the range. Am-241 and Cd-109 test the low end, where many detectors respond very differently from how they respond at Cs-137; the kerma from Cd-109 is carried by silver K X-rays rather than by its 88 keV gamma, which is emitted in only 3.6% of decays.

Two choices are made because a long-lived nuclide imitates a short-lived one. Co-57's 122 keV line sits close to the photon energy of Tc-99m, so it stands in for Tc-99m in activity-meter checks and in the flood sources used to test gamma-camera uniformity. Ba-133's 356 keV line sits close to I-131's 364 keV, and Ba-133 is used as a long-lived substitute for I-131 in the same way. In both cases the substitute is not a perfect match — the other lines in its spectrum differ — and an instrument calibrated with the substitute alone carries a small correction that should be stated rather than assumed away.

Eu-152 sits at the other extreme: it needs 15 lines to account for nine-tenths of its kerma, and its recorded lines above the cutoff run from 40 keV to 1408 keV. That spread is a nuisance for dose-rate work and is exactly what a germanium spectrometer's efficiency calibration needs — many points across the energy range from one source with one certificate. Y-88 extends such a calibration above Co-60, at the cost of the short half-life noted above.

Daughters a certificate depends on

Several common sources are, in the radiation they actually deliver, sources of their daughter. Cs-137 is the clearest case. The 662 keV photon is emitted when Ba-137m de-excites, not by Cs-137 itself. The decay data record it against Cs-137 at 85.1% per decay, and against Ba-137m at 89.9% per decay; the ratio of the two, 94.7%, is the share of Cs-137 decays that pass through Ba-137m. The Cs-137 figure therefore assumes the daughter is present in equilibrium. Ten half-lives of Ba-137m are 25.5 minutes, so in any sealed source the assumption holds; in a freshly separated solution it does not, and that solution's photon output rises over its first half hour.

Sr-90 beta sources follow the same pattern with a larger consequence. Sr-90's own betas reach 0.55 MeV; those of its daughter Y-90 reach 2.28 MeV, and Y-90 is back in equilibrium within 26.7 days. What a Sr-90 check source tests — the penetration through a detector window, the response to energetic electrons — is set by Y-90. Ge-68 sources, used for PET calibration, have no photon line of their own in this table at all; the field is the annihilation radiation from their daughter Ga-68, which is back in equilibrium within 11.3 hours.

Beta and alpha sources

For beta sources the endpoint energy decides what is being tested. A low endpoint tests the detector window, because only a thin window lets those electrons through; a high one tests response to electrons that reach the sensitive volume easily. The range in acrylic gives a sense of the spread.

The low end of that list is where efficiency falls fastest and where a source's own construction matters most: an electron that can be stopped by a fraction of a millimetre of plastic can be stopped by the cover of the source. This is the practical reason contamination monitor calibrations are expressed as surface emission rate.

Alpha sources raise a different question: how many photons come with the alphas. Pu-239's recorded photon lines above 20 keV add up to 0.064 photons per hundred decays, against 5.16 MeV alphas in every decay. Am-241's 59.5 keV line alone is emitted in 35.9 of every hundred decays, alongside its 5.49 MeV alpha. On an instrument with separate alpha and beta–gamma channels an Am-241 source therefore registers on both, and the spill between channels has to be measured with the source in place rather than assumed from the alpha emission alone.

Decay correction at the bench

The correction itself is one line: the activity now is the certified activity multiplied by 2−t/T½, where t is the time since the reference date. Ten years after its reference date a Cs-137 source has 79.4% of its certified activity; three years after its reference date a Na-22 source has 45.0%. Leaving the correction out is an error of exactly the complement of those figures. The decay calculator does the arithmetic and shows the intermediate values; the reference date and time zone on the certificate are the inputs worth checking twice.

Over long intervals the half-life's own uncertainty enters the corrected value, in proportion to the number of half-lives elapsed. For a source a fraction of a half-life from its reference date the effect is negligible; for a short-lived source used across several half-lives, the evaluated uncertainty of the half-life belongs in the uncertainty budget.

Limits of this note

Everything above is computed from the nuclide alone. A real source adds things the table cannot know: radionuclidic impurities, which certificates list and which matter most in multi-line sources; absorption of low-energy X-rays in the encapsulation, which can remove the very lines that made the nuclide attractive; and scatter from the source holder. None of this note replaces the certificate or the manufacturer's statement of construction.

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