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Half-value and tenth-value layers for common gamma emitters

Half-value and tenth-value layers for common gamma emitters

The half-value layer (HVL) is the thickness of a material that halves the dose rate from a source, and the tenth-value layer (TVL) the thickness that reduces it to a tenth. They are the quickest way to size a shield in your head: ten half-value layers take a dose rate down by a factor of about a thousand, and each tenth-value layer adds a factor of ten. This note gives the two layers in lead, iron and ordinary concrete for six nuclides that account for most practical gamma shielding work, explains why the values here differ from the single number found in many tables, and sets out what they leave out.

How these values were computed

Most published tables give one half-value layer per nuclide, taken from the attenuation coefficient at a single representative energy. That is exact for a nuclide with one photon line and an approximation for everything else. The values below are solved instead for the nuclide's whole photon spectrum. Every line in the evaluated decay data above 20 keV is attenuated by its own coefficient, weighted by the air kerma it contributes, and the thickness that brings the sum to one half or one tenth is found by bisection. The line data are the IAEA Livechart evaluation of the nuclear structure and decay data files, and the attenuation coefficients are the NIST tables, with densities of 11.35 g/cm³ for lead, 7.874 g/cm³ for iron and 2.3 g/cm³ for concrete. This is the same calculation the gamma shielding calculator and the nuclide sheets use, and a test in the repository fixes every value in the tables to it.

The figures are for attenuation only. A photon that interacts in the shield is counted as removed, which is the narrow-beam condition. No buildup factor is applied. The section on broad beams below explains what that means for a real shield.

The tables

Each table gives the first half-value layer, the first tenth-value layer, and the second tenth-value layer, which is the extra thickness needed to go from one tenth to one hundredth. When the second tenth-value layer is larger than the first, the spectrum is hardening as it passes through the material.

Lead

NuclideHVL (mm)TVL (mm)2nd TVL (mm)
Cs-137 5.34 18.1 18.3
Co-60 10.3 34.4 34.6
Ir-192 2.25 9.01 13.1
I-131 2.32 8.78 13.4
Tc-99m 0.229 0.827 0.856
Am-241 0.0865 0.362 0.396

Iron (steel)

NuclideHVL (mm)TVL (mm)2nd TVL (mm)
Cs-137 11.7 39.5 39.8
Co-60 16.5 54.8 54.9
Ir-192 8.94 30.6 32.2
I-131 8.87 30.7 32.2
Tc-99m 3.60 13.0 13.4
Am-241 0.517 2.18 2.41

Ordinary concrete

NuclideHVL (cm)TVL (cm)2nd TVL (cm)
Cs-137 3.72 12.6 12.7
Co-60 5.20 17.3 17.3
Ir-192 3.01 10.1 10.5
I-131 2.96 10.1 10.5
Tc-99m 1.81 6.53 6.76
Am-241 0.849 3.41 3.73

Narrow beam, attenuation only, air kerma from all lines above 20 keV. Half-lives: Cs-137 30.08 years, Co-60 1925.28 days, Ir-192 73.829 days, I-131 8.0252 days, Tc-99m 6.0072 hours, Am-241 432.6 years.

Why the first layer is thinner than the next

For a single photon energy, the tenth-value layer is exactly 3.32 half-value layers, because attenuation is a pure exponential. The ratio in the tables departs from that wherever the spectrum contains photons of very different energies. Low-energy lines are absorbed in the first millimetres, so the first layer removes them as well as half of the main line, and the beam that leaves it is harder than the one that entered.

Cs-137 shows the effect at its smallest. Besides its 662 keV line it emits barium K X-rays near 32 keV, which carry little dose but are stopped almost at once. The first half-value layer in lead is therefore 5.34 mm, a little thinner than the 5.50 mm that the second tenth-value layer implies for the 662 keV line alone. Ir-192 shows it at its largest among these six: its first half-value layer in lead is 2.25 mm, its first tenth-value layer 9.01 mm — 4.0 half-value layers rather than 3.3 — and its second tenth-value layer 13.1 mm. The lines between 296 and 317 keV carry most of the dose in front of the shield; behind a centimetre of lead the 468 and 604 keV lines carry most of what is left. I-131 behaves the same way, with a second tenth-value layer in lead of 13.4 mm against a first of 8.78 mm.

The practical point is that half-value layers are not additive when the spectrum hardens. To take an Ir-192 source down by a factor of a thousand, three first tenth-value layers suggest 27.0 mm of lead; the first tenth-value layer followed by two second ones gives 35.2 mm. For a thick shield, use the later layers, or better, let the calculator solve the thickness for the whole spectrum.

Notes on each nuclide

Co-60. Two lines of almost equal intensity at 1173 and 1332 keV make it the hardest spectrum here. The lead half-value layer is 10.3 mm and the ratio is close to the single-line value, so one half-value layer serves well at any depth. In concrete the half-value layer is 5.20 cm, which is why rooms for high-activity Co-60 sources have concrete walls a metre or more thick.

Cs-137. The usual reference source for survey meter checks and calibration. Its concrete half-value layer of 3.72 cm and lead tenth-value layer of 18.1 mm are useful benchmarks: if a shielding estimate for a nuclide of similar energy differs greatly from these, check the input.

Ir-192. The common source for industrial radiography and high-dose-rate brachytherapy. Its hardening means that a collimator or a shielded container sized from the first half-value layer will be too thin.

I-131. Its main line is at 364 keV, and its layers in iron and concrete are close to those of Ir-192. In therapy wards the patient is the source, and the body attenuates and scatters the photons before any shield does; the point-source figures here are an upper bound for that situation.

Tc-99m. Its 140 keV line is easy to shield with lead: the half-value layer is 0.229 mm and the tenth-value layer 0.827 mm, so a few millimetres of lead in a syringe shield or a vial pot reduce the dose rate by orders of magnitude. Iron and concrete are far less effective per centimetre at this energy, as the tables show.

Am-241. Its 59.5 keV gamma ray and the neptunium L X-rays near 17 keV are stopped by a fraction of a millimetre of lead — the first half-value layer is 0.0865 mm. The low-energy photons do not count in these tables below 20 keV, and in practice they are absorbed by any source capsule. Because Am-241 is mainly an alpha emitter, contamination control matters more than its photon shielding.

Narrow beam against broad beam

In a real shield, photons that Compton-scatter do not all disappear. Some change direction, keep most of their energy and still reach the point being protected. The dose rate behind the shield is the attenuated dose rate multiplied by a buildup factor B, which is 1 at the surface and grows with thickness — slowly in lead, quickly in light materials such as concrete and water, and more at lower energy. Broad-beam half-value layers, measured with the scattered photons included, are therefore thicker than the narrow-beam values here; for Cs-137 in lead the commonly quoted broad-beam figure is about 6.5 mm.

The buildup factor most often used for point sources is the geometric-progression fit published in the standard ANSI/ANS-6.4.3, whose coefficients are copyright and are not reproduced on this site. The gamma calculator accepts buildup coefficients in the two-parameter Berger form, B = 1 + a·µx·eb·µx, from whatever reference you are working to, and shows the difference they make. For rooms in medical facilities, broad-beam transmission data for the specific radiation and material are published in shielding reports such as AAPM Task Group 108 for PET, and a design should use those.

Using the numbers safely

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