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Ce-144 shielding — lead half-value layer and dose rate

Cerium-144

Ce-144 · Cerium, Z = 58, A = 144

At 1.18e+14 Bq/g — 3.18e+3 Ci/g — a gigabecquerel of Ce-144 amounts to 8.49 µg, which is why activity rather than mass is how anyone states the quantity. Cerium-144 decays by beta-minus decay with a half-life of 284.91 days, falling to 92.96% of today's activity in a month and 41.12% in a year.

The air kerma rate constant is small — 0.00334 mGy·m²/(GBq·h), 23× less than Cs-137 and 91× less than Co-60, ranking 79 of 96 by Γ — near the bottom of the photon emitters, but above the cutoff, which 51 nuclides in this dataset are not. 1 GBq at 1 m reads 0.00334 mGy/h, and 1 Ci at the same distance 0.124 mGy/h. It takes 5.98 GBq at a metre to reach 20 µSv/h from the photons alone.

11 lines clear the 20 keV cutoff, but 5 of them carry 90% of the dose rate. The leading one is 133.5 keV at 49.7% of the total — its emission probability is 11.09%, which is also the highest.

Shielding barely arises: 0.0859 mm of lead halves the air kerma rate and 0.552 mm takes it to a tenth, thicknesses a source capsule is likely to exceed on its own. Steel does the halving in 0.731 mm. At 1 GBq and a metre it is already under 20 µSv/h with nothing in the way. The tenth-value layer runs 6.4 times the half-value layer, not the 3.32 a single energy would give.

The beta endpoint is 0.318 MeV, mean 0.0821 MeV over 3 branches. That endpoint stops in 0.724 mm of acrylic or 0.342 mm of glass. Of Ce-144's own beta energy, 0.07% turns into X-rays in acrylic and 0.91% in lead.

Ce-144 does not stand alone. Pr-144 follows it with a half-life of 17.28 minutes, so ingrowth is complete within 2.02 hours of separation. Its endpoint is 3.00 MeV and stops in 12.6 mm of acrylic, 17× the thickness above. The shield is sized on Pr-144, and so is the bremsstrahlung: 0.63% of that energy turns into X-rays in acrylic and 8.60% in lead.

Half-life, specific activity, dose rate and beta energies

Half-life284.91 days (2.462e+7 s)
Decay modebeta-minus decay
Specific activity1.18e+14 Bq/g (3.18e+3 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.00334 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.00334 mGy/h
Dose rate, 1 Ci at 1 m0.124 mGy/h
Kerma-weighted mean photon energy86.81 keV
Beta endpoint / mean0.318 MeV / 0.0821 MeV

11 lines above the cutoff, and what each contributes

1 further line below the 20 keV cutoff, the highest at 5.64 keV and 1.51% emission probability in all, is excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
133.5111.0949.71
36.034.5008520.42
35.552.4646611.46
41.271.719786.20
40.861.369265.00
80.121.364073.61
41.770.350531.24
33.570.199621.03
40.980.257290.94
53.400.099810.27
99.960.039920.13

0.0859 mm of lead halves this spectrum

Solved numerically across all 11 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead0.08590.5526.42
tungsten0.06250.3916.26
iron0.7318.6711.87
copper0.5076.5712.96
concrete9.7947.54.85
water32.51173.60
aluminum7.8941.75.28

A single energy would give 3.32. What a spread of energies does instead.

0.724 mm of acrylic stops the 0.318 MeV endpoint

Katz–Penfold fit to the 0.318 MeV endpoint — ±10%, and a stopping thickness rather than an attenuation length. Why the material matters more than the thickness.

AbsorberRange for the endpoint (mm)
acrylic0.724
aluminum0.316
water0.854
glass0.342
Shield materialFraction of beta energy converted to X-rays
acrylic (Z ≈ 6)0.07%
lead (Z = 82)0.91%

Activity over months and years

Ten half-lives is 7.80 years — a storage problem rather than a disposal one, with 41.12% of today's activity still there after a year. The mean life 1/λ is 1.13 years.

ElapsedFraction remaining
1 half-life50.0 %
2 half-lives25.0 %
5 half-lives3.13 %
10 half-lives0.0977 %
Time to fall to 10 % of today's activity2.59 years
Time to fall to 1 %5.18 years
Time to fall to 0.1 %7.77 years

Limits of these dose rates

Gamma, beta and decay calculators for Ce-144

Other Cerium nuclides: Ce-139, Ce-139m, Ce-141

Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.