Fig. 1.

Fig. 2.
![Decay of VHLW from reprocessing of 1 ton of spent fuel [4].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/673e51378b676d152c200408/j_nuka-2024-0029_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKOWFFFBTO%2F20260120%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260120T054153Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjENj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJGMEQCIH%2Bpq2hgLFGcj7bFySLpRlu%2FXG0UcJjvnevbeRaOB%2BD9AiBIcVWCpJMExuv3Y5pY0DZ8aqpUzolCBhJ1ptd01ydNWCrFBQih%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMjh9er%2F0IyrUuWVB4KpkFxX35EvH7bqUZfEGKlH%2FBouLfsHXHl7ZmuZtbQTSg1VttbrYCLX5wNcgn3prm5VOe7KZdqmU46DKtf%2BY0TsuTkWnz0mgaRv6TbN9d9jYCZlWm%2BIFCIWSN53hSoPKp9EVTmW3kl2FK1dU%2BOXVuBFtdWyEpgDiFIrwu98GToq8W7yO0IMGOVeDg0O7oQQ7b7F3RnWPkMdY2RVXzkMrMvAoORnd%2Bqn%2BWVWSfyNUmDf9fGoCfD1Gz7mSiw4Tl8URodXhOlrWgqFLYGkVazRsEcLcM8lqyLqKnADNHdrUfCXnAgJrMPsup9bH%2FfrBn5LqQH%2Fkhp11zOKBtKAqxmwwHhBDSBtdFuh%2Fk1arB3njAFiRnAM3rWsRWCiU8fwEkRcTNzIV9%2F76FkjWd1qMerAn1fW52eiZftJ0qt2V0uSW1XsF2YVCnrfMg7bj0O%2FH62qw3JWDzOSkrHfVbx%2BQf%2FkA01fgl7URJ4XXPOI1qQhduQvRHjSDAx4N2aopx%2F06K14GXzbJ71eKxfH%2FIi8mdKUmUUO2C8Ygw8wBg%2BcSIkfrH79%2FcSDNg1iyxoE9C8%2B2X8T1kHvhxnv4zXdnpDGN7YEIW1%2B6n8zUBe6vpimWO57hMT0q3uCm5dT8BDZlIc%2B6XDRmvGVeoQX5gUWtjvDocS2isYFqG9M1HCI4PYyEc8vddOEYXHh81wTy7ymN2YQ%2Fy0aBnhBsEIpzRh1%2BvnVSO6wfwKxRW93%2BOVPKS7fckZJJDxMCXMqZb13qEkHMLzuJ%2BRbYr4exgdtpwvX7LDE0T2LHrvlUVlmNZGWh9aV0QDrsuXBSpC7f4sacF%2FmjiB18MPa8D9RMJcEVp14RZNaWkRDtMDNnKLPfySpO3buTE0wNpXSvL%2BOyre811YCqyy0swkZS7ywY6sgH1lht%2BlkVFQHs5F2i3Gp2lWvXW6M28OsN3GcbbMuIMMrSFuFd2JFjurQpaNRLGXhJfTUjNCng5c2gxj2kl2D0bk%2BDd7WbMR46rQzhmIM4550kLdC%2FaBGSe7%2BrC2VBYHfBsHXEXJV0MjKK%2FsZ7TLBBROP%2BoTNzQlm8j6AfVjrIpr%2FSX2IQymyaCWlwfekHULZhhYZLWuwvZV9MOoy2pLb%2F3COsD0e9h%2Bb9Yni8YazZdzONb&X-Amz-Signature=092f27d83d92d9e20f86a6ab5ff387f707ac95e5c32749a5ed368589c89bb0fa&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 3.
![Radiological dose rate in Sv/h from two French HLW drill cores. C2 is VHLW; CU1 is SF (p. 25 in Ref. [2] and p. 533 in Ref. [7]).](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/673e51378b676d152c200408/j_nuka-2024-0029_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKOWFFFBTO%2F20260120%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260120T054153Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjENj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJGMEQCIH%2Bpq2hgLFGcj7bFySLpRlu%2FXG0UcJjvnevbeRaOB%2BD9AiBIcVWCpJMExuv3Y5pY0DZ8aqpUzolCBhJ1ptd01ydNWCrFBQih%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMjh9er%2F0IyrUuWVB4KpkFxX35EvH7bqUZfEGKlH%2FBouLfsHXHl7ZmuZtbQTSg1VttbrYCLX5wNcgn3prm5VOe7KZdqmU46DKtf%2BY0TsuTkWnz0mgaRv6TbN9d9jYCZlWm%2BIFCIWSN53hSoPKp9EVTmW3kl2FK1dU%2BOXVuBFtdWyEpgDiFIrwu98GToq8W7yO0IMGOVeDg0O7oQQ7b7F3RnWPkMdY2RVXzkMrMvAoORnd%2Bqn%2BWVWSfyNUmDf9fGoCfD1Gz7mSiw4Tl8URodXhOlrWgqFLYGkVazRsEcLcM8lqyLqKnADNHdrUfCXnAgJrMPsup9bH%2FfrBn5LqQH%2Fkhp11zOKBtKAqxmwwHhBDSBtdFuh%2Fk1arB3njAFiRnAM3rWsRWCiU8fwEkRcTNzIV9%2F76FkjWd1qMerAn1fW52eiZftJ0qt2V0uSW1XsF2YVCnrfMg7bj0O%2FH62qw3JWDzOSkrHfVbx%2BQf%2FkA01fgl7URJ4XXPOI1qQhduQvRHjSDAx4N2aopx%2F06K14GXzbJ71eKxfH%2FIi8mdKUmUUO2C8Ygw8wBg%2BcSIkfrH79%2FcSDNg1iyxoE9C8%2B2X8T1kHvhxnv4zXdnpDGN7YEIW1%2B6n8zUBe6vpimWO57hMT0q3uCm5dT8BDZlIc%2B6XDRmvGVeoQX5gUWtjvDocS2isYFqG9M1HCI4PYyEc8vddOEYXHh81wTy7ymN2YQ%2Fy0aBnhBsEIpzRh1%2BvnVSO6wfwKxRW93%2BOVPKS7fckZJJDxMCXMqZb13qEkHMLzuJ%2BRbYr4exgdtpwvX7LDE0T2LHrvlUVlmNZGWh9aV0QDrsuXBSpC7f4sacF%2FmjiB18MPa8D9RMJcEVp14RZNaWkRDtMDNnKLPfySpO3buTE0wNpXSvL%2BOyre811YCqyy0swkZS7ywY6sgH1lht%2BlkVFQHs5F2i3Gp2lWvXW6M28OsN3GcbbMuIMMrSFuFd2JFjurQpaNRLGXhJfTUjNCng5c2gxj2kl2D0bk%2BDd7WbMR46rQzhmIM4550kLdC%2FaBGSe7%2BrC2VBYHfBsHXEXJV0MjKK%2FsZ7TLBBROP%2BoTNzQlm8j6AfVjrIpr%2FSX2IQymyaCWlwfekHULZhhYZLWuwvZV9MOoy2pLb%2F3COsD0e9h%2Bb9Yni8YazZdzONb&X-Amz-Signature=340068f9f87e54e4111932dab481e5258d9168d16571e383470abd7c671e6d9c&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 4.
![Accrued, external dose from drill cores of several kinds of present and future French VHLW after a 10-min exposure, 40 cm from the drill core, and as a function of time [9].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/673e51378b676d152c200408/j_nuka-2024-0029_fig_004.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKOWFFFBTO%2F20260120%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260120T054153Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjENj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJGMEQCIH%2Bpq2hgLFGcj7bFySLpRlu%2FXG0UcJjvnevbeRaOB%2BD9AiBIcVWCpJMExuv3Y5pY0DZ8aqpUzolCBhJ1ptd01ydNWCrFBQih%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMjh9er%2F0IyrUuWVB4KpkFxX35EvH7bqUZfEGKlH%2FBouLfsHXHl7ZmuZtbQTSg1VttbrYCLX5wNcgn3prm5VOe7KZdqmU46DKtf%2BY0TsuTkWnz0mgaRv6TbN9d9jYCZlWm%2BIFCIWSN53hSoPKp9EVTmW3kl2FK1dU%2BOXVuBFtdWyEpgDiFIrwu98GToq8W7yO0IMGOVeDg0O7oQQ7b7F3RnWPkMdY2RVXzkMrMvAoORnd%2Bqn%2BWVWSfyNUmDf9fGoCfD1Gz7mSiw4Tl8URodXhOlrWgqFLYGkVazRsEcLcM8lqyLqKnADNHdrUfCXnAgJrMPsup9bH%2FfrBn5LqQH%2Fkhp11zOKBtKAqxmwwHhBDSBtdFuh%2Fk1arB3njAFiRnAM3rWsRWCiU8fwEkRcTNzIV9%2F76FkjWd1qMerAn1fW52eiZftJ0qt2V0uSW1XsF2YVCnrfMg7bj0O%2FH62qw3JWDzOSkrHfVbx%2BQf%2FkA01fgl7URJ4XXPOI1qQhduQvRHjSDAx4N2aopx%2F06K14GXzbJ71eKxfH%2FIi8mdKUmUUO2C8Ygw8wBg%2BcSIkfrH79%2FcSDNg1iyxoE9C8%2B2X8T1kHvhxnv4zXdnpDGN7YEIW1%2B6n8zUBe6vpimWO57hMT0q3uCm5dT8BDZlIc%2B6XDRmvGVeoQX5gUWtjvDocS2isYFqG9M1HCI4PYyEc8vddOEYXHh81wTy7ymN2YQ%2Fy0aBnhBsEIpzRh1%2BvnVSO6wfwKxRW93%2BOVPKS7fckZJJDxMCXMqZb13qEkHMLzuJ%2BRbYr4exgdtpwvX7LDE0T2LHrvlUVlmNZGWh9aV0QDrsuXBSpC7f4sacF%2FmjiB18MPa8D9RMJcEVp14RZNaWkRDtMDNnKLPfySpO3buTE0wNpXSvL%2BOyre811YCqyy0swkZS7ywY6sgH1lht%2BlkVFQHs5F2i3Gp2lWvXW6M28OsN3GcbbMuIMMrSFuFd2JFjurQpaNRLGXhJfTUjNCng5c2gxj2kl2D0bk%2BDd7WbMR46rQzhmIM4550kLdC%2FaBGSe7%2BrC2VBYHfBsHXEXJV0MjKK%2FsZ7TLBBROP%2BoTNzQlm8j6AfVjrIpr%2FSX2IQymyaCWlwfekHULZhhYZLWuwvZV9MOoy2pLb%2F3COsD0e9h%2Bb9Yni8YazZdzONb&X-Amz-Signature=8f1572497e55bdadefc70ef0bf17debf5f675a4d03ff150f5c549f2eef94341c&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 5.

Exposure time in hours for getting the annual ICRP dose constraint of 0_3 mSv as a function of time at three distances from POLLUX-8 cask assemblies, neglecting the shielding of the cask
| Decay time (million years) | Exposure (h) at contact | Exposure (h) at 40 cm | Exposure (h) at 10 m |
|---|---|---|---|
| 1 | 0.046 | 0.430 | 10.8 |
| 10 | 0.108 | 1.034 | 25.9 |
| 100 | 0.112 | 1.064 | 26.6 |
| 1000 | 0.130 | 1.234 | 30.8 |
Gamma dose rate (mSv/h) at three distances from a POLLUX-8 cask loaded with 8 UO2 fuel assemblies, neglecting the shielding of the cask
| Decay time (million years) | Next to surface (4 cm) | 40 cm (extrapolated) | 10 m |
|---|---|---|---|
| 1 | 6.56 | 0.697 | 0.0279 |
| 10 | 2.77 | 0.290 | 0.0116 |
| 100 | 2.68 | 0.282 | 0.0113 |
| 1000 | 2.31 | 0.243 | 0.00974 |
Density and HVL for various materials depending on the energy of the gamma rays
| Material | Density (g/cm3) | HVL (cm) for 0.3 MeV | HVL (cm) for 0.6 MeV | HVL (cm) for 1.0 MeV | HVL (cm) for 1.5 MeV |
|---|---|---|---|---|---|
| Concrete | 2.3 | 2.08 | 4.02 | 6.69 | 7.70 |
| R7T7 glass | 2.6 | 2.22 | 4.10 | 5.92 | 6.50 |
| UO2 | 10.97 | 0.26 | 0.49 | 0.79 | 1.33 |
Transmission factors for energies 0_944 MeV and 0_312 MeV in R7T7 glass waste forms of radii 21 cm and 5 cm
| Energy (MeV) | Cylinder radius (cm) | HVL (cm) | Transmission factor (%) |
|---|---|---|---|
| 0.944 | 21 | 3.757 | 8.53 |
| 0.312 | 21 | 1.576 | 0.28 |
| 0.944 | 5 | 3.757 | 56.80 |
| 0.312 | 5 | 1.576 | 27.90 |
Dose rate computation coefficients for the German spent fuel of Table 1
| Ai (mSv/h) | λi (1/106 years) | |
|---|---|---|
| U-238 | 2.697 | 1.55 × 10−4 |
| Np-237 | 2.910 | 0.324 |
| U-234 | 29.670 | 2.820 |
Highest gamma energies in the (4n + 2) and (4n + 1) chains_ The weighted averages values are based on the data obtained from Japan Atomic Energy Agency [15,16,17,18]
| Radionuclide | Weighted average gamma energy per emission (keV) |
|---|---|
| Bi-214 | 944.00 |
| Pb-214 | 318.38 |
| Pa-233 | 311.86 |
| Th-229 | 47.96 |
Elemental activity ratios (at 10 000 years) and chain activity ratios (at one million years) for French VHLW
| Time (years) | Np-237/(U-234 + U-238) | Np-237/U-238 | U-234/U-238 |
|---|---|---|---|
| 10 000 | 576.73 | 19 220.62 | 32.34 |
| 1 000 000 | 4672.93 | 13 896.10 | 1.97 |
Relative contributions from the three actinide chains to the gamma dose from a block of unshielded eight UO2 fuel assemblies (same assemblies as mentioned in Table 1)
| Decay time (million years) | U-238 chain (%) | Np-237 chain (%) | Excess U-234 chain (%) | Total, surface dose rate (mSv/h) |
|---|---|---|---|---|
| 1 | 41.12 | 32.10 | 26.78 | 6.56 |
| 2 | 62.41 | 35.16 | 2.41 | 4.32 |
| 4 | 77.28 | 22.71 | – | 3.49 |
| 6 | 92.31 | 7.69 | – | 2.92 |
| 8 | 95.73 | 4.27 | – | 2.81 |
| 10 | 96.29 | 3.72 | – | 2.77 |
| 14 | 98.86 | 1.14 | – | 2.72 |
| 20 | 99.83 | 0.17 | – | 2.69 |
| 100 | 100 | – | – | 2.68 |
| 1000 | 100 | – | – | 2.31 |
Main contributors to the gamma dose rate from SF as a function of time The original calculations were based on LWR fuel but, for the past 105 years, say, they apply to any U-fuel, as the differences among uranium fuel types smooth out_ in million years for the configuration of Table 1_ The (4n + 2) elements are denoted in bold and the (4n + 1) elements are denoted in italics
| 0.1 My | 1 My | 10 My | 100 My | 1000 My |
|---|---|---|---|---|
| Bi-214 | Bi-214 | Bi-214 | Bi-214 | Bi-214 |
| Sb-126m | Pa-233 | Pb-214 | Pb-214 | Pb-214 |
| Pb-214 | Th-229 | Pa-234m | Pa-234m | Pa-234m |
| Pa-233 | Bi-213 | Pa-233 | Bi-210 | Bi-210 |
| Sb-126 | Pb-214 | Th-229 | U-235 | Th-234 |
| Th-229 | Tl-209 | Bi-213 | Ra-223 | |
| Np-237 | Np-237 | Bi-210 | ||
| Bi-213 | Fr-221 | U-235 | ||
| Bi-210 | Ac-225 | Ra-223 | ||
| Tl-209 | Ra-225 | Tl-209 |