Fig. 1.
![Decay of VHLW from reprocessing 1 metric ton of SF (p. 17 in Ref. [1]).](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68a8bde5afc50a4de0964f13/j_nuka-2025-0009_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKL7IWZU34%2F20260113%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260113T020502Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEC8aDGV1LWNlbnRyYWwtMSJGMEQCIBemo2RDz6JQyP5ax7S4n3JssOwrmcV56ms4Gio6Jb7wAiAQmviEWOEzFmbIStQp6wAZhoPdykJDbgqJFF3fwSzktSrFBQj4%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMBMOTAGNK1cjuT8KMKpkFiFBk11mXU9LcbYtVt8ipmxd%2FobrZEDCf1EFuRId2YrsQrv8BESATmNIaxR5Eoha5L8bPyOhpAVNPKRTkFGzpNHIrWmeMQC5qu%2BPBNy%2FEy9EslC24PfbY%2FdKQz8MxroD2uQqGhtBonh%2BnLvci5NSURzuq7zG4ow3%2ByMtCE9GVw%2FJM20LfZxb6qotHiVLAvp7cjx1rqR%2FAOF7FpZObgF5z2vVeSIBSbwmUPdVk7KknxBSGAPUCWCOOhka0EwtqTD1Jz4SLjMcf%2Bu3deX%2Ft6Cu%2B4TDb3lyqaNRoupT8BkIX%2FIc8ikZ6opDRzjmcCEv89asWmUVIVWlV991RWJqI9LSO8lrOsaXi%2FShaUWUFpgWPtUtvb8lVXGt6ePGkQMQiiWY9hRkzpn9tD1lAOE6%2B%2BOhCO7%2FEslqspJ8ommnsGmdzm2gfzKcxLQUOAviv7gWjrp6avAPMEAx5GArhFnSzTXYfDoBBN1%2Bu906O14QHxmyji%2FKlNVubcpsyTRG81Vo0kURt2nxu7%2FZ3XoLFUgEGQeQDYDOCreU%2B6H0RrWXgzt8f%2FwGADVzL8bP7fhVeBFKittLNEDUGNAMrV3fUsq1Y%2BPf0JHh%2BkEA2OCFR%2BuEsLGL0JXjH9shYseA%2BiOs%2BFc4xvKjb%2BHlctfHzfwjQVKoYrZg2Nf0zSmJ0sQVe888D1YJbFG6mBoHQHCas93HtpTgYAeRz8TcNJvNlqWAI4U4e8gwdC64Xd8x7Ncyij1QpGV%2FXMKrCXP6MH%2FSqec1hyImjHEbiAypKYld%2FsByvRq4Kqos1GS3%2FbOoAf1Glt91dAkAYlI4rSOdva9kdngGtS7fjRjpKYf3jypw%2FujjwQ1lbnXBjYLJ3497FDdkiJBNef3V2m4TlpEWZldUew%2Bgw5PmVywY6sgExAzY4UvmZd%2FcqRhwjcR6WoCEvgcP2gor7oxrBshN9zBnZ4%2FZGnbUOB4ub8%2FYNm99S5rMGoVKVS0MoXiPf8X0Rcc0NlyyX37x%2FVPtNjHokaG9w4k0gA1S2jfAMtDJ%2FEEHXlSsuNf3x5HFWAgs9eSnW5x0HxJlJfNhp2Y10ZtWdxV5ASo%2BSqa0lSaH%2FbBLLZHwK%2BGXa8HJOUj%2FwQ%2BrvMaXml%2B1rATRWBaRZhDn9PtiFjIYo&X-Amz-Signature=dd9d03667b8349447f70413c45d9b66e1e70958dd6e95308b4f1e5472ff722ef&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 2.
![Decay of activity content of 1 metric ton of Swedish SF (p. 16 in Ref. [3]).](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68a8bde5afc50a4de0964f13/j_nuka-2025-0009_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKL7IWZU34%2F20260113%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260113T020502Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEC8aDGV1LWNlbnRyYWwtMSJGMEQCIBemo2RDz6JQyP5ax7S4n3JssOwrmcV56ms4Gio6Jb7wAiAQmviEWOEzFmbIStQp6wAZhoPdykJDbgqJFF3fwSzktSrFBQj4%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMBMOTAGNK1cjuT8KMKpkFiFBk11mXU9LcbYtVt8ipmxd%2FobrZEDCf1EFuRId2YrsQrv8BESATmNIaxR5Eoha5L8bPyOhpAVNPKRTkFGzpNHIrWmeMQC5qu%2BPBNy%2FEy9EslC24PfbY%2FdKQz8MxroD2uQqGhtBonh%2BnLvci5NSURzuq7zG4ow3%2ByMtCE9GVw%2FJM20LfZxb6qotHiVLAvp7cjx1rqR%2FAOF7FpZObgF5z2vVeSIBSbwmUPdVk7KknxBSGAPUCWCOOhka0EwtqTD1Jz4SLjMcf%2Bu3deX%2Ft6Cu%2B4TDb3lyqaNRoupT8BkIX%2FIc8ikZ6opDRzjmcCEv89asWmUVIVWlV991RWJqI9LSO8lrOsaXi%2FShaUWUFpgWPtUtvb8lVXGt6ePGkQMQiiWY9hRkzpn9tD1lAOE6%2B%2BOhCO7%2FEslqspJ8ommnsGmdzm2gfzKcxLQUOAviv7gWjrp6avAPMEAx5GArhFnSzTXYfDoBBN1%2Bu906O14QHxmyji%2FKlNVubcpsyTRG81Vo0kURt2nxu7%2FZ3XoLFUgEGQeQDYDOCreU%2B6H0RrWXgzt8f%2FwGADVzL8bP7fhVeBFKittLNEDUGNAMrV3fUsq1Y%2BPf0JHh%2BkEA2OCFR%2BuEsLGL0JXjH9shYseA%2BiOs%2BFc4xvKjb%2BHlctfHzfwjQVKoYrZg2Nf0zSmJ0sQVe888D1YJbFG6mBoHQHCas93HtpTgYAeRz8TcNJvNlqWAI4U4e8gwdC64Xd8x7Ncyij1QpGV%2FXMKrCXP6MH%2FSqec1hyImjHEbiAypKYld%2FsByvRq4Kqos1GS3%2FbOoAf1Glt91dAkAYlI4rSOdva9kdngGtS7fjRjpKYf3jypw%2FujjwQ1lbnXBjYLJ3497FDdkiJBNef3V2m4TlpEWZldUew%2Bgw5PmVywY6sgExAzY4UvmZd%2FcqRhwjcR6WoCEvgcP2gor7oxrBshN9zBnZ4%2FZGnbUOB4ub8%2FYNm99S5rMGoVKVS0MoXiPf8X0Rcc0NlyyX37x%2FVPtNjHokaG9w4k0gA1S2jfAMtDJ%2FEEHXlSsuNf3x5HFWAgs9eSnW5x0HxJlJfNhp2Y10ZtWdxV5ASo%2BSqa0lSaH%2FbBLLZHwK%2BGXa8HJOUj%2FwQ%2BrvMaXml%2B1rATRWBaRZhDn9PtiFjIYo&X-Amz-Signature=964e287037c2f10cc5b7d168c1fcbee9fae925e2c98fb8f1b5cc374078e0bbab&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 3.
![External radiation 1 m away from 1 metric ton of Swedish SF (p. 23 in Ref. [3]).](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68a8bde5afc50a4de0964f13/j_nuka-2025-0009_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKL7IWZU34%2F20260113%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260113T020502Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEC8aDGV1LWNlbnRyYWwtMSJGMEQCIBemo2RDz6JQyP5ax7S4n3JssOwrmcV56ms4Gio6Jb7wAiAQmviEWOEzFmbIStQp6wAZhoPdykJDbgqJFF3fwSzktSrFBQj4%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMBMOTAGNK1cjuT8KMKpkFiFBk11mXU9LcbYtVt8ipmxd%2FobrZEDCf1EFuRId2YrsQrv8BESATmNIaxR5Eoha5L8bPyOhpAVNPKRTkFGzpNHIrWmeMQC5qu%2BPBNy%2FEy9EslC24PfbY%2FdKQz8MxroD2uQqGhtBonh%2BnLvci5NSURzuq7zG4ow3%2ByMtCE9GVw%2FJM20LfZxb6qotHiVLAvp7cjx1rqR%2FAOF7FpZObgF5z2vVeSIBSbwmUPdVk7KknxBSGAPUCWCOOhka0EwtqTD1Jz4SLjMcf%2Bu3deX%2Ft6Cu%2B4TDb3lyqaNRoupT8BkIX%2FIc8ikZ6opDRzjmcCEv89asWmUVIVWlV991RWJqI9LSO8lrOsaXi%2FShaUWUFpgWPtUtvb8lVXGt6ePGkQMQiiWY9hRkzpn9tD1lAOE6%2B%2BOhCO7%2FEslqspJ8ommnsGmdzm2gfzKcxLQUOAviv7gWjrp6avAPMEAx5GArhFnSzTXYfDoBBN1%2Bu906O14QHxmyji%2FKlNVubcpsyTRG81Vo0kURt2nxu7%2FZ3XoLFUgEGQeQDYDOCreU%2B6H0RrWXgzt8f%2FwGADVzL8bP7fhVeBFKittLNEDUGNAMrV3fUsq1Y%2BPf0JHh%2BkEA2OCFR%2BuEsLGL0JXjH9shYseA%2BiOs%2BFc4xvKjb%2BHlctfHzfwjQVKoYrZg2Nf0zSmJ0sQVe888D1YJbFG6mBoHQHCas93HtpTgYAeRz8TcNJvNlqWAI4U4e8gwdC64Xd8x7Ncyij1QpGV%2FXMKrCXP6MH%2FSqec1hyImjHEbiAypKYld%2FsByvRq4Kqos1GS3%2FbOoAf1Glt91dAkAYlI4rSOdva9kdngGtS7fjRjpKYf3jypw%2FujjwQ1lbnXBjYLJ3497FDdkiJBNef3V2m4TlpEWZldUew%2Bgw5PmVywY6sgExAzY4UvmZd%2FcqRhwjcR6WoCEvgcP2gor7oxrBshN9zBnZ4%2FZGnbUOB4ub8%2FYNm99S5rMGoVKVS0MoXiPf8X0Rcc0NlyyX37x%2FVPtNjHokaG9w4k0gA1S2jfAMtDJ%2FEEHXlSsuNf3x5HFWAgs9eSnW5x0HxJlJfNhp2Y10ZtWdxV5ASo%2BSqa0lSaH%2FbBLLZHwK%2BGXa8HJOUj%2FwQ%2BrvMaXml%2B1rATRWBaRZhDn9PtiFjIYo&X-Amz-Signature=fb460b82897292af77ce71fa61b4d5d77744713e3d9b16895a875097caf33625&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 4.
![Radiological dose rate, in Sv/h, 40 cm from two French HLW drill cores. The C2 drill core is VHLW; the CU1 drill core is SF (p. 533 in Ref. [5]).](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68a8bde5afc50a4de0964f13/j_nuka-2025-0009_fig_004.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKL7IWZU34%2F20260113%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260113T020502Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEC8aDGV1LWNlbnRyYWwtMSJGMEQCIBemo2RDz6JQyP5ax7S4n3JssOwrmcV56ms4Gio6Jb7wAiAQmviEWOEzFmbIStQp6wAZhoPdykJDbgqJFF3fwSzktSrFBQj4%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMBMOTAGNK1cjuT8KMKpkFiFBk11mXU9LcbYtVt8ipmxd%2FobrZEDCf1EFuRId2YrsQrv8BESATmNIaxR5Eoha5L8bPyOhpAVNPKRTkFGzpNHIrWmeMQC5qu%2BPBNy%2FEy9EslC24PfbY%2FdKQz8MxroD2uQqGhtBonh%2BnLvci5NSURzuq7zG4ow3%2ByMtCE9GVw%2FJM20LfZxb6qotHiVLAvp7cjx1rqR%2FAOF7FpZObgF5z2vVeSIBSbwmUPdVk7KknxBSGAPUCWCOOhka0EwtqTD1Jz4SLjMcf%2Bu3deX%2Ft6Cu%2B4TDb3lyqaNRoupT8BkIX%2FIc8ikZ6opDRzjmcCEv89asWmUVIVWlV991RWJqI9LSO8lrOsaXi%2FShaUWUFpgWPtUtvb8lVXGt6ePGkQMQiiWY9hRkzpn9tD1lAOE6%2B%2BOhCO7%2FEslqspJ8ommnsGmdzm2gfzKcxLQUOAviv7gWjrp6avAPMEAx5GArhFnSzTXYfDoBBN1%2Bu906O14QHxmyji%2FKlNVubcpsyTRG81Vo0kURt2nxu7%2FZ3XoLFUgEGQeQDYDOCreU%2B6H0RrWXgzt8f%2FwGADVzL8bP7fhVeBFKittLNEDUGNAMrV3fUsq1Y%2BPf0JHh%2BkEA2OCFR%2BuEsLGL0JXjH9shYseA%2BiOs%2BFc4xvKjb%2BHlctfHzfwjQVKoYrZg2Nf0zSmJ0sQVe888D1YJbFG6mBoHQHCas93HtpTgYAeRz8TcNJvNlqWAI4U4e8gwdC64Xd8x7Ncyij1QpGV%2FXMKrCXP6MH%2FSqec1hyImjHEbiAypKYld%2FsByvRq4Kqos1GS3%2FbOoAf1Glt91dAkAYlI4rSOdva9kdngGtS7fjRjpKYf3jypw%2FujjwQ1lbnXBjYLJ3497FDdkiJBNef3V2m4TlpEWZldUew%2Bgw5PmVywY6sgExAzY4UvmZd%2FcqRhwjcR6WoCEvgcP2gor7oxrBshN9zBnZ4%2FZGnbUOB4ub8%2FYNm99S5rMGoVKVS0MoXiPf8X0Rcc0NlyyX37x%2FVPtNjHokaG9w4k0gA1S2jfAMtDJ%2FEEHXlSsuNf3x5HFWAgs9eSnW5x0HxJlJfNhp2Y10ZtWdxV5ASo%2BSqa0lSaH%2FbBLLZHwK%2BGXa8HJOUj%2FwQ%2BrvMaXml%2B1rATRWBaRZhDn9PtiFjIYo&X-Amz-Signature=fe5c3f911187a75f384ff512631eddb5d76a9a5372c98b6ca012224cf1a81703&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 5.

Fig. 6.
![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 (p. 352 in Ref. [9]).](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68a8bde5afc50a4de0964f13/j_nuka-2025-0009_fig_006.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKL7IWZU34%2F20260113%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260113T020502Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEC8aDGV1LWNlbnRyYWwtMSJGMEQCIBemo2RDz6JQyP5ax7S4n3JssOwrmcV56ms4Gio6Jb7wAiAQmviEWOEzFmbIStQp6wAZhoPdykJDbgqJFF3fwSzktSrFBQj4%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMBMOTAGNK1cjuT8KMKpkFiFBk11mXU9LcbYtVt8ipmxd%2FobrZEDCf1EFuRId2YrsQrv8BESATmNIaxR5Eoha5L8bPyOhpAVNPKRTkFGzpNHIrWmeMQC5qu%2BPBNy%2FEy9EslC24PfbY%2FdKQz8MxroD2uQqGhtBonh%2BnLvci5NSURzuq7zG4ow3%2ByMtCE9GVw%2FJM20LfZxb6qotHiVLAvp7cjx1rqR%2FAOF7FpZObgF5z2vVeSIBSbwmUPdVk7KknxBSGAPUCWCOOhka0EwtqTD1Jz4SLjMcf%2Bu3deX%2Ft6Cu%2B4TDb3lyqaNRoupT8BkIX%2FIc8ikZ6opDRzjmcCEv89asWmUVIVWlV991RWJqI9LSO8lrOsaXi%2FShaUWUFpgWPtUtvb8lVXGt6ePGkQMQiiWY9hRkzpn9tD1lAOE6%2B%2BOhCO7%2FEslqspJ8ommnsGmdzm2gfzKcxLQUOAviv7gWjrp6avAPMEAx5GArhFnSzTXYfDoBBN1%2Bu906O14QHxmyji%2FKlNVubcpsyTRG81Vo0kURt2nxu7%2FZ3XoLFUgEGQeQDYDOCreU%2B6H0RrWXgzt8f%2FwGADVzL8bP7fhVeBFKittLNEDUGNAMrV3fUsq1Y%2BPf0JHh%2BkEA2OCFR%2BuEsLGL0JXjH9shYseA%2BiOs%2BFc4xvKjb%2BHlctfHzfwjQVKoYrZg2Nf0zSmJ0sQVe888D1YJbFG6mBoHQHCas93HtpTgYAeRz8TcNJvNlqWAI4U4e8gwdC64Xd8x7Ncyij1QpGV%2FXMKrCXP6MH%2FSqec1hyImjHEbiAypKYld%2FsByvRq4Kqos1GS3%2FbOoAf1Glt91dAkAYlI4rSOdva9kdngGtS7fjRjpKYf3jypw%2FujjwQ1lbnXBjYLJ3497FDdkiJBNef3V2m4TlpEWZldUew%2Bgw5PmVywY6sgExAzY4UvmZd%2FcqRhwjcR6WoCEvgcP2gor7oxrBshN9zBnZ4%2FZGnbUOB4ub8%2FYNm99S5rMGoVKVS0MoXiPf8X0Rcc0NlyyX37x%2FVPtNjHokaG9w4k0gA1S2jfAMtDJ%2FEEHXlSsuNf3x5HFWAgs9eSnW5x0HxJlJfNhp2Y10ZtWdxV5ASo%2BSqa0lSaH%2FbBLLZHwK%2BGXa8HJOUj%2FwQ%2BrvMaXml%2B1rATRWBaRZhDn9PtiFjIYo&X-Amz-Signature=b1d02d82f1268d820ec7a4b4bed1fc83b0a2cd29d0aeb8c3dc3e3fb6c76becb7&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Decay constants in per-million-year units
| Chain | λ |
|---|---|
| U-238 | 1.55 × 10−5 |
| Excess U-234 | 2.82 |
| Np-237 | 0.324 |
Calculated shield thicknesses at 1 million years depending on each nuclear chain and using the proximity criterion_ In bold are the required envelope thicknesses for each waste form_ These values will decrease in time to reach the values for U-238, reported in italics
| Surface dose rates | C2 VHLW full-size | C2 VHLW drill core | 8 PWR SF assemblies | CU1 SF drill core |
|---|---|---|---|---|
| S238 | 16.6 | – | 61.9 | 41.1 |
| S234 | 24.3 | – | 57.3 | 36.5 |
| S238 + S234 | 28.8 | – | 67.5 | 46.7 |
| S237 | 53.5 | 48.1 | 43.5 | 28.2 |
Gamma dose rate (mSv/h) at three distances from a Pollux-8 cask loaded with eight PWR UO2 fuel assemblies, neglecting the shielding of the cask [2]
| Decay time (million years) | Surface (4 cm) | Surface (2 cm extrapolated) |
|---|---|---|
| 1 | 6.6 | 13.1 |
| 10 | 2.8 | 5.5 |
| 100 | 2.7 | 5.4 |
| 1000 | 2.3 | 4.6 |
Calculated shield thicknesses at 1 million years depending on each nuclear chain and using the tolerability criterion_ In bold are the required envelope thicknesses for each waste form_ These values will decrease in time to reach the calculated for U-238, reported in italics
| Surface dose rates | C2 VHLW full-size | C2 VHLW drill core | 8 PWR SF assemblies | CU1 SF drill core |
|---|---|---|---|---|
| S238 | 42.1 | 5.2 | 87.4 | 66.6 |
| S234 | 49.8 | 13.5 | 82.7 | 61.9 |
| S238 + S234 | 54.3 | 17.8 | 93.0 | 72.2 |
| S237 | 72.2 | 66.9 | 62.2 | 46.9 |
Dose rate (mSv/h) 2 cm from reference unshielded VHLW and SF at 1 million years [2]
| Surface dose rates | C2 VHLW full-size | C2 VHLW drill core | 8 PWR SF assemblies | CU1 SF drill core |
|---|---|---|---|---|
| S238 | 0.09 | 0.0032 | 5.4 | 0.82 |
| S234 | 0.18 | 0.0068 | 3.54 | 0.54 |
| S237 | 14.42 | 7.45 | 4.2 | 0.64 |
| Total | 14.69 | 4.46 | 13.14 | 2.00 |