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compute granddaughter buildup for 2-stage decay#128

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add-daughter-buildup
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compute granddaughter buildup for 2-stage decay#128
pkienzle wants to merge 2 commits into
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add-daughter-buildup

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@pkienzle pkienzle commented May 28, 2026

Compute the buildup of the secondary β⁻ decay products after exposure is complete. Closes #95

Here is 146Nd before the PR (without burnup):
image

and after (with burnup). Note the buildup in 147Pm and the 18x increase in decay time.
image

The main change is to use the Bateman equation (Wikipedia) during decay. We currently have the granddaughter decay as $I(t) = I(0) \exp(-λ_d t)$ but we are changing it to:
$I_d(t) = I_d(0) \exp(-λ_d t) + λ_d/(λ_d - λ_p)I_p(0)(\exp(-λ_p t) - \exp(-λ_d t)) $
where $I_d(0)$ is the granddaughter activity when exposure is complete and $I_p(0)$ is the activity of the transient activation product.

This doesn't correctly cover the 3-stage 150Nd (n,γ) 151Nd (β⁻ t=12 m) 151Pm (β⁻ t=28.4 h) 151Sm (β⁻ t=94.6 y) 151Eu decay chain (see #127).

Note that the 152m2Eu decay chain is incomplete. It only has 151Eu -> 152m2Eu -> 152Eu internal transition, not the subsequent 152Eu -> 152Gd beta decay (see #126).

@bpedersen2 Please check the code

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Decay times for 'b' mode production are underestimated

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