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Error analysis of large-time approximations for decay chains |
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| Authors: | Frank Massey Jeffrey Prentis |
| Affiliation: | University of Michigan-Dearborn, Dearborn, MI 48128, United States |
| Abstract: | Consider a radioactive decay chain X1 → ? → Xn→ and let Nn(t) be the amount of Xn at time t. This paper establishes error bounds for large-time approximations to Nn(t) that include and generalize the transient equilibrium approximations and other known approximations. The error bounds allow one to find the range of t for which these approximations can be used with a given degree of precision. |
| Keywords: | Radioactive decay chain Transient equilibrium Bateman&rsquo s formula Large-time approximation Error bound Exponential convolution Reduced chain |
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