# Depletion Functions and Their Use in the Calculation of Isotope Transmutations

*Atomkernenergie-Kerntechnik*, 42 (1): 33-38 1983

## Abstract

The basic points in the calculation of transmutations of isotopes are
analyzed using the so-called "depletion functions". It is shown that
conventional criteria used for selecting the most important nuclide chains
and for eliminating of the short-lived isotopes from them are sometimes
misleading. In particular, the usual neglection of the short-lived nuclides
may appear to be incorrect. At small irradiation time *t* the error introduced
by this approximation is about

ε ≈ (*n*-2)/λ_{k}t, where *n* is the number
of nuclides in the chain and λ_{k} is the destruction rate of the neglected
isotope. At large *t* is ε ≈ -λ_{m}/λ_{k} where λ_{m}
is the lowest destruction rate in the chain. As a result, the error does not
tend to zero when *t* goes to infinity unless at least one nuclide is not
depleted at all. Simple formulae for the sensitivity of the calculated
nuclide concentrations to the adopted values of nuclear constants are
obtained. To illustrate the results we consider production of actinides.

#### Keywords: depletion functions, isotope transmutation

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