Depletion Functions and Their Use in the Calculation of Isotope Transmutations

Alexander I. Shlyakhter

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


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)/λkt, where n is the number of nuclides in the chain and λk is the destruction rate of the neglected isotope. At large t is ε ≈ -λmk where λm 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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