Determination of the formation cross section by γ spectrometry: Derivation of universal correction formulas for ingrowth during irradiation

We have derived generalized correction formulas for the effect of ingrowth from the precursor during irradiation in the determination of the formation cross section by γ spectrometry. The correction formulas enabled one to carry out the correction quite easily. They require no detailed decay schemes of involved nuclides, except for the half-lives and, in the case where nuclear isomers exist, the fraction of transition between any pair of nuclides, and thus make it possible to get rid of the tedious derivation of individual correction formulas. The whole procedure is easily programmed in a personal computer and one can instantaneously judge whether a correction is necessary for a relevant nuclide. Further, it supplies correction factors to deduce both the independent and cumulative yields of a nuclide from the extrapolated yield to the end-of-bombardment (EOB) in the decay analysis, on the one hand, and also those to be applied to the chemically separated activities at EOB on the other. The latter set of correction factors are applicable to physically separated activities in ISOL or gas-jet transport experiments as well, provided that the effective retention duration of the product nuclides in the reaction chamber is known.