Role of precursor nuclei in heavy-ion induced reactions at low energies

In heavy-ion induced reactions, generally, a large number of residues are populated through different reaction channels. In some cases the same residue is populated via two different modes viz., (i) directly from a given reaction and (ii) via beta and/or electron capture decay of a nuclide (precursor). Separation of the two is required for a better understanding of reaction dynamics. The procedure existing in the literature for extracting the independent production cross section from the cumulative cross section employs the assumptions of half-life of the daughter being much larger in comparison to the half-life of the precursor (t(1/)(2)(p)<< t(1/)(2)(d)) and require the counting to be performed after large cooling times (t(l) -> infinity). A general and more exact expression is obtained in the present work surpassing the assumptions as well as difficulties reported earlier. Analysis of the experimental reaction data sets covering a broader range of possibilities (t(1/)(2)(p )> t(1/)(2)(d); t(1/2)(p) approximate to t(1/)(2)(d); t(1/)(2)(p) < t(1/)(2)(d)) presented shows the importance of the current formulations. The advantage of the generalized expression even when the assumptions hold true is also discussed. A comparison of results obtained from the traditional method in the context of its assumptions instead of the calculations from the exact expression has been made. The results obtained with the presently derived formulations are found to give justified values of cross sections for all the cases in contrast to the traditional formulation.