Half-life from Fraction of Decay Curve

2 Half-life from Fraction of Decay Curve 

Schmidt [16] thoroughly analyzed the problem of uncertainties in measuring the mean lifetime with a small number of detected nuclei, including the presence of a stochastic background. The crucial point was that the measurement was supposed to last until complete decay of the nuclide. The treatment was based on the maximum likelihood approach the 90 percent confidence intervals were tabulated. 

To simulate the likelihood function for employing the Bayesian approach it was necessary to choose a reasonable range for the uniform prior distribution of the mean lifetime tx. A minimum of 0.1 seconds was safe, taking into account the time distribution of the 14 decay events. The maximal tx leaned upon the total effective production cross section of s.f. nuclei, which was measured in physical experiments. Obviously, 14 decays in 0.7 seconds with the upper tx should not correspond to many more events than was the observed total. 

The crosses mark the fission events in which both fragments were registered. 

Reproduced (adapted) from Radiokhimiya, 11(2), Zvara I, Chuburkov YuT, Caletka R, Shalaevskii MR, Experiments on chemistry of element 104 II. Chemical study of the spontaneous fission isotope, 163-174, 1969, with permission of Academizdatcenter Nauka Publishers. 

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