Reply to Comment on ‘Analysis of decay chains of superheavy nuclei produced in the 249 Bk + 48 Ca and 243 Am + 48 Ca reactions’

Published 22 November 2018 Abstract Forsberg and Leino ( 2019 J. Phys. G: Nucl Part Phys 46 018001 ) question the validity of criticism ( 2017 J. Phys. G: Nucl. Part. Phys. 44 075107 ) of the method proposed by Forsberg et al ( 2016 Nucl. Phys. A 953 117 ) . In this reply, we show that this method is based on unclear principles and its implementation leads to the results that contradict the conclusions al N N 1 where t stands for individual decay times observed in N decays of nucleus ( N  >  1 ) and τ is an average lifetime determined from N values t 1 Function f ( t ) reaches maximum at t  ≈  τ and f ( t )  →  0 and at t  →  ∞ . In an attempt the decay times of all of the nuclei in the chain, the authors calculate the FoM 1 – 3 values which correspond to individual decay times of in the three-step decay chain. the calculated FoM 1 3 values, geometrical mean values FoM geom were calculated for each chain. Then, the

In a paper by Forsberg et al [1], a new method was suggested for statistical treatment of decay times of nuclei in the decay chains arising in the decay of parent nucleus. A Figure-of-Merit (FoM) was proposed as a probability density function for the decay times of nuclei: where t stands for individual decay times observed in N decays of nucleus (N>1) and τ is an average lifetime determined from N measured values of t [1]. Function f (t) reaches maximum at t≈τ and f (t)→0 at t→0 and at t→∞. In an attempt to analyze simultaneously the decay times of all of the nuclei in the chain, the authors calculate the FoM 1-3 values which correspond to individual decay times of nuclei in the three-step decay chain. From the calculated FoM 1-3 values, their geometrical mean values FoM geom were calculated for each chain. Then, the arithmetic mean of FoM geom (FoM ar ) over all of the N chains was calculated for the total data set.
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To compare the FoM ar value, calculated from experimental data, with at least some a priori unknown value, the same procedure was repeatedly performed for simulated decays that were generated using the Monte Carlo method with lifetimes calculated from the experiment. The resulting distribution of FoM ar values from such simulation was used to determine the interval within which the simulated values are located with a probability of 90%. Thus, 5% of chains with the lowest FoM ar values and 5% of chains with the highest ones are rejected.
We have doubts about the applicability of this method for several reasons: 1. Most important, the results of application of the method of [1] disagree with conclusions (see [2]) following from traditional methods of mathematical statistics whose reliability was proven for many decades. In these methods, the decays of each nucleus in chains are treated separately because decay times of parent and descendant nuclei do not depend on each other. . These calculations demonstrate a discrepancy between the method [1] and the above values FoM ar which are based on experimental decay times. 6. Application of the same method in [3] results in a conclusion by Forsberg et al: 'the evaluation of the congruence of the first four short element 115 chains fails the hypothesis of a single radioactive source with >95% confidence level', 'adding the three short chains from the LBNL experiment and, further, the seven short chains from the GSI experiment into the statistical analysis, the hypothesis of a common origin of all 14 chains can be rejected on a >99% confidence level', 'the hypothesis that the ten short element 117 chains form one common sequence must also be rejected on a >95% confidence level', 'the ten element 117 chains together with the four element 115 chains from Dubna do not, on a close to 100% confidence level, form a common ensemble', 'adding the [three Dubna] chains, to the ten element 117 chains does not, with a confidence level of >99%, produce a congruent data set'. However, examining the relations shown in figure 2 of [2] is enough to be sufficiently convinced in the ambiguity of all of the above statements.
Finally, the sentence by Forsberg and Leino reads 'The non-congruence is seen only when entire decay chains are considered'. However, it seems to us that without a strong justification of the initial basic principles of the method and its reliability, the discussion of the results of its use does not make sense.