Extending the applicability of the RVT technique for the randomized radioactive decay chain model

In this paper, we improve the existing analysis on the randomized radioactive decay chain model based on Bateman master equations, by Hussein and Selim (2020). For a decay chain of three species of radionuclides, the authors derived the probability density function for the concentrations, by using t...

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Bibliographic Details
Published in:European physical journal plus 2022-03, Vol.137 (3), p.405, Article 405
Main Authors: Calatayud, Julia, Jornet, Marc
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Approximation
Atomic
Bandwidths
Complex Systems
Condensed Matter Physics
Mathematical and Computational Physics
Mathematical models
Molecular
Monte Carlo simulation
Optical and Plasma Physics
Physics
Physics and Astronomy
Probability density functions
Radioactive decay
Radioisotopes
Random variables
Regular Article
Stochastic models
Theoretical
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Summary:In this paper, we improve the existing analysis on the randomized radioactive decay chain model based on Bateman master equations, by Hussein and Selim (2020). For a decay chain of three species of radionuclides, the authors derived the probability density function for the concentrations, by using the random variable transformation technique. We extend this application to the general solution of Bateman equations. The density function is expressed as an expectation, which has important implications for parametric density estimation. This may improve the classical kernel estimation when the random dimensionality is not low. Numerical examples are included, where the decay parameters and the initial concentrations are assigned different probability distributions.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-022-02625-7