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Bulletin of the Russian Academy of Sciences Physics

Statistical Description for the Decay of an Ensemble of Emitter Nuclei in the Context of a Sub-Poisson Distribution

Т. Н. Корбут, Ed. A. Rudak, A. M. Petrovskiy

Published Oct 1, 2018• 5 citations
Publisher

Abstract

Abstract A new formalism that combines the simplicity of the mathematical apparatus of the Poisson distribution and a correct description of the decay of the last nucleus of a system in a binomial distribution is proposed, based on Poisson and binomial distributions. The mathematical apparatus of the model for the creation and death of particles in a sub-Poisson distribution is presented, along with the results from comparing descriptions of the radioactive decay of nuclei using Poisson, binomial, and sub-Poisson distributions for a medium based on uranium-235.

DOI
10.3103/s1062873818100155

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Abstract A new formalism that combines the simplicity of the mathematical apparatus of the Poisson distribution and a correct description of the decay of the last nucleus of a system in a binomial distribution is proposed, based on Poisson and binomial distributions. The mathematical apparatus of the model for the creation and death of particles in a sub-Poisson distribution is presented, along with the results from comparing descriptions of the radioactive decay of nuclei using Poisson, binomial, and sub-Poisson distributions for a medium based on uranium-235.
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The particle decay problem in the random-set approach leads naturally to the q -Poisson distribution. Motivated by the fact that in the classical quantum mechanical description of particle decay one ends up with a composite system, we construct a Hilbert space using the eigenstates of the average particle number operator N . In this approach, time is represented by integer multiples of an observation quantum . It is shown that these considerations lead to the redefined q -oscillator and an element of acts like a reversal operator on n time-ordered states.
A method on how to take into account pump statistics and spontaneous atomic decays when calculating the photon-number distribution of lasers in photon-number representation is presented. The intracavity phonon-number and extracavity photocount distributions with binomial pump and spontaneous atomic decays are calculated. In two limit cases, the results of calculations transit respectively to the photon-number distributions of systems with common Poissonian pump and regular pump, and both with the spontaneous atomic decays being suppressed.