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Fractional Calculus in Nuclear Multistep Decay: Analytical Solutions, Existence and Uniqueness Analysis of the Actinium Series

by Mohammed Shqair, Areej Almuneef, Emad Jaradat, Rahat Zarin and Ahmed Hagag

Fractal Fract. 2025, 9(9), 601; https://doi.org/10.3390/fractalfract9090601 - 16 Sep 2025

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Abstract

This paper provides a thorough examination of the Actinium radioactive decay series, which converts Uranium-235 into the stable Lead-207 isotope via a succession of alpha, beta, and gamma decays. For the first time, the series is modeled using fractional calculus, employing two innovative analytical methods: the Sumudu Residual Power Series Method (SRPSM) and the Temimi Ansari Method (TAM). The study discusses the well-posedness of the fractional-order model in the Caputo sense within a Banach space setting. These fractional models capture complex, non-ideal decay behaviors more accurately than traditional exponential models. Mathematica is used to do numerical computations for four different Actinium series scenarios. The results are tabulated and visually depicted to show how radionuclide concentrations change over time. The findings demonstrate that SRPSM and TAM effectively simplify the complex differential equations governing nuclear decay, offering enhanced precision and flexibility. This work provides a robust framework for modeling the Actinium series, with potential applications in nuclear physics, radiometric dating, and radiation safety studies. Full article

(This article belongs to the Special Issue Recent Developments in Multidimensional Fractional Differential Equations and Fractional Difference Equations)

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Open AccessArticle

The New Physics in LILITA_N21: An Improved Description of the Reaction 190 MeV ⁴⁰Ar + ²⁷Al

by Antonio Di Nitto, Federico Davide, Emanuele Vardaci, Davide Bianco, Giovanni La Rana and Daniela Mercogliano

Appl. Sci. 2022, 12(9), 4107; https://doi.org/10.3390/app12094107 - 19 Apr 2022

Cited by 3 | Viewed by 1651

Abstract

In this paper, light charged particle emission in the evaporation residue channel for the 190 MeV

^{40}

Ar +

^{27}

Al reaction leading to

^{67} Ga

composite nuclei at

E_{x}

= 91 MeV and angular momentum up to 46 ℏ has been [...] Read more.

In this paper, light charged particle emission in the evaporation residue channel for the 190 MeV

^{40}

Ar +

^{27}

Al reaction leading to

^{67} Ga

composite nuclei at

E_{x}

= 91 MeV and angular momentum up to 46 ℏ has been re-analyzed. The main goal was to study the decay of

^{67} Ga

on the basis of an extended set of observables in order to provide a description of the evaporative decay cascades using the multistep Monte Carlo approach. The proton and

α

-particle energy spectra along with their angular distributions and ratios of differential multiplicities have been considered. The measured observables were compared with statistical model calculations. Having used a single-step Monte Carlo approach and standard parameters decades ago, the model does not provide a good description of the full dataset. Only a subset of the data was reproduced by assuming emitting nuclei with very large deformed shapes in a previous work published in the late 1980s. In the reported analysis, better agreement has been observed. Using the new transmission coefficients from the Optical Model, the parameters of which have recently been derived, the multi-step approach and the introduction of a nuclear shape description based on the nuclear stratosphere allowed us to realize a significant improvement. Full article

(This article belongs to the Special Issue Monte Carlo Simulation in Quantum Science and Applied Physics)

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