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International Journal of Physics and Applications

Quantum Tunneling and Radioactive Decay: The Case of Alpha Emission

Haadiya Ali

Published Jul 1, 2025• 0 citations
Publisher

Abstract

Alpha decay Abstract Alpha decay is one of the foremost and most well- studied forms of radioactive decay, involving the emigration of a nascence flyspeck — two protons and two neutrons bound together — from an unstable infinitesimal nexus. Classical drugs, with its energy- grounded rules, suggests that such a flyspeck should be confined within the nexus indefinitely, unfit to overcome the immense implicit hedge posed by nuclear and electrostatic forces. Yet, in reality, nascence patches escape routinely, with remarkably harmonious powers and predictable half- lives This incongruity remained undetermined until the emergence of amount mechanics in the early 20th century, which introduced the conception of amount tunneling — a miracle where patches have a finite probability of" tunneling" through walls they warrant the energy to surmount. This paper takes a detailed look at the drugs of amount tunneling and its part in enabling nascence decay. We explore the literal development of the proposition, the fine frame behind tunneling chances, and the deep perceptivity this conception provides into nuclear geste. We also examine real- world exemplifications, similar as uranium- 238, and highlight broader operations of tunneling in fields ranging from nuclear drug to amount computing.

DOI
10.33545/26647575.2025.v7.i2d.211

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Alpha decay Abstract Alpha decay is one of the foremost and most well- studied forms of radioactive decay, involving the emigration of a nascence flyspeck — two protons and two neutrons bound together — from an unstable infinitesimal nexus. Classical drugs, with its energy- grounded rules, suggests that such a flyspeck should be confined within the nexus indefinitely, unfit to overcome the immense implicit hedge posed by nuclear and electrostatic forces. Yet, in reality, nascence patches escape routinely, with remarkably harmonious powers and predictable half- lives This incongruity remained undetermined until the emergence of amount mechanics in the early 20th century, which introduced the conception of amount tunneling — a miracle where patches have a finite probability of" tunneling" through walls they warrant the energy to surmount. This paper takes a detailed look at the drugs of amount tunneling and its part in enabling nascence decay. We explore the literal development of the proposition, the fine frame behind tunneling chances, and the deep perceptivity this conception provides into nuclear geste. We also examine real- world exemplifications, similar as uranium- 238, and highlight broader operations of tunneling in fields ranging from nuclear drug to amount computing.
Abstract Quantum tunneling, wherein a quanject has a non-zero probability of tunneling into and then exiting a barrier of finite width and height, is the subject of Chapter 13. The description for the one-dimensional case is extended to the barrier being inverted, which forms an attractive potential well. The first application of this analysis is to the emission of alpha particles from the decay of radioactive nuclei, where the alpha-nucleus attraction is modeled by a potential well and the barrier is the repulsive Coulomb potential. Excellent results are obtained. Ditto for the similar analysis of proton burning in stars and yet a different analysis that explains tunneling through a Josephson junction, the connector between two superconductors. The final application is to the scanning tunneling microscope, a device that allows the microscopic surfaces of solids to be mapped via electrons from the surface molecules tunneling into the tip of the STM probe.
La radiactividad es el proceso de desintegración y transformación espontánea de núcleos atómicos volátiles, seguido de la emisión de radiación. George Gamow fue capaz de utilizar la mecánica cuántica para explicar el fenómeno radiactivo del decaimiento alfa a través de un proceso llamado tunelización. Las partículas α son estructuralmente equivalentes al núcleo de un átomo de Helio y constan de dos protones y dos neutrones. Básicamente el argumento es que una partícula alfa no necesita tener suficiente energía para superar la barrera potencial del núcleo, simplemente tunelea a través de él. En este artículo se hace una revisión a los conceptos y se desentrañan los cálculos que utilizó Gamow para poder explicar su teoría de decaimiento. Palabras Clave: Decaimiento alfa, radiactividad, tunelamiento cuántico, mecánica cuántica. Abstract Radioactivity is the process of spontaneous decay and transformation of volatile atomic nuclei, followed by the emission of radiation. George Gamow was able to use quantum mechanics to explain the radioactive phenomenon of alpha decay through a process called tunneling. The α-particles are structurally equivalent to the nucleus of a helium atom and consist of two protons and two neutrons. Basically the argument is that an alpha particle does not need enough energy to overcome the potential barrier of the nucleus, it tunnels through it. This article reviews the concepts and unravels the calculations that Gamow used to explain his theory of decay. Keywords: Alpha decay, radioactivity, quantum tunneling, quantum mechanics. Referencias [1] Leon van Dommelen. Quantum Mechanics for Engineers, Version 5.55 alpha. 2012. [2] G. Gamow. Quantum Theory of the Atomic Nucleus. 1928. [3] David J. Griffiths. Introduction to Quantum Mechanics (2nd Edition). 2nd. Pearson Prentice Hall. isbn: 0131118927. [4] Michael F L’Annunziata. Radioactivity: introduction and history, from the quantum to quarks; 2nd ed. Amsterdam: Elsevier, 2016. url: https : / / cds . cern . ch / record / 2210635. [5] W.E. Lee M.I. Ojovan. An Introduction to Nuclear Waste Immobilisation; 2nd ed. Elsevier, 2014. [6] A C Melissinos and Jim Napolitano. Experiments in modern physics; 2nd ed. New York, NY: Academic Press, 2003. url: https://cds.cern.ch/ record/897801. [7] Eugen Merzbacher. “The Early History of Quantum Tunneling”. In: Physics Today 55.8 (Aug. 2002), pp. 44–49. doi: 10.1063/1.1510281. url: https://doi.org/10. 1063/1.1510281. [8] Curt A. Moyer Raymond A. Serway Clement J. Moses. Modern Physics, Third Edition. David Harris, 2005. [9] Thaddeus J. Trenn. “Rutherford on the AlphaBetaGamma Classification of Radioactive Rays”. In: Isis 67.1 (1976), pp. 61–75. issn: 00211753, 15456994. url: http: //www.jstor.org/ stable/231134.
According to theories of classical physics, a moving particle cannot move to an environment with greater potential energy than its total energy during movement. But according to quantum theories, this event is known to be. This event is called tunneling. Tunneling is a probability, and it is measured by transition coefficient. Correct calculation of this coefficient is particularly important because extremely sensitive and important instruments have been developed based on this event, and many events in nature can be explained by tunneling. This coefficient was generally calculated by semi-classical approaches (WKB) and the known formula is an approximate formula. In the previous papers, the general transmission coefficient of a potential barrier with arbitrary form is calculated by a simple method without any approximation. The results were applied to calculate the half-life values of the nuclei that emit alpha particle. In this article, the half-life calculation formulas obtained in previous studies were made simpler. It has been shown that it is applicable to all radioactive decays (alpha, beta, gamma etc.). The half-life values obtained from our calculations have been compared with the experimental values, and it has been found that the new half-life values are exactly consistent with the experimental values.
The halflife of αradioactive elements has already been measured out through experiments. But, classical theory's failure to explain the phenomenon of αDecay is found in this article according to the analysis of the mechanism of αDecay. And in this article, this problem is completely settled through introducing of the theory of quantum tunneling effect yet. Furthermore, the halflife of αDecay of238U is illustrated and figured out with this theory, and is approximately in accordance with the figure of experiments.
This study investigates three-dimensional quantum tunneling through analytical solutions of the Schr¨odinger equation in Cartesian and spherical coordinates. By develop ing transmission coefficients for both square and spherical potential barriers, we establish a theoretical framework for α-decay via the Gamow model. The analysis reveals how angular momentum and energy dependence govern tunneling probabilities, with experimental valida tion showing agreement within 15% for high-energy decays. The results bridge fundamental quantum mechanics with nuclear physics applications.
Application of quantum mechanics to a simple model of the nucleus gives the phenomenon of radioactive disintegration. The statistical nature of the quantum mechanics gives directly disintegration as a chance phenomenon without any special hypothesis. \textsection{}1 contains a presentation of those features of quantum mechanics which are here used and gives a simple calculation of the disintegration constant. \textsection{}2 discusses the qualitative application of the model to the nucleus. \textsection{}3 presents quantitative calculations amounting to a theoretical interpretation of the Geiger-Nuttall relation between the rate of disintegration and the energy of the emitted $\ensuremath{\alpha}$-particle. In getting this relation one arrives at the rather remarkable conclusion that the law of force between emitted $\ensuremath{\alpha}$-particle and the rest of the nucleus is substantially the same in all the atoms even where the decay rates stand in the ratio 1022{10}^{22}1022. \textsection{}4 calls attention to the natural way in which the paradoxical results of Rutherford and Chadwick on the scattering of fast $\ensuremath{\alpha}$-particles by uranium receive explanation with the model here used. \textsection{}5 discusses certain limitations inherent in the methods employed.