Calculation a New Transmission Coefficient of Tunneling for an Arbitrary Potential Barrier and Application to Alpha Decay
Journal of Photonic Materials and Technology
Volume 5, Issue 2, December 2019, Pages: 24-31
Received: Jan. 15, 2019; Accepted: Feb. 18, 2019; Published: Dec. 25, 2019
Views 74      Downloads 29
Author
Hasan Hüseyin Erbil, Physics Department, Faculty of Science, Ege University, Bornova – Izmir, Turkey
Article Tools
Follow on us
Abstract
According to classical physics theories, 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 a transition coefficient. Correct calculation of this coefficient is very important because very sensitive and important instruments have been developed based on this event, and many events in nature can be explained by tunneling. This coefficient is generally calculated by semi-classical approaches (WKB) and the known formula is an approximate formula. In this paper, the general transmission coefficient of a potential barrier with arbitrary form is calculated by a simple method without any approximation. The results are applied to calculate the half-life values of the nuclei that emit alpha particles. The half-life values obtained from our calculations and the classical method (WKB) have been compared, and it has been found that the new half-life values are exactly consistent with the experimental values.
Keywords
Tunneling, Transmission Coefficient, Alpha Decay, Half-Life of Alpha Decay
To cite this article
Hasan Hüseyin Erbil, Calculation a New Transmission Coefficient of Tunneling for an Arbitrary Potential Barrier and Application to Alpha Decay, Journal of Photonic Materials and Technology. Vol. 5, No. 2, 2019, pp. 24-31. doi: 10.11648/j.jmpt.20190502.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
H. H. Erbil, “A Simple solution of the time-independent Schrödinger equation in one dimension and some applications,” in The International Review of Physics Vol. 1, 2007, 4, 197-213.
[2]
H. H. Erbil, “A Simple solution of the radial Schrödinger equation for spherically symmetric potentials and some applications,” in The International Review of Physics Vol. 2, 2008, 1, 1-10.
[3]
H. H. Erbil, “General solution of the Schrödinger equation with potential field quantization,” in Turkish Journal of Physics, 42, 2018, 527-572.
[4]
F. Schwabl, Quantum Mechanics, Translated by Ronald Kates, 2nd ed.; Springer-Verlag, Berlin Heidelberg New York, USA, 1995.
[5]
J. L. Powell and B. Crasemann, Quantum Mechanics, Addison-Wesley Publishing Company Inc., USA, 1965.
[6]
L. D. Landau and E. M. Lifstits, Quantum Mechanics, Pergamon Press, 1958.
[7]
J. Griffiths, Introductory Quantum Mechanics, Prentice Hall, 1994.
[8]
H. H. Erbil, Analitik ve Kuantum Mekaniği, Nobel Akademik Yayıncılık, 2014, Ankara, Turkey.
[9]
K. S. Krane, Introductory Nuclear Physics, John-Wiley & Sons. 1988. Translated to Turkish by Başar Şarer, Palme Yayıncılık, Ankara, Turkey, 1988.
[10]
S. Y. F Chu, L. P. Exström and R. B. Firestone, The Lund/LBNL Nuclear Data Search, Nucleardata.nuclear.lu.se/toi/index,asp, Summary drawings for A=1-277.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186