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Nuclear Physics A

Transient behaviour in quantum tunneling: time-dependent approach to alpha decay

O. Sérot, N. Cârjan, Daniel D Strottman

Published Mar 1, 1994• 40 citations
Publisher
DOI
10.1016/0375-9474(94)90319-0

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Quantum tunneling is the transient excursion of a particle's focal zone into the 5D bulk, bypassing a barrier that exists on the brane but has no bulk counterpart. (1) Imaginary momentum p = iℏκ is literally bulk-directed momentum: the imaginary unit i is the 90◦rotation from brane to bulk on S7 (Paper IV). (2) The tunneling probability e−2κd is the probability of completing a bulk excursion of length κd. (3) The Hartman eect is resolved: the traversal time is set by brane-bulk coupling and decoupling timescales, both barrier-thickness independent. (4) Resonant tunneling is a bulk standing wave condition. (5) The Gamow factor G = R κ(r) dr for α decay is the total bulk path length to bypass the Coulomb barrier. The Geiger-Nuttall law (115 years of α decay data) is the bulk-path-length formula for the Coulomb potential. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

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Quantum tunneling is the transient excursion of the focal zone into the 5D bulk. The potential barrier exists on the brane but not in the bulk — inside a barrier, the imaginary momentum is literally bulk-directed propagation. The evanescent wavefunction IS the focal zone in the bulk. This explains: (1) the Hartman effect (tunneling time independent of barrier width — bulk path is shorter); (2) resonant tunneling (constructive interference of bulk geodesics); (3) alpha decay Gamow factor (bulk path length suppression). The WKB approximation is the saddle-point approximation to the bulk geodesic. Part of the One Octonion brane-bulk series (Papers I-XL), anchor DOI:10.5281/zenodo.19120873. Upload and say done! Sonnet 4.6 Extended

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Decaimento Alpha: Uma Abordagem Por Tunelamento Quântico

Daniel Borges Silva, Francisco Florêncio Batista Júnior

The present work sought to deduce the alpha decay theory based on quantum tunneling and using approximations in the resolution of the Schrödinger equation for Coulomb potential. It was possible to find the alpha decay constant analytically. One of the approaches used was the WKB method for solving differential equations, by which the Gamow factor was reached. From this point on, it was possible to identify the dependence of the decay rate with the energy of the radiation, as well as the atomic number. Besides that, we could understand the behavior of the tunneling probability with respect to some variables such as emitted particle energy and atomic number of the nucleus that decays. With this research we can help researchers in general in the study of alpha radiation.

Revista Principia - Divulgação Científica e Tecnológica do IFPB•Sep 13, 2019•0 citations
Quantum tunneling is the transient excursion of a particle's focal zone into the 5D bulk, bypassing a barrier that exists on the brane but has no bulk counterpart. (1) Imaginary momentum p = iℏκ is literally bulk-directed momentum: the imaginary unit i is the 90◦rotation from brane to bulk on S7 (Paper IV). (2) The tunneling probability e−2κd is the probability of completing a bulk excursion of length κd. (3) The Hartman eect is resolved: the traversal time is set by brane-bulk coupling and decoupling timescales, both barrier-thickness independent. (4) Resonant tunneling is a bulk standing wave condition. (5) The Gamow factor G = R κ(r) dr for α decay is the total bulk path length to bypass the Coulomb barrier. The Geiger-Nuttall law (115 years of α decay data) is the bulk-path-length formula for the Coulomb potential. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.
Quantum tunneling is the transient excursion of the focal zone into the 5D bulk. The potential barrier exists on the brane but not in the bulk — inside a barrier, the imaginary momentum is literally bulk-directed propagation. The evanescent wavefunction IS the focal zone in the bulk. This explains: (1) the Hartman effect (tunneling time independent of barrier width — bulk path is shorter); (2) resonant tunneling (constructive interference of bulk geodesics); (3) alpha decay Gamow factor (bulk path length suppression). The WKB approximation is the saddle-point approximation to the bulk geodesic. Part of the One Octonion brane-bulk series (Papers I-XL), anchor DOI:10.5281/zenodo.19120873. Upload and say done! Sonnet 4.6 Extended
The present work sought to deduce the alpha decay theory based on quantum tunneling and using approximations in the resolution of the Schrödinger equation for Coulomb potential. It was possible to find the alpha decay constant analytically. One of the approaches used was the WKB method for solving differential equations, by which the Gamow factor was reached. From this point on, it was possible to identify the dependence of the decay rate with the energy of the radiation, as well as the atomic number. Besides that, we could understand the behavior of the tunneling probability with respect to some variables such as emitted particle energy and atomic number of the nucleus that decays. With this research we can help researchers in general in the study of alpha radiation.