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Physical Review C

Quantum mechanical tunneling of composite particle systems: Linkage to sub-barrier nuclear reactions

Alan C. Shotter, Martin Shotter

Published May 31, 2011• 16 citations
Publisher

Abstract

A variety of physical phenomena have at their foundation the quantum tunneling of particles through potential barriers. Many of these phenomena can be associated with the tunneling of single inert particles. The tunneling of composite systems is more complex than for single particles due to the coupling of the tunneling coordinate with the internal degrees of freedom of the tunneling system. Reported here are the results of a study for the tunneling of a two-component projectile incident on a potential energy system which differs for the two components. A specific linkage is made to sub-Coulomb nuclear reactions.

DOI
10.1103/physrevc.83.054621

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A variety of physical phenomena have at their foundation the quantum tunneling of particles through potential barriers. Many of these phenomena can be associated with the tunneling of single inert particles. The tunneling of composite systems is more complex than for single particles due to the coupling of the tunneling coordinate with the internal degrees of freedom of the tunneling system. Reported here are the results of a study for the tunneling of a two-component projectile incident on a potential energy system which differs for the two components. A specific linkage is made to sub-Coulomb nuclear reactions.
Tunneling is a supreme quantum effect. Every introductory text [1] on quantum mechanics gives the paradigm example of a particle tunneling through a one-dimensional potential barrier despite having a total energy less than the barrier height. Indeed, the reader typically works through a number of exercises, all involving one-dimensional potential barriers of one form or another modeling several key physical phenomena ranging from atom transfer reactions to the decay of α-particles [2]. However, one seldom encounters coupled multidimenisonal tunneling in such texts since an analytical solution of the Schro¨dinger equation in such cases is not possible. Interestingly, the richness and complexity of the tunneling phenomenon manifest themselves in full glory in the case of multidimensional systems [3]. Thus, for instance, the usual one-dimensional expectation of increasing tunneling splittings as one approaches the barrier top from below is not necessarily true as soon as one couples another bound degree of freedom to the tunneling coordinate. In the context of molecular reaction dynamics, multidimensional tunneling can result in strong mode-specificity and fluctuations in the reaction rates [4]. In fact, a proper description of tunneling of electrons and hydrogen atoms is absolutely essential [5,6] even in molecular systems as large as enzymes and proteins. Although one usually assumes tunneling effects to be significant in molecules involving light atom transfers, it is worth pointing out that neglecting the tunneling of even a heavy atom like carbon is the difference between a reaction occurring or not occurring. In particular, one can underestimate rates by nearly hundred orders of magnitude [7]. Interestingly, and perhaps paradoxically, several penetrating insights into the nature and mechanism of multidimensional barrier tunneling have been obtained from a phase-space perspective [8,9]. The contributions by Creagh, Shudo and Ikeda, and Takahashi in the present volume provide a detailed account of the latest advances in the phasespace-based understanding of multidimensional barrier tunneling.
The tunnel effect, commonly defined as the phenomenon in which a microparticle overcomes a potential barrier that exceeds its total energy, is often cited in quantum mechanics. However, this effect does not actually occur in its described form in nature, and the quantum mechanical interpretation of tunneling does not accurately represent the real physical processes involved, but rather provides a mathematical model. The true physical mechanism of the tunnel effect remains unidentified. An analysis of the tunnel effect reveals that its manifestation creates a “paradox” in classical physics. Explanations based on the Heisenberg uncertainty principle and the wave nature of particles fail to offer a comprehensive understanding of the actual physical process.This study proposes a new explanation of the tunneling phenomenon based on the principles of classical physics and electrodynamics. It is shown that the overcoming of the Coulomb barrier by low-energy microparticles occurs exclusively due to brief localized decreases in potential within the Coulomb barrier, allowing certain charged microparticles to penetrate. The formation mechanism of these short-lived localized regions, which manifest as volume channels with lower potential within the Coulomb barrier, is examined.It is established that the creation of these channels is linked to the properties of atomic nuclear and their associated electric fields. This facilitates the supra barrier penetration of the Coulomb barrier by individual low-energy microparticles that pass through these channels while experiencing a reduction in their total energy. This explanation resolves the “paradox” of the tunneling effect, eliminating the contradiction with classical physics laws.Moreover, the derived estimates of the tunneling process parameters are in qualitative agreement with the results obtained from quantum-mechanical models. The proposed framework aligns with nuclear physics findings, is supported by experimental evidence, and provides a new mechanism for controlling the tunneling effect in various energy-related applications.
We consider a method for solving the problem of quantum tunneling through repulsive potential barriers for a composite system consisting of several identical particles coupled via pair oscillator-type potentials in the oscillator symmetrized-coordinate representation. We confirm the efficiency of the proposed approach by calculating complex energy values and analyzing metastable states of composite systems of three, four, and five identical particles on a line, which leads to the effect of quantum transparency of the repulsive barriers.
Abstract We study quantum tunneling of a composite object, which has a dipole or quadrupole moment coupled with quantized (photon or gravitational) radiation field, through a potential barrier. The dipole or quadrupole moment is represented by an oscillator in the relative coordinate of two constituent particles of the object. The center of mass degrees of freedom of the object is not directly coupled with the radiation field. However, we show that, for the object with the oscillator in the excited state, dissipation caused by the radiation field can suppress its quantum tunneling rate in the center of mass degrees of freedom. In addition, when the initial energy of its center of mass motion is similar to that of the excited state of the oscillator, a spatial superposition state of the object prepared by the barrier can decohere due to the radiation field. The main purpose of this article is to investigate how two different interplays (i) among the center of mass, the relative coordinate degrees of freedom and the potential barrier, and (ii) between the relative coordinate degrees of freedom and the radiation field, can affect the quantum tunneling and the creation of the spatial superposition state of the object. Our toy model can give insight into tests of quantum tunneling and quantum superposition of atoms or molecules with its dipole or quadrupole moment coupled with the radiation field.
Some aspects of quantum tunnelling of a composite particle are clarified by a simple model. We calculate the probability that a couple of point particles bound to each other by a square well potential with a hard core tunnel through a rectangular potential barrier. It is shown that resonance structures appear in the transmission spectrum in some cases, which reflects the existence of quasi-bound-states of the centre of mass motion around the potential barrier. It is also shown that an inelastic tunnelling occurs in which the transitions in the relative motion are induced by the tunnelling of the centre of mass.