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Physics of Atomic Nuclei

Resonant tunneling of a few-body cluster through repulsive barriers

Alexander A. Gusev, Sergue Il'ich Vinitsky, Ochbadrakh Chuluunbaatar, L. L. Hai, Vladimir Leonardovich Derbov, ANDRZEJ GÓŹDŹ, Pavel M. Krassovitskiy

Published Mar 1, 2014• 16 citations
Publisher

Abstract

A model for quantum tunnelling of a cluster comprised of A identical particles, interacting via oscillator-type potential, through short-range repulsive barrier potentials is introduced for the first time in symmetrized-coordinate representation and numerically studied in the s -wave approximation. A constructive method for symmetrizing or antisymmetrizing the ( A − 1)-dimensional harmonic oscillator basis functions in the new symmetrized coordinates with respect to permutations of coordinates of A identical particles is described. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, their number A = 2, 3, 4 and the type of their symmetry, is analyzed. It is shown that the total transmission coefficient demonstrates the resonance behavior due to the existence of barrier quasi-stationary states, embedded in the continuum.

DOI
10.1134/s1063778814030107

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A model for quantum tunnelling of a cluster comprised of A identical particles, interacting via oscillator-type potential, through short-range repulsive barrier potentials is introduced for the first time in symmetrized-coordinate representation and numerically studied in the s -wave approximation. A constructive method for symmetrizing or antisymmetrizing the ( A − 1)-dimensional harmonic oscillator basis functions in the new symmetrized coordinates with respect to permutations of coordinates of A identical particles is described. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, their number A = 2, 3, 4 and the type of their symmetry, is analyzed. It is shown that the total transmission coefficient demonstrates the resonance behavior due to the existence of barrier quasi-stationary states, embedded in the continuum.
Quantum tunnelling of a cluster comprised of several identical particles, coupled via an oscillator-type potential, through short-range repulsive barrier potentials is studied in the s-wave approximation of the symmetrized coordinate representation. A procedure is briefly described that allows the construction of states, symmetric or asymmetric with respect to permutations of A identical particles, from the harmonic oscillator basis functions expressed via the newly introduced symmetrized coordinates. In the coupled-channel approximation of the -matrix approach, the effect of quantum transparency is analysed; it manifests itself in non-monotonic resonance dependence of the transmission coefficient upon the energy of the particles, their number A = 3, 4 and the symmetry types of their states. The total transmission coefficient is shown to demonstrate resonance behaviour with probability density growth in the vicinity of the potential energy local minima, which is a manifestation of the barrier quasi-stationary states, embedded in the continuum.
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.
The quantum model of a cluster, consisting of A identical particles, coupled by the internal pair interactions and affected by the external field of a target, is considered. A symbolic-numerical algorithm for generating A-1-dimensional oscillator eigenfunctions, symmetric or antisymmetric with respect to permutations of A identical particles in the new symmetrized coordinates, is formulated and implemented using the MAPLE computer algebra system. Examples of generating the symmetrized coordinate representation for A-1 dimensional oscillator functions in one-dimensional Euclidean space are analyzed. The approach is aimed at solving the problem of tunnelling the clusters, consisting of several identical particles, through repulsive potential barriers of a target.
A method for solving the problem of quantum transmission through potential barriers or potential wells for a compound system consisting of several identical particles coupled via pair oscillator-type potentials in the oscillator representation of the symmetrized coordinates is considered. The efficiency of the proposed approach, algorithms and programs is demonstrated by the examples of calculation of complex energy values and analysis of metastable states of compound systems of two, three, and four identical particles on a straight line, which lead to the effect of quantum transparency of the potential barriers or quantum reflection from the wells.
Results are here reported of a model calculation for the one-dimensional tunneling of a particle coupled to a quantum harmonic oscillator. Interaction is at the barrier, to mimick the influence on transmission of possible surface excitations. The tunneling process turns out to be fast with respect to low energy modes such as surface phonons. Total transmission is enhanced with respect to the case without coupling, while the elastic one shows a kind of dissipative behaviour. On the contrary, the time scale for resonant tunneling is ?, where ? is the halfwidth of the resonance. Virtual excitation of high energy modes (e.g., surface plasmons) acts as a van der Waals-type force which renormalizes the barrier and increases the elastic transmission.
Numerical simulations of quantum tunneling with time-dependent barriers show that there is a resonance, with a marked increase in the transmission coefficient. For a raised cosine potential, and for low energies with square barriers, the resonance occurs when a modulation quantum can take a tunneling particle to the top of the barrier. For energies near the top of a square barrier the resonance may be understood by hypothesizing that a tunneling particle may travel from end to end of the barrier until it is ultimately either transmitted or reflected.