Symbolic-numerical Algorithm for Generating Cluster Eigenfunctions: Tunneling of Clusters Through Repulsive Barriers

TL;DR

This paper introduces a symbolic-numerical algorithm to analyze quantum tunneling of particle clusters through barriers, revealing resonance effects linked to quasistationary states within a new symmetrized-coordinate framework.

Contribution

It presents the first implementation of a symbolic-numerical method for calculating cluster eigenfunctions and tunneling effects using a novel symmetrized-coordinate representation.

Findings

Resonance effects cause nonmonotonic transmission coefficients.

Quasistationary states are responsible for resonance behavior.

The method applies to clusters of 2-4 particles with different symmetries.

Abstract

A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate representation and studied within the s-wave approximation. The symbolic-numerical algorithms for calculating the effective potentials of the close-coupling equations in terms of the cluster wave functions and the energy of the barrier quasistationary states are formulated and implemented using the Maple computer algebra system. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, the number of the particles A=2,3,4, and their symmetry type, is analyzed. It is shown that the resonance behavior of the total transmission coefficient is due to the existence of barrier quasistationary states imbedded in the continuum.