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Penetration of two coupled particles through a repulsive barrier is considered. A simple mechanism of the appearance of barrier resonances is demonstrated that makes the barrier anomalously transparent as compared to the probability of penetration of structureless objects. It is indicated that the probabilities of tunnelling of two interacting particles from a false vacuum can be considerably larger than it was assumed earlier.

Resonance penetration of two coupled particles through a repulsive barrier is considered. It is shown that a local minimum of the total potential generates metastable bound states, and their spectrum determines the position of resonances in the penetration probability. It is pointed out that the probabilities of tunneling of two interacting particles from the false vacuum can be essentially higher than it has been assumed earlier.PACS number(s): 03.65. Nk, 11.10.Jj, 21.45.+v In paper by N.Saito and Y.Kayanuma [1], it was pointed out that there exists a new quantum phenomenon -resonance transparency of a single repulsive barrier for a coupled pair of particles. To consider this effect, a one-dimensional rectangular repulsive barrier and an infinite one-dimensional rectangular potential well coupling the pair were chosen. Since the interactions were simple, it was possible to solve the initial two-dimensional Schroedinger equation by reducing it to a system of onedimensional equations by means of projection onto 7 eigenfunctions. However, there still remained the question of how this effect manifests itself in other systems.This note continues the study of the effect of resonance transparency of two type one-dimensional barriers for a pair of identical particles coupled by the oscillatory interaction. This pair interaction allows us to reduce the problem of three-dimensional scattering of a three-dimensional oscillator to the solution of a twodimensional equation analogous to the equation derived in ref. [1]. Besides, it is just this sort of pair interaction that is used in literature [2] devoted to the probability of induced decay of the false vacuum in collisions of high-energy particles (see, for instance, [3,4]). It was pointed out there that it is possible to describe the processes of transition from the false vacuum on the basis of quantum-mechanical tunneling of a pair of particles through the barrier; but the study was performed for a system where only one of the oscillator particles interacts with the barrier. Here, we show that, when the two particles interact with the barrier, there arises the same effect of resonance transparency as in ref.[1].The first potential barrier we study is taken in the Gauss form from ref.[2] in order to show that it is possible to drastically increase the probability of induced decay of the false vacuum. The second potential barrier of the Coulomb form is investigated in order to draw attention to the fact that the resonance tunneling of the barrier is feasible in the problems of fusion of heavy nuclei. The method of investigation is based on the numerical solution of the two-dimensional Schroedinger equation without any further simplifications.Consider the penetration of a pair of identical parti-cles with masses m 1 = m 2 = m, and coordinates r 1 and r 2 coupled by an oscillatory interaction through the potential barrier V 0 (x 1 ) + V 0 (x 2 ). The Hamiltonian of this system (h = 1)written in coordinates of the center of inertia of the pair R = (r 1 + r 2 )/2 and in an ...

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