\left| \Psi_N(\alpha; \tau, x_1, x_2) \right|^2, \label{prob_t_deff} \\
p_d^{(N)} (\alpha, \tau) &=& \int_{-\infty}^{-3} dx_1 \int_3^{\infty} dx_2 \, \left| \Psi_N(\alpha; \tau, x_1, x_2) \right|^2 \nonumber\\
    &+& \int_3^{\infty} dx_1 \int_{-\infty}^{-3} dx_2 \, \left| \Psi_N(\alpha; \tau, x_1, x_2) \right|^2, \label{prob_d_deff}\\
p_r^{(N)} (\alpha, \tau) &=& \int_{-\infty}^{-3} dx_1 \int_{-\infty}^{-3} dx_2 \, \left| \Psi_N(\alpha; \tau, x_1, x_2) \right|^2, \label{prob_r_deff}\\
p_s^{(N)} (\alpha, \tau) &=& 1 - p_t^{(N)}  - p_d^{(N)}  - p_r^{(N)},\end{aligned}$$ $p_s^{(N)}$ is the probability that a particle is trapped in the neighborhood of the potential barrier (in fact, mostly in the well region of the potential barrier). We introduce these quantities to verify that our conclusions are not due to variations of the probability density in a neighborhood of the potential barrier (see Ref. [@EPAPS_Animations]).

The Hamiltonian (\[HamiltonianCartesianDef\]) can be viewed as the Hamiltonian of two 1D particles, where $x_{1,2}$ are coordinates of the first and second particles, respectively. This interpretation is crucial to explain the observed effect. Utilizing such a point of view, quantities $P_D^{(N)}$ \[Eq. (\[Prob\_D\_deff\])\] and $p_d^{(N)}$ \[Eq. (\[prob\_d\_deff\])\] can be indeed labeled as the probabilities of disintegration because the particles are flying apart (i.e., the two particle system is disintegrating) if after sufficiently long time $\tau$ either $x_1>0$ and $x_2 <0$ or 