answer this question, let us look at collective tunneling from the point of view of the (time-independent) multichannel formalism, which is the most common method employed to the problem at hand (see, e.g., Refs. [@Zakhariev1964; @Amirkhanov1966; @Zakhariev2002; @Saito1994; @Penkov2000; @Chabanov2000; @Penkov2000a; @Razavy2003a; @Goodvin2005; @Goodvin2005a; @Lee2006; @Hnybida2008; @Shegelski2008; @Zakhariev2008]). According to the multi-channel approach, using the expansion $\Psi(R, \rho) = { \mathop{\hbox to4pt{ $\sum$ \hss}{\displaystyle\int}} }_n \phi_n(\rho)\chi_n (R)$, the stationary Schrödinger equation, $\hat{H}\Psi(R, \rho) = E\Psi(R, \rho)$, is reduced to the following system of ordinary differential equations for unknown functions $\chi_n(R)$: $$\begin{aligned}
\nonumber
\frac{1}{2M} \frac{d^2\chi_n(R)}{dR^2} -  { \mathop{\hbox to4pt{ $\sum$ \hss}{\displaystyle\int}} }_{n'} Z_{nn'}(R) \chi_{n'}(R) = (E_n-E)\chi_n(R),\end{aligned}$$ where $Z_{nn'}(R)$ being effective potentials, $$\begin{aligned}
\label{Effective_Potential_Def}
Z_{nn'}(R) &=& \int d\rho \, \phi^*_n(\rho)\left[ V_1\left( R - \frac{\mu}{m_1} \rho\right) + \right.  \nonumber\\
&& \left. + V_2\left( R + \frac{\mu}{m_2} \rho\right) \right]\phi_{n'}(\rho).\end{aligned}$$ Such an effective potential may be interpreted as the potential barrier that the center of mass encounters while incident in the state $n'$ and reflected or transmitted in the state $n$.

Let $g$ denote the ground as well as the single bound state of the potential $U_1(\rho)$ \[Eq. (\[Un\_potentials\])\], and $c$ a low-lying odd (unbound) state of the continuum spectrum, which is normalized to the 