\neq 0 : \frac{d}{dx} V_{\sigma}^{eff} \Bigr\rvert_{x_0}= 0.$$ Assuming one-body densities to be unperturbed harmonic oscillator ground states, we obtain the following effective potentials: $$\begin{aligned}
\label{eq:barrier_criterion_M_pot}
    && V_{M}^{eff}(z) \approx \frac{1}{2}z^2 
    + g_{_{MI}} N_I \sqrt{\frac{\eta}{\pi}} e^{-\eta z^2} \\
\label{eq:barrier_criterion_I_pot}
    && V_{I}^{eff}(z) \approx \frac{1}{2}\eta^2 z^2 
    + g_{_{MI}} N_M \sqrt{\frac{1}{\pi}} e^{-z^2},\end{aligned}$$ and the corresponding barrier conditions: $$\begin{aligned}
\label{eq:barrier_criterion_M}
    && \frac{\sqrt{\pi}}{2 N_I \sqrt{\eta^3}}   
    \hat{=} g_{_{MI}}^M < g_{_{MI}} \\
\label{eq:barrier_criterion_I}
    &&  \frac{\sqrt{\pi} \eta^2}{2 N_M} 
    \hat{=} g_{_{MI}}^I< g_{_{MI}}.\end{aligned}$$ For given particle numbers $N_M$, $N_I$ and trap ratio $\eta$ either condition or condition will be fulfilled first upon increasing the coupling $g_{_{MI}}$ and thus either the majority or the impurity will form a shell. We remark that the above criterion for barrier formation is inversely proportional to the particle number of the other component, while the dependence on the trap ratio $\eta$ for the majority differs substantially from the one for the impurity. Furthermore, for a fixed particle number ratio there is a critical trap ratio $\eta_c$, for which and can be fulfilled simultaneously. $$\sqrt{1/\eta_c}=\sqrt[7]{N_I/N_M}$$ Around this critical region we expect that none of the components will occupy the trap center. We summarize our findings in a simple formula, which determines the type of phase separation at the 