We will see later in Sec. \[sec:few\_body\_MLX\] that the species entropy has here its global maximum. Note that each phase diagram features critical points, where three different phases can coexist (green circles).

![image](MF_few_body.eps){width="0.75\linewidth"}

Now that we have identified the phases, we are going to shed some light on the mechanism behind the phase separation taking place for different specific coupling strength $g_{_{MI}}$ for a fixed trap ratio $\eta$. In particular, we will provide a simple formula, which determines which of the core-shell structures is energetically more favorable. Additionally, we provide an estimate on the miscible-immiscible transition region and on the $SB$ phase boundary.

Let us make two horizontal cuts across the phase diagram of Fig. \[fig:MF\_few\_body.eps\]b) at $a_I/a_M=0.5$ and at $a_I/a_M=1.1$. In Fig. \[fig:dw\_picture.eps\] we take a closer look at the variation of the one-body densities $\rho_{_{MF}}^{\sigma}$ being part the effective one-body potential $V_{\sigma}^{eff}$ when increasing the coupling strength $g_{_{MI}}$. First, let us focus on columns 1 and 2, corresponding to $a_I/a_M=0.5$. For very weak coupling (first row), every atom to a good approximation populates the energetically lowest harmonic oscillator orbital of the respective potential $V_{\sigma}$. The induced potential $V_{\sigma}^{ind}$ gains an amplitude linearly with $g_{_{MI}}$ and with the density 