0 \ \land \Delta_{_{M}} = 1 \ \land \Delta_{_{I}} = 1 \\
    \text{IMI} & \mbox{:} \
    d = 0 \ \land \Delta_{_{M}} = 1 \ \land \Delta_{_{I}} < 1 \\
    \text{MIM} & \mbox{:} \
    d = 0 \ \land \Delta_{_{M}} < 1 \ \land \Delta_{_{I}} = 1 \\
    \text{CF} & \mbox{:} \
    d = 0 \ \land \Delta_{_{M}} < 1 \ \land \Delta_{_{I}} < 1 \\
    \text{SB} &\mbox{:} \
    d > 0 \ \land \Delta_{_{M}} < 1 \ \land \Delta_{_{I}} < 1
    \end{cases}$$

In Fig. \[fig:MF\_few\_body.eps\] we depict the ground state phases within the mean-field approximation for $N_B=5$ with a) $N_I=1$ and b) $N_I=2$ impurities as a function of the inter-component coupling strength $g_{_{MI}}$ and the impurity localization $a_{I}/a_{M}$. As expected $CF$ is not among the phases in Fig. \[fig:MF\_few\_body.eps\]. The transition region on the $a_{I}/a_{M}$ axis, where core-shell $MIM$ is replaced by core-shell $IMI$, can be tuned by variation of the particle number ratio such that for $N_I=N_M$ it lies at $a_{I}/a_{M}=1$ (not shown), while for increasing particle imbalance $N_I/N_M<1$ it is shifted towards a lower $a_{I}/a_{M}$ ratio. This is also the point, where the coupling strength $g_{_{MI}}$, required for the realization of the $SB$ phase, is the smallest. 