Intrawell fragmentation refers to the filamentation tendency of the one-body density, i.e. to the appearance of several local maxima occurring in $\rho_\sigma^{(1)}(x)$ within each well, see the dashed rectangle in Fig. \[abb:gs3-1\] (a) where two sub maxima are present. Interestingly enough, within the HF approximation the mixture becomes immiscible with $\rho_A^{(1)}(x)$ and $\rho_B^{(1)}(x)$ being phase separated as it can be observed by their asymetric distribution with respect to $x=0$ illustrated in Fig. \[abb:gs3-1\] (b). This latter behavior can be thought of as the few-body analog of the Stoner’s instability [@jacquod2000supression; @jacquod2001ground] which is a well-known phenomenon in solid state physics being responsible for magnetization effects emerging in itinerant systems. Indeed, within the HF approximation in the strongly interacting regime the energy of a miscible state is larger when compared to the energy of a phase separated (immiscible) one due to the strong impact of the interaction energy [@stoner1933lxxx; @snoke2009solid]. Thus, the particle number assymetry favors a phase separated state with $\rho_B^{(1)}(x)$ being localized in one of the wells and $\rho_A^{(1)}(x)$ distributing around it, see Fig. \[abb:gs3-1\] (b). Since the double-well is symmetric, the same occupation structure of $\rho_A^{(1)}(x)$ and $\rho_B^{(1)}(x)$ with interchanged wexlls possesses an equal energy, i.e. the two 