the present results can be translated to the mass-imbalanced case. By choosing $a_{M}$ and $\hbar \omega_{M}$ as length and energy scales we arrive at the rescaled Hamiltonian: $$\begin{aligned}
\label{eq:hamiltonian}
    H && = H_M + H_I + H_{MI} \\
      && = \sum_{i=1}^{N_M} \left( -\frac{1}{2} \frac{\partial^2}{\partial x_i^2} +
            \frac{1}{2} x_i^2 \right)
         + \sum_{i=1}^{N_I} \left( -\frac{1}{2} \frac{\partial^2}{\partial y_i^2} +
            \frac{1}{2} \eta^2 y_i^2 \right) + \nonumber \\
      && \quad + g_{_{MI}} \sum_{i=1}^{N_M} \sum_{j=1}^{N_I} \delta(x_i-y_j), \nonumber\end{aligned}$$ where $x_i$ labels the spatial coordinate of the $i$-th majority particle, $y_i$ of the $i$-th impurity particle and $\eta=\omega_I/\omega_M$ denotes the trap frequency ratio.

In the present work we focus on the ground state characterization and consider both attractive and repulsive interactions ranging from weak to intermediate couplings $g_{_{MI}}\in[-2,2]$ with the impurity being localized or delocalized w.r.t. the majority species, i.e.  $a_I/a_M=\sqrt{1/\eta} \in [0.5, 1.5]$. We also study the impact of the particle number ratio $N_I/N_M$ on the system’s properties.

Computational Approach {#sec:methodology}
======================

To find the ground state of our binary mixture we employ imaginary time propagation by means of the Multi-Layer Multi-Configurational Time-Dependent Hartree Method for atomic mixtures (ML-MCTDHX). For reasons of brevity we call it ML-X from now on. This multi-configurational wave function based method for 