Accumulation of bosons between fermions due to the Pauli exclusion principle

We examine the quantum field theoretical impact of the Pauli exclusion principle on the formation of the ground state of two fermions that are coupled with each other through the interaction with bosons. As expected, in case where the two fermions are indistinguishable, their binding strength due to the force-mediating bosons is reduced and their spatial distribution in the ground state is wider compared to the corresponding state for the distinguishable particles. Surprisingly, the spatial distribution of the bosons in the ground states is even fundamentally different for both systems. In fact, the Pauli exclusion principle leads to a strong accumulation of the bosons between the two fermions.