  We give a bound on the ground state energy of a system of $N$ non-interacting
fermions in a three dimensional cubic box interacting with an impurity particle
via point interactions. We show that the change in energy compared to the
system in the absence of the impurity is bounded in terms of the gas density
and the scattering length of the interaction, independently of $N$. Our bound
holds as long as the ratio of the mass of the impurity to the one of the gas
particles is larger than a critical value $m_c\approx 0.36$, which is the same
regime for which we recently showed stability of the system.
