  We consider a quantum system in dimension three composed by a group of $N$
identical fermions, with mass 1/2, interacting via zero-range interaction with
a group of $M$ identical fermions of a different type, with mass $m/2$.
Exploiting a renormalization procedure, we construct the corresponding
quadratic (or energy) form and define the so-called Ter-Martirosyan-Skornyakov
extension $H_{\alpha}$, which is the natural candidate as a possible
Hamiltonian of the system. In the particular case M=1, under a suitable
condition on the parameters $m$, $N$, we show that the quadratic form is
unbounded from below. In the same setting we prove that $H_{\alpha}$ is not a
self-adjoint and bounded from below operator and this in particular suggests
that the so-called Thomas effect could occur.
