  We consider a quantum mechanical three-particle system made of two identical
fermions of mass one and a different particle of mass $ m $, where each fermion
interacts via a zero-range force with the different particle. In particular we
study the unitary regime, i.e., the case of infinite two-body scattering
length. The Hamiltonians describing the system are, by definition, self-adjoint
extensions of the free Hamiltonian restricted on smooth functions vanishing at
the two-body coincidence planes, i.e., where the positions of two interacting
particles coincide. It is known that for $ m $ larger than a critical value $
m^* \simeq (13.607)^{-1} $ a self-adjoint and lower bounded Hamiltonian $ H_0 $
can be constructed, whose domain is characterized in terms of the standard
point-interaction boundary condition at each coincidence plane. Here we prove
that for $ m \in( m^*,m^{**}) $, where $ m^{**} \simeq (8.62)^{-1} $, there is
a further family of self-adjoint and lower bounded Hamiltonians $ H_{0,\beta}
$, $ \beta \in \mathbb{R} $, describing the system. Using a quadratic form
method, we give a rigorous construction of such Hamiltonians and we show that
the elements of their domains satisfy a further boundary condition,
characterizing the singular behavior when the positions of all the three
particles coincide.
