01837nas a2200145 4500008004100000245007900041210006900120520133000189100002201519700002901541700002001570700002901590700002101619856005101640 2015 en d00aA class of Hamiltonians for a three-particle fermionic system at unitarity0 aclass of Hamiltonians for a threeparticle fermionic system at un3 aWe 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.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/34469