@article {2015,
	title = {A class of Hamiltonians for a three-particle fermionic system at unitarity},
	year = {2015},
	note = {This SISSA preprint is composed of 29 pages and is recorded in PDF format},
	abstract = {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.},
	url = {http://urania.sissa.it/xmlui/handle/1963/34469},
	author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Domenico Finco and Alessandro Michelangeli and Alessandro Teta}
}
