Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three

Abstract We study the Hamiltonian for a system of three identical bosons in dimension interacting via zero-range forces. In order to avoid fall center phenomenon emerging standard Ter-Martirosyan–Skornyakov (TMS) Hamiltonian, known as Thomas effect, we develop detail suggestion given seminal paper Minlos and Faddeev 1962 construct regularized version TMS which is self-adjoint bounded from below. The regularization by an effective three-body force, acting only at short distance, that reduces zero strength interactions when positions particles coincide. analysis based on construction suitable quadratic form shown be closed Then, domain action corresponding are completely characterized regularity result elements given. Furthermore, show norm resolvent limit Hamiltonians with rescaled non-local interactions, also called separable potentials, suitably renormalized coupling constant.