On the spectrum of the Schrödinger operator for a three-particle system on a lattice

A three-particle discrete Schrödinger operator $H_{\mu, \gamma} ( K):\equiv H_{\mu, \gamma} (\mathbf {K}), $ $\mathbf{K} = (K, K, K) \in \mathbb{T}^3$, which is associated with a system of three particles (two fermions of mass $1$ and one other particle of mass $m = 1/\gamma $,) interacting via pairwise repulsive contact potentials $\mu > 0$ on a three-dimensional lattice $\mathbb{Z}^3$, was analyzed. Critical values of mass ratios $\gamma_{s}({K})$ and $\gamma_{as}({K})$ were determined such that the operator $H_{\mu, \gamma}(K)$ has no eigenvalues if ${\gamma \in (0, \gamma_s(K))}$, the operator $H_{\mu, \gamma}(K)$ has a single eigenvalue if ${\gamma \in (\gamma_s(K), \gamma_{as}(K))}$, and the operator ${H_{\mu, \gamma}(K)}$ has three eigenvalues lying to the right of the essential spectrum for sufficiently large ${\mu>0}$ if ${\gamma \in (\gamma_{as}({K}),+\infty)}$.