Absence of positive eigenvalues for hard-core $N$-body systems

We show absence of positive eigenvalues for generalized 2-body hard-core Schrödinger operators under the condition of bounded strictly convex obstacles. A scheme for showing absence of positive eigenvalues for generalized $N$-body hard-core Schrödinger operators, $N > 2$, is presented. This scheme involves high energy resolvent estimates, and for $N=2$ it is implemented by a Mourre commutator type method. A particular example is the Helium atom with the assumption of infinite mass and finite extent nucleus.