Decay rates of bound states at the spectral threshold of multi-particle Schr\"odinger operators

We consider $N$-body Schr"odinger operators with $N\ge 3$ particles in dimension $d\ge 3$ in the critical case when the lowest eigenvalue coincides with the bottom of the essential spectrum of the operator. We give the asymptotic behaviour of the corresponding eigenfunction in dependence of the dimension and the number of particles of the system.