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We study in dimension d ⩾ 2 low-energy spectral and scattering asymptotics for two-body d-dimensional Schrodinger operators with a radially symmetric potential falling off like − γ r − 2 , γ > 0 . We consider angular momentum sectors, labelled by l = 0 , 1 , … , for which γ > ( l + d / 2 − 1 ) 2 . In each such sector the reduced Schrodinger operator has infinitely many negative eigenvalues accumulating at zero. We show that the resolvent has a non-trivial oscillatory behaviour as the spectral parameter approaches zero in cones bounded away from the negative half-axis, and we derive an asymptotic formula for the phase shift.

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling., Comment: 30 pages, 2 figures