The 1/r expansion for the critical multiple well problem

We consider the critical multiple well problem H=-δ+μV(x-rxsub(i)), where -δ+V(x) has a zero energy resonance. We prove that all eigenvalues and resonances of H tending to zero as 1/r2 are analytic in 1/r. We give an explicit equation for the lowest nonvanishing coefficient in the 1/r expansion for any of these eigenvalues or resonances and observe that H has infinitely many resonances tending to zero. For n=2 and n=3, we compute the coefficients explicitly and for n=2, we also give the next coefficient in the 1/r expansion. (orig./HPOE)