We present some results on the perturbation of eigenvalues embedded at thresholds in a two channel model Hamiltonian with a small off-diagonal perturbation. Examples are given of the various types of behavior of the eigenvalue under perturbation.

We consider Schrodinger operatorsH = - d² /dr² +V onL²([0, ∞)) with the Dirichlet boundary condition. The potentialV may be local or non-local, with polynomial decay at infinity. The point zero in the spectrum ofH is classified, and asymptotic expansions of the resolvent around zero are obtained, with explicit expressions for the leading coefficients. These results are applied to the perturbation of an eigenvalue embedded at zero, and the corresponding modified form of the Fermi golden rule.