Adiabatic perturbation theory for the degenerate case. II. Perturbation of degenerate bound states embedded in the continuum

An adiabatic formula for the contracted Hamiltonian in a reference space containing bound-state eigenfunctions of degenerate energy levels embedded in the continuum is derived. A general factorization theorem for the dynamic operatorS_α(0, – ∞/λ) is proved, and the cancellation of the pole singularities in the perturbation series of the contracted Hamiltonian in adiabatic form is discussed.