  In this paper we continue the study of the energy-momentum spectrum of a
class of translation invariant, linearly coupled, and massive Hamiltonians from
non-relativistic quantum field theory. The class contains the Hamiltonians of
E. Nelson and H. Froehlich. One of us previously investigated the structure of
the ground state mass shell and the bottom of the continuous energy-momentum
spectrum. Here we study the continuous energy-momentum spectrum itself up to
the two-boson threshold, the threshold for energetic support of two-boson
scattering states. We prove that non-threshold embedded mass shells have finite
multiplicity and can accumulate only at thresholds. We furthermore establish
the non-existence of singular continuous energy-momentum spectrum. Our results
hold true for all values of the particle-field coupling strength but only below
the two-boson threshold. The proof revolves around the construction of a
certain relative velocity vector field used to construct a conjugate operator
in the sense of Mourre.
