RELATIVELY COMPACT INTERACTIONS IN MANY PARTICLE SYSTEMS

For many-particle relatively compact interactions the essential spectrum of the N-particle Schrödinger Hamiltonian is shown to consist of a continuum [λN, + ∞[ where λN is the lowest many-body threshold of the system. This result applies in particular to separable interactions and some spin-orbit couplings. The N-particle Green's function is studied with the help of the Weinberg equation for many-body forces whose kernel is shown to be compact in the complementary set of [ΛN, + ∞[. © 1969 Springer-Verlag.