A NOTE ON THE THEORY OF SINGLE PARTICLE POTENTIALS

Abstract: It is well known that corresponding to the discrete (d) and continuous (c) energyspectra of the nuclei (N+1) and (N-1), the Lehmann representation of the singleparticle (sp) Green function G_αβ(ω) may be separated into two parts: G_αβ(ω)=G_αβ^d(ω)+G_αβ^c(ω). Although G_αβ^d(ω) is a meromorphic function, G_αβ^c(ω) contains branch cuts. In ourprevious discussion of the non-hermitian sp potential u_αβ=M_αβ(ε_β) defined in termsof the mass operator M_αβ(ω), we have only considered G_αβ^d(ω) explicitly. This corres-ponds to a truncation approximation. In this paper, the consequences due to G_αβ^c(ω) are further investigated. It is shown that besides a few new conclusions, all the resultsobtained previously remain true.