Solution of Dyson's equation employing Siegert boundary conditions

The use of Siegert boundary conditions in a direct solution of the Dyson equation for poles of the one-particle Green's function corresponding to resonances of the ($N\pm 1$)-particle systems is discussed and the pertinent complex pseudoeigenvalue problem is formulated as an implicit matrix eigenvalue equation. Thus the calculational setup is very similar to the methods employed in calculating atomic and molecular ionization potentials. Particular emphasis is laid upon the asymptotic expansion of the diverging Siegert orbital.