One-Particle Green Function Defined for the s-d Bound State. II--A General Formalism with the Ordinary s-d Hamiltonian--

A state with an electron-spin pair is assumed to have finite amplitude in the singlet ground state of the s-d Hamiltonian. An electron Green function is calculated on this assumpt'ion by means of perturbation expansion. The electron Green function is separated into two parts, a normal part describing the ordinary scattering process, and an anomalous part describing the exchange with an electron bound around a target. As applications, discussions are given on the correlation function of spin operators and the lifetime of an electron on the Fermi surface. For the latter, we obtain an expression which does not depend on a coupling constant. There are three types of approaches to the theory of an electron system coupled with a localized spin by an s-d exchange Hamiltonian. SuhFl and Hamann2l derived integral equations for the transition matrix. Their equations have been solved not only by themselves3) ' 4) but also by other authors. The present autho