General Framework For Nuclear-resonance Theories In Terms of Bloch Formalism

The method of the boundary condition operator introduced by Bloch is exploited in order to set up in a compact form the «generalized collision matrices» formalism, with particular reference to the S and K matrices. It is shown that with each generalized collision matrix M a suitably defined «natural Green's function» is associated; explicit representations of this operator lead to the generalization of the Kapur-Peierls and of the Weinberg state theories. These representations enable us to consider in a simple way the analytic continuation of M and to deduce its poles and residues; for S and K matrices the results coincide with the well-known ones, obtained by the matching method. We are also naturally led to consider the expansion of M in a power series of the energy; in this connection the Padé and Hadamard methods for the analytic continuation are exploited. The generalized Heitler relation holding for any two collision matrices is finally obtained. © 1974 Società Italiana di Fisica.