PROPERTIES OF RPA THEORY OF NUCLEAR SCATTERING

The analytic properties of the S-matrix for particle-hole scattering are examined within the framework of the random phase approximation (RPA). In contrast to the Tamm-Dancoff approximation (TDA) or the case of scattering from cutoff potentials, the RPA S-matrix displays left-hand singularities in the E-plane, which are due to the existence of ground state correlations. For S(E), the Riemann surface is constructed and the motion of poles investigated. In the k-plane, S(k) is expressed in terms of an appropriately defined lost function. A pole decomposition of S(E) is obtained, and sum rules relating total and partial widths are derived and their range of validity explored. Some consequences of these sum rules are studied in simple cases. © 1969.