Hadron-nucleus forward dispersion relations

Abstract

Forward elastic scattering of pions and nucleons from complex nuclei is investigated by dispersion relations (FDR). Explicit applications cover πD, π 4He , π 9Be , π 12C , π 4He and n 12C . Partly unpublished numerical evaluations are given. Results are expected to be typical for a wide range of nuclei. The unphysical region for π-scattering on I = 0 nuclei is unimportant. For the I = 1 2 nucleus 9Be, an effective π-nuclear coupling constant (ƒ 2) eff ≈ 0.06 is determined. With simple assumptions, general sum rules are shown to give universally (ƒ 2) eff = ƒ 2 nucleon as well as small unphysical contributions to the isospin-independent amplitude. Important exchange contributions from exchange diagrams (poles and cuts) are shown to appear in nucleon scattering at lower energies. This is shown to be consistent with single-particle potential scattering (optical model). The phenomenological potential scattering background term in slow neutron scattering is largely due to such exchange contributions. Antiparticle cross sections are shown to give small effects in low-energy nucleon scattering. A non-relativistic approximation to the relativistic FDR is compared to FDR for potential scattering and the Born term is empirically determined for n 4He. Good agreement is obtained by comparison with the empirical potential for differential n 4He scattering at low energy. A self-contained elementary discussion and review of FDR is given. The relation between asymptotic wave functions and pole residues is discussed in detail. Particular attention is drawn to the importance of an exponential dependence of residues on binding and radius, and it is illustrated by simple models.