Progress in the Development of Global Medium-Energy Nucleon-Nucleus Optical Model Potentials

Two existing global medium-energy nucleon-nucleus phenomenological optical model potentials are described and compared with experiment and with each other. The rst of these employs a Dirac approach (second-order reduction) that is global in projectile energy and projectile isospin and applies to the target nucleus Pb. Here the standard S-V (isoscalar-scalar, isoscalar-vector) model has been extended to include the corresponding isovector components by introduction of a relativistic Lane model. The determination of the energy range, energy dependence, and isospin dependence are discussed, as are the predictions for neutron scattering observables, and also the correlations and ambiguities found in Dirac phenomenology. The second of these employs a relativistic equivalent to the Schrodinger equation (including relativistic kinematics) that is global in projectile energy, projectile isospin, and target (Z,A). Here, particular attention is given to predictions for the integrated scattering observables { neutron total cross sections and proton total reaction cross sections { and their sensitivity to the absorptive parts of the potential. Finally, current work is described and the in uence of the nuclear bound state problem (treated in relativistic mean eld theory) on the Dirac scattering problem is mentioned. Spherical target nuclei are treated in the present work and strongly-collective target nuclei (rotational and vibrational) requiring coupled-channels approaches will be treated in a future paper. A Global Phenomenological Dirac Potential The potential described in this section consists of a global medium-energy nucleon-nucleus phenomenological Dirac potential for the target nucleus Pb. The potential is global in projectile energy and projectile isospin and it was determined [1] by least-squares adjustment of calculated scattering observables (model parameters) with respect to corresponding measured scattering observables for both proton and neutron scattering over a wide range in projectile energy. The Dirac equation is used in the mean eld approximation by which the nucleon (meson) elds are replaced by their expectation values. Proton-nucleus (or neutron-nucleus) scattering is then described using isoscalarscalar and isoscalar-vector mean elds. Here these are taken, respectively, as a spherically symmetric complex Lorentz scalar potential S0(r; E; :::) corresponding to the ( ctitious) meson eld and a spherically symmetric complex Lorentz vector potential V0(r; E; :::) (time-like component of Lorentz four-vector) corresponding to the ! meson eld, together with a spherically symmetric Coulomb potential Vc. However, a description of nucleon-nucleus scattering requires the explicit addition of isovector-scalar and isovector-vector potentials (mean elds) S1(r; E; :::) and V1(r; E; :::), respectively, yielding