Neutron scattering from 208Pb at 30.4 and 40.0 MeV and isospin dependence of the nucleon optical potential

Background: Analysis of data involving nuclei far from stability often requires the optical potential (OP) for neutron scattering. Because neutron data are seldom available, whereas proton scattering data are more abundant, it is useful to have estimates of the difference of the neutron and proton optical potentials. This information is contained in the isospin dependence of the nucleon OP. Here we attempt to provide it for the nucleon-Pb-208 system. Purpose: The goal of this paper is to obtain accurate n + Pb-208 scattering data and use it, together with existing p + Pb-208 and Pb-208(p,n)(208)Bi-IAS* data, to obtain an accurate estimate of the isospin dependence of the nucleon OP at energies in the 30-60-MeV range. Method: Cross sections for n + Pb-208 scattering were measured at 30.4 and 40.0 MeV, with a typical relative (normalization) accuracy of 2-4% (3%). An angular range of 15. to 130. was covered using the beam-swinger time-of-flight system at Michigan State University. These data were analyzed by a consistent optical-model study of the neutron data and of elastic p + Pb-208 scattering at 45 and 54 MeV. These results were combined with a coupled-channel analysis of the Pb-208(p, n) reaction at 45 MeV, exciting the 0+ isobaric analog state (IAS) in Bi-208. Results: The new data and analysis give an accurate estimate of the isospin impurity of the nucleon-Pb-208 OP at 30.4 MeV caused by the Coulomb correction to the proton OP. The corrections to the real proton OP given by the CH89 global systematics were found to be only a few percent, whereas for the imaginary potential it was greater than 20% at the nuclear surface. On the basis of the analysis of the measured elastic n + Pb-208 data at 40 MeV, a Coulomb correction of similar strength and shape was also predicted for the p + Pb-208 OP at energies around 54 MeV. Conclusions: Accurate neutron scattering data can be used in combination with proton scattering data and (p, n) charge exchange data leading to the IAS to obtain reliable estimates of the isospin impurity of the nucleon OP.