Missing monopole strength in Ni-58 and uncertainties in the analysis of alpha-particle scattering

Analyses of recent measurements of the scattering of alpha particles by Ni-58 at energies of 129 and 240 MeV have indicated that only about a third of the sum rule limit for isoscalar monopole transitions was found in the giant resonance region of excitation energies (E(x) from 10 to 30 MeV). Here we examine the theoretical aspects of these analyses of inelastic scattering, both in the optical potentials obtained from elastic data and in the models used to represent the inelastic transitions. In particular we introduce the folding model and compare the use of folded optical and transition potentials with those obtained by deforming phenomenological optical potentials. We also study the effects of dynamic corrections on the folding interaction when this is density dependent. Both aspects are shown to have significant effects. We use more extensive elastic data at 139 and 340 MeV to illustrate the need for a density dependence in the folding interaction, as well as a need for different shapes for the real and imaginary parts of the potentials. Although these various features are shown to have nonnegligible effects on the theoretical cross sections for the excitations at small angles, none of them is sufficient to account for all the apparently missing strength. We estimate, based upon the most realistic folding models, that about 50% of the sum rule limit for monopole excitation was observed within the two components of the spectra centered at 17.42 and 20.76 MeV. The sharing between these two components depends upon the assumptions made about the distribution of the giant dipole strength which also results in angular distributions that peak at 0 degrees. Thus about one-half of the sum rule Limit appears to have been observed, rather than the one-third originally inferred from these data using the deformed potential model. These conclusions are based, on the one hand, upon the spectral decomposition proposed for the results of the 240 MeV experiment and, on the other hand, upon assuming that the simple breathing mode form is adequate for the monopole transition densities. The results may be sensitive to deviations from either assumption. In a similar way we also infer that at least 55%, and perhaps as much as 70%, of the isoscalar quadrupole sum rule limit may be present in this giant resonance range of excitation energies in Ni-58.