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 b y 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 f ound in the giant resonance region of excitation energies (E(x) from 1 0 to 30 MeV). Here we examine the theoretical aspects of these analyse s of inelastic scattering, both in the optical potentials obtained fro m elastic data and in the models used to represent the inelastic trans itions. In particular we introduce the folding model and compare the u se of folded optical and transition potentials with those obtained by deforming phenomenological optical potentials. We also study the effec ts of dynamic corrections on the folding interaction when this is dens ity dependent. Both aspects are shown to have significant effects. We use more extensive elastic data at 139 and 340 MeV to illustrate the n eed for a density dependence in the folding interaction, as well as a need for different shapes for the real and imaginary parts of the pote ntials. Although these various features are shown to have nonnegligibl e effects on the theoretical cross sections for the excitations at sma ll angles, none of them is sufficient to account for all the apparentl y 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 17.4 2 and 20.76 MeV. The sharing between these two components depends upon the assumptions made about the distribution of the giant dipole stren gth which also results in angular distributions that peak at 0 degrees . Thus about one-half of the sum rule Limit appears to have been obser ved, rather than the one-third originally inferred from these data usi ng the deformed potential model. These conclusions are based, on the o ne hand, upon the spectral decomposition proposed for the results of t he 240 MeV experiment and, on the other hand, upon assuming that the s imple breathing mode form is adequate for the monopole transition dens ities. The results may be sensitive to deviations from either assumpti on. In a similar way we also infer that at least 55%, and perhaps as m uch as 70%, of the isoscalar quadrupole sum rule limit may be present in this giant resonance range of excitation energies in Ni-58.