Calculation of Inelastic Alpha-Particle Scattering byNi58

A distorted-wave calculation is presented for excitation of the 1.45-MeV $2^{+}$ level of ${\mathrm{Ni}}^{58}$ by inelastic scattering of 43-MeV alpha particles. The collective one-phonon state is taken to be an eigenfunction of the pairing plus $Q·Q$ potential, and the finite-range alpha-nucleon interaction is taken from ($p, \alpha$) elastic-scattering analysis. It is shown how the collective enhancement and the surface-peaked interaction form factor arise. Qualitative agreement with experimental differential cross sections and with the predictions of the vibrational nuclear model are obtained, but quantitative agreement for the angular distributions is lacking. The cause of the disagreement is discussed. The calculated absolute cross sections are in good agreement with experimental data.