Scattering of 22-MeV Alpha Particles by ${\mathrm{Fe}}^{56}$, ${\mathrm{Zn}}^{64}$, ${\mathrm{Zn}}^{66}$, and ${\mathrm{Zn}}^{68}$

Angular distributions for elastic scattering and for inelastic scattering to the lowest $2^{+}$ and $3^{-}$ states in ${\mathrm{Fe}}^{56}$, ${\mathrm{Zn}}^{64}$, ${\mathrm{Zn}}^{66}$, and ${\mathrm{Zn}}^{68}$ have been measured using 22.2-MeV alpha particles. The elastic distributions extend from 20 to 167° and the $2^{+}$ distributions from 30 to 167°. The $3^{-}$ distribution extends from 30 to 107° for ${\mathrm{Fe}}^{56}$, whereas for the Zn isotopes the range is from 60 to 167°. The optical model has been used to fit the elastic-scattering distributions, and the parameters thus found have been used in fitting the $2^{+}$ distributions using a distorted wave Born approximation calculation. Three sets of optical-model parameters were found that would fit the elastic scattering distributions (for $\Theta \le 125°$). The real parts of the optical-model potential for these three sets are $V_0=-20, -40, \mathrm{and} -70\mathrm{}$ MeV. It was found that only the set with $V_0=-20\mathrm{}$ MeV also gave good fits to the $2^{+}$ distributions. For $\Theta >125\mathrm{}°$, the fits were found to be quite poor. Two suggestions have been made to explain the failure of the theory at such large scattering angles. Nuclear deformabilities obtained by fitting the inelastic $2^{+}$ data are in good agreement with those obtained by inelastic proton scattering and electromagnetic methods. Approximations and limitations associated with the theoretical interpretation are discussed.