Study of the Strongly Excited $2^{+}$ and $3^{-}$ States in the ${\mathrm{Fe}}^{54,56}$ and ${\mathrm{Ni}}^{58,60,62}$ Isotopes by Proton Scattering at 18.6 and 19.1 MeV

Elastic and inelastic proton-scattering angular distributions were obtained at incident proton energies of about 19 MeV from ${\mathrm{Fe}}^{54}$, ${\mathrm{Fe}}^{56}$, ${\mathrm{Ni}}^{58}$, ${\mathrm{Ni}}^{60}$, and ${\mathrm{Ni}}^{62}$. The elastic angular distributions were fitted with the nuclear optical model and the parameters so determined were compared to ascertain systematic variations. Generally the fits are good. The parameters were also used as input for distorted-wave Born-approximation (DWBA) calculations of the inelastic scattering. Of special interest was the excitation of the collective $2^{+}$ and $3^{-}$ states in these nuclei. The inelastic cross sections were assumed to be a result of a direct reaction exciting collective states, and in addition for the iron isotopes, calculations were made assuming single-configuration shell-model wave functions for the first $2^{+}$ excited states. Although the calculated cross section is greater in ${\mathrm{Fe}}^{56}$ than in ${\mathrm{Fe}}^{54}$, it is still far too small to explain the large difference seen experimentally. Cross sections for collective excitations were calculated assuming the DWBA, and also using the coupled-equation method. Comparisons between the two methods are made in terms of the shapes of the angular distributions as well as the magnitude of the cross sections. The forward peak is reasonably fitted in all the isotopes by both the DWBA and coupled-equations calculations, but the remainder of the angular distribution is not as well reproduced. The cross section for excitation of the first $2^{+}$ state in ${\mathrm{Fe}}^{54}$ is not explained adequately by either the collective or particle model calculations. The identification of the collective $3^{-}$ excited state in ${\mathrm{Fe}}^{54}$ could not be made unambiguously.