Scattering of 64.3-MeV Alpha Particles from Nickel-58 and Iron-58

Abstract

For 64.3-MeV $\ensuremath{\alpha}$ particles the differential cross sections for elastic scattering and excitation of the first ${2}^{+}$ collective state have been measured for the ${\mathrm{Ni}}^{58}$ and ${\mathrm{Fe}}^{58}$ isobars at approximately 0.5\ifmmode^\circ\else\textdegree\fi{} intervals between 10\ifmmode^\circ\else\textdegree\fi{} and 82\ifmmode^\circ\else\textdegree\fi{} in the center-of-mass system. The measurements were made with sufficient precision to follow the rapid variations and deep minima in the angular distributions, and the data have been exhaustively studied for possible errors; an extensive discussion of the uncertainties is given. An analyzed beam (energy spread 100 keV) of high-energy alpha particles was afforded by the Berkeley 88-in. sector-focused cyclotron. The analyzed beam was characterized by high intensity (0.5 \ensuremath{\mu}A), small angular divergence (0.17\ifmmode^\circ\else\textdegree\fi{}), small beam width (0.06 in.), and by small energy variation during the experiment (\ifmmode\pm\else\textpm\fi{}100 keV). A precise scattering chamber (typical tolerance 0.01\ifmmode^\circ\else\textdegree\fi{}) and solid-state detectors with small angular acceptance (0.5\ifmmode^\circ\else\textdegree\fi{}) and sufficient energy resolution (150 keV) were used. No attempt has been made to fit the angular distributions in detail but approximate fits to the elastic scattering obtained using an optical potential show: (a) It is not possible to account for the differences observed between the elastic scattering cross sections for the two isobars merely in terms of their different charge or charge distribution. (b) At large angles the elastic scattering from ${\mathrm{Fe}}^{58}$, about half as intense as from ${\mathrm{Ni}}^{58}$, can be qualitatively described by using a deeper absorptive potential for ${\mathrm{Fe}}^{58}$. Analysis of the elastic- and inelastic-scattering cross sections for ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}50\ifmmode^\circ\else\textdegree\fi{}$ using the smooth cutoff model of Blair, Sharp, and Wilets gives the quadrupole deformation parameter $\ensuremath{\beta}$ as 0.15 (${\mathrm{Ni}}^{58}$) and 0.17 (${\mathrm{Fe}}^{58}$).