Elastic Scattering of Alpha Particles by Helium Between 53 and 120 MeV

The differential cross section for elastic scattering of $\ensuremath{\alpha}$ particles by ${\mathrm{He}}^{4}$ has been measured at center-of-mass angles between 10 and 90\ifmmode^\circ\else\textdegree\fi{} at laboratory bombarding energies of 53.40\ifmmode\pm\else\textpm\fi{}0.15 MeV, 58.49\ifmmode\pm\else\textpm\fi{}0.16 MeV, 63.91\ifmmode\pm\else\textpm\fi{}0.18 MeV, 69.91\ifmmode\pm\else\textpm\fi{}0.20 MeV, 77.55\ifmmode\pm\else\textpm\fi{}0.22 MeV, 99.60\ifmmode\pm\else\textpm\fi{}0.28 MeV, and 119.86\ifmmode\pm\else\textpm\fi{}0.34 MeV. These differential cross sections have been analyzed in terms of complex phase shifts $\mathrm{Re}{\ensuremath{\delta}}_{l}+i\mathrm{Im}{\ensuremath{\delta}}_{l}$. The real parts of the phase shifts vary smoothly as a function of energy; the $l=0, 2, \mathrm{and} 4$ phase shifts continue the trends apparent at lower energies; a broad $l=6$ resonance is found at a center-of-mass energy of about 26 MeV and evidence is found for an $l=8$ resonance. The imaginary parts of the phase shifts are appreciable at all the energies of measurement. The real parts of the phase shifts obtained from these and previous measurements have been fitted with an $l$-dependent potential constructed from a Saxon-Woods repulsive core and a complex Saxon-Woods attractive well of larger radius. The potential is found to be in qualitative agreement with theoretical predictions. Approximate fits have been made to the real parts of the phase shifts using the single level dispersion theory. The energies and reduced widths of the resonances given by these fits are approximately proportional to $J(J+1)$.