Study of theα+αsystem below 15 MeV (c.m.)

Differential cross sections for $\alpha +\alpha$ elastic scattering have been measured at lab energies of 18.00, 21.12, 24.11, 25.50, 26.99, 28.50, and 29.50 MeV. The majority of the data have relative errors less than 1%, and the additional error in absolute scale is 0.30%. A phase-shift analysis of the data has been performed, and most of the phase shifts have been determined to within $\pm \frac{1}{3}°$. These phase shifts and others from the literature were used to study properties of the $\alpha +\alpha$ system in the center of mass energy range 1.50 to 14.74 MeV. First, an $R$-matrix analysis was made of the $l=4\mathrm{}$ phase shifts; this analysis yields a resonance energy of 11.7 ± 0.4 MeV and a level width at resonance of 4.0 ± 0.4 MeV. Second, comparison was made of the $\alpha +\alpha$ phase shifts with results of previous resonating-group calculations, and this comparison shows good agreement with a calculation which includes one inelastic channel and a nucleon-nucleon repulsive core. Third, an $\alpha +\alpha$ potential model was constructed. This model contains an attractive potential obtained by folding Gaussian $\alpha$-particle densities together with a Yukawa-shaped direct part of a nucleon-nucleon potential and, in addition, contains phenomenological short-range repulsive components in the $l=0\mathrm{}$ and $l=2\mathrm{}$ states. The model reproduces the experimental phase shifts quite well when the Yukawa potential is taken to have a range corresponding to a two-pion mass.