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

Abstract

Differential cross sections for $\ensuremath{\alpha}+\ensuremath{\alpha}$ 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 $\ifmmode\pm\else\textpm\fi{}\frac{1}{3}\ifmmode^\circ\else\textdegree\fi{}$. These phase shifts and others from the literature were used to study properties of the $\ensuremath{\alpha}+\ensuremath{\alpha}$ system in the center of mass energy range 1.50 to 14.74 MeV. First, an $R$-matrix analysis was made of the $l=4$ phase shifts; this analysis yields a resonance energy of 11.7 \ifmmode\pm\else\textpm\fi{} 0.4 MeV and a level width at resonance of 4.0 \ifmmode\pm\else\textpm\fi{} 0.4 MeV. Second, comparison was made of the $\ensuremath{\alpha}+\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}+\ensuremath{\alpha}$ potential model was constructed. This model contains an attractive potential obtained by folding Gaussian $\ensuremath{\alpha}$-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 $l=0$ and $l=2$ 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.NUCLEAR REACTIONS $^{4}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\alpha})^{4}\mathrm{He}$, $E=18.00\ensuremath{-}29.50$ MeV; measured $\ensuremath{\sigma}(E; \ensuremath{\theta})$; deduced phase shifts $l=0,2,4,6$. $R$-matrix analysis $l=4$. Comparison with resonating-group calculations. Potential-model analysis.