Static Nuclear Deformation and the Total Reaction Cross Section

An empirical study is made of the total reaction cross sections for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ reactions with ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$, and ${}_{}{}^{237}{}_{}{}^{}\mathrm{Np}$. Systematic differences are revealed that are attributed to the effects of nuclear deformation. This behavior can be accounted for by a reduction of the average interaction barrier by 0.3 to 0.6 MeV or by an increase in the width of the spectrum of barriers by 0.4 to 0.7 MeV.