On the Resonance Scattering of Alpha-Particles

The elastic scattering of alpha-particles is considered from the point of view of the many-body theory. The restriction is made to scattering by nuclei of zero spin since in this case a unique determination of the angular momentum of the resonance level (of the compound nucleus) responsible for the anomalous scattering is possible. The procedures which have been used for the determination of the resonance energies and the assignments of angular momenta are discussed and criticized. These methods are based on a comparison of the experimental data with the dispersion formula for mono-energetic alpha-particles and thus do not take into account the straggling of the incident beam which is of primary importance under the actual experimental conditions. In addition, in the determinations of resonance energies and the widths of resonance levels the interference scattering should be considered. An alternative method is suggested for obtaining the angular momenta directly from measurements of the angular distribution of the scattering at fixed energies. This method is essentially independent of the straggling of the alpha-particles and of the details of the theory as well. The only requirement is fairly good angular resolution, viz., a range of scattering angles of about 10^∘{} would be sufficient and this resolution is already attained in the experiments. A procedure for a more accurate determination of the energies and widths of resonance levels is given. Here again the straggling is eliminated insofar as the straggling parameter (width of the primary energy distribution) does not appear explicitly. Instead, the resonance energy and width depend only on readily measurable quantities: mean alpha-particle energy, scattering angle, angular momentum of the resonance level and the strengths of the resonance extrema as observed from the energy distribution of the scattering. The result for the resonance energy, in particular, is rather insensitive to errors in measurement and to approximations made in the derivation of the formulas.