Investigation of theAl27(α,p)Reaction by Cross-Section Fluctuation Studies

Cross sections for the reaction ${\mathrm{Al}}^{27}(\alpha ,p){\mathrm{Si}}^{30}$ have been measured with energy resolutions which, in the incoming alpha-particle channel, are finer than the energy width of the overlapping levels of the compound system ${\mathrm{P}}^{31}$. Fluctuations in these cross sections were analyzed for the coherence widths of this compound nucleus and for details of the reaction mechanism, such as the behavior of reaction amplitudes as shown by the form of the frequency distribution of the cross section, the independence of the reactions leading to the different magnetic substates, and the amounts of compound-nucleus and direct-interaction processes. Cross sections were measured at 11 angles between 0° and 175° and at 5-keV energy steps for energies between 5.8 and 8.6 MeV. Lack of a cross correlation between the yields of protons to the ground ($0^{+}$) and first excited ($2^{+}$) states of ${\mathrm{Si}}^{30}$ confirmed the expected overlapping of levels of the compound nucleus, which is a basic requirement of fluctuation analysis. The coherence width of the compound-nucleus ${\mathrm{P}}^{31}$ was found to increase from 8 to 18 keV over the range of excitation energy 14.7 to 17.1 MeV. At the back angles of 175° and 170° the frequency distributions of cross sections for protons to the ground state of ${\mathrm{Si}}^{30}$ agree with ${\chi }^2$ distributions with only slightly more than two effective degrees of freedom. This number corresponds to the slightly more than one effective magnetic substate allowed by angular-momentum properties near 180°. This agreement substantiates cross-section fluctuation theory and indicates negligible direct interaction at these back angles. At 140° and 160° direct interactions were assumed still to be negligible, and then from the frequency distributions of cross sections the number of independent magnetic quantum states at these angles was found to be less than expected from an analysis based on angular-momentum properties and a Hauser-Feshbach calculation. This difference is a consequence of the small orbital angular momenta involved in the ($\alpha ,p$) reaction at these energies. These effective numbers of magnetic substates were used at the corresponding forward angles to determine the amounts of compound-nucleus and direct-interaction processes from fluctuations in cross sections. At the lowest energies of incident alpha particles the amount of direct interaction was too low to be determined with accuracy, but at the highest energies the maximum direct-interaction cross section was roughly equal to the compound-nucleus cross section. The direct-interaction cross section was found to vary with angle roughly as expected from distorted-wave Born-approximation calculations.