Fluctuation Studies of the (α,p) Reaction onF19,Na23, andP31

The ($\alpha ,p$) reaction for many angles between 0° and 175° has been used for fluctuation studies with target nuclei ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, and ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$. Incident energies were 5.2 to 8.0 MeV, 5.9 to 7.9 MeV, and 13.0 to 15.7 MeV, and the measured coherence widths were 50, 35, and 33 keV, respectively. Cross-section peaks were unusually correlated between yields at different angles and between yields to different final states for 5.2- to 5.6-MeV alphaparticle energy on ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, and so only data above 5.6 MeV were analyzed for fluctuations for this target. The resulting sample sizes in the analyses were then 17, 20, and 27, respectively. Calculations of the effective number of sets of angular-momentum projections damping the fluctuations in the cross sections were used at all angles to determine the additional damping that results from the fraction of direct reactions. For the most forward angles, 0° to 30°, the fraction of direct reactions was generally found to be less than ½ for the ground-state reactions and about 0.6 for the first-excited-state reactions. Even though the data were analyzed for the whole span of energies measured, the modest sample sizes available in these studies resulted in large uncertainties in determining these fractions of direct reactions. Nevertheless, the measured cross sections were in qualitative agreement with both distorted-wave Born-approximation calculations of the direct-reaction cross sections and Hauser-Feshbach calculations of the compound-nucleus cross sections.