Critical analysis of statistical methods used to detect resonances in nuclear reactions

The effectiveness of several existing statistical tests in locating resonances in compound nuclear reactions above the Coulomb barrier is examined, and a new test based on the number of maxima at any single bombarding energy in a set of excitation functions is introduced. It was found that only the three tests based on the deviation functions, summed cross sections, and the distribution of maxima were suitable for the detection of resonances, and that the latter test was the most sensitive. The various tests were used to analyze ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$,$\alpha$)${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$,$\alpha$)${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$,$\alpha$)${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ excitation functions. Evidence for nonstatistical structure was found in all three reactions by examining the distribution of maxima.