A statistical analysis has been made of the narrow structure appearing in the excitation functions for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ induced interactions for elastic scattering ($13.5\le E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 37.5$ MeV), inelastic scattering ($20\le E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 30$ MeV), and $\alpha$ particle production ($16\le E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 21$ MeV). Average fluctuation widths, strengths and cross correlations predicted by the statistical models of nuclei and of nuclear reactions are compared with those obtained from the analysis of suitably reduced experimental data. Good agreement is found. The effects of gross structure, possible structure of intermediate width, and a small ratio of level width to spacing ($\frac{\Gamma }{D}$) on the analysis of the narrow structure were studied using synthetic excitation functions. Appropriate correction factors were obtained in this way for application to parameters extracted directly from the reduced data. The results of the studies with synthetic excitation functions support the validity of the present statistical analysis. Compound processes are found to contribute up to ∼20% of the measured elastic scattering cross section at 90° c.m. New experimental results reported herein for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, \alpha ){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}_{}^{*}{}_{}{}^{}$ reactions also suggest a large direct component, in contrast to earlier measurements on this reaction at lower energies. Hauser-Feshbach predictions of absolute compound cross sections show over-all good agreement with the average fluctuating cross sections deduced from the experimental data. It is concluded that the structure with widths ∼0.3 MeV observed in the experimental excitation functions studied here is of statistical origin, and that the statistical model can also explain the occasional structural features with individual widths up to ∼0.8 MeV. Apart from the gross structure associated with potential scattering, no evidence is found in the elastic scattering data for structure requiring nonstatistical mechanisms for its explanation.

NUCLEAR REACTIONS Statistical model analysis of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, $13.5\le E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 37.5$ MeV; ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ (4.43) $20\le E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 30$ MeV; ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, \alpha ){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}_{}^{*}{}_{}{}^{}$ $16\le E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 21$ MeV. Deduced average widths, fluctuation intensity, cross correlations. Hauser-Feshbach calculations. Measured $\frac{d\sigma }{d\Omega }$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{12}{}_{}{}^{}\mathrm{C}, \alpha ){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}_{}^{*}{}_{}{}^{}$ at ${\theta }_{\alpha }\simeq 0°$, $16\le E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 21$ MeV.

• Received 15 April 1974

DOI:https://doi.org/10.1103/PhysRevC.10.1063