Energy dependence of the cross sections for theMg24(16O,12C)28Si(g.s.) reaction

Excitation functions have been measured at 0° and 180° for the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ ${(}^{16}$O${,}^{12}$C${)}^{28}$ Si(g.s.) reaction, and at 180° for the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ ${(}^{16}$O${,}^{12}$C${)}^{28}$ Si($2^{+}$) reaction over the energy range 36 MeV≤$E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$≤54 MeV. Angular distributions were measured at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=35.5 and 36.2 MeV where, for the latter energy, much of the angular range between 0° and 180° was covered. These data, combined with earlier measurements at lower energies, establish that the reaction cross section is strongly influenced by resonances of the compound system over a large energy range. At the higher energies, however, both the energy averaged cross section and the resonance amplitudes fall off sharply. An attempt is made to reproduce the observed structure in the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(g.s.) 0° and 180° excitation functions by fitting to the data a band of Breit-Wigner resonances with an energy dependence proportional to J(J+1). The general behavior of the 0° and 180° yield is well reproduced by this procedure, even though there are twice as many resonance poles as there are clear bumps in the data. Some regularity is evident in the resulting resonance parameters, although the fitted resonance amplitudes show greater scatter than expected for a nuclear molecular band.