Intermediate structure and statistical fluctuations in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>12</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>+<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Mg</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>24</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>system

The 180\ifmmode^\circ\else\textdegree\fi{} c.m. excitation function of the elastic and inelastic scattering of $^{12}\mathrm{C}$ on a $^{24}\mathrm{Mg}$ target has been measured between 12- and 27-MeV c.m. energy. A statistical analysis of the data has been performed and it has turned out that the presence of intermediate structures cannot be completely ruled out in the compound dinuclear system $^{36}\mathrm{Ar}$. Unfortunately, a complete phase shift analysis of several elastic scattering angular distributions measured on the maxima of these resonant structures shows that no spin assignment can be made. Therefore these intermediate structures appear to be spoiled by a more complex statistical resonance noise. At low incident energy, the Blair phase rule for oscillations in angular distributions is verified between the first ${2}^{+}$ target inelastic scattering and the elastic scattering.NUCLEAR REACTIONS Measured elastic and inelastic excitation functions at ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=180\ifmmode^\circ\else\textdegree\fi{}$ for $^{12}\mathrm{C}$+$^{24}\mathrm{Mg}$, $12&lt;{E}_{\mathrm{c}.\mathrm{m}.}&lt;27$ MeV. Deduced average width and autocorrelation and cross-correlation functions of the observed structure. Complete phase shift analysis of the elastic angular distributions measured at 24.8, 27.70, 28.60, 31.20, and 34.80 MeV $^{12}\mathrm{C}$ incident energy; angular range 10\ifmmode^\circ\else\textdegree\fi{} to 180\ifmmode^\circ\else\textdegree\fi{} c.m. Inelastic scattering data at the same energies. Partial observation of the Blair phase rule.