Possible hyperdeformed band in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Ar</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>36</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>observed in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:mmultiscripts><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Mg</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>24</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>elastic scattering

Fifteen strongly oscillating angular distributions of the elastic scattering of $^{12}\mathrm{C}+^{24}\mathrm{Mg}$ at energies around the Coulomb barrier (${E}_{\mathrm{c}.\mathrm{m}.}=10.67\text{\ensuremath{-}}16.00$ MeV) are reproduced by adding five Breit-Wigner resonance terms to the $l=2,4,6,7$, and 8 elastic $S$ matrix. The nonresonant, background elastic scattering $S$ matrix ${S}_{l}^{0}$ is calculated using the S\~ao Paulo potential. The $J=2,4,6,7$, and 8 $\ensuremath{\hbar}$ molecular resonances fit well into a rotational molecular band, together with other higher lying resonances observed in the $^{16}\mathrm{O}+^{20}\mathrm{Ne}$ elastic scattering. We propose that the presently observed, largely deformed molecular band corresponds to the hyperdeformed band, which has been found previously in $\ensuremath{\alpha}$-cluster calculations, as well as in a new Nilsson model calculation. Systematic study of its possible clusterizations predicts the preference of the $^{12}\mathrm{C}+^{24}\mathrm{Mg}$ and $^{16}\mathrm{O}+^{20}\mathrm{Ne}$ molecular structure, in accordance with our present results.

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