Application of the semimicroscopic algebraic cluster model to core<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mi>α</mml:mi></mml:mrow></mml:math>nuclei in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:math>shells

The semimicroscopic algebraic cluster model (SACM) is applied to the systems ${}^{12}\mathrm{C}+\ensuremath{\alpha}$ $\ensuremath{\rightarrow}$ ${}^{16}$O, ${}^{14}\mathrm{C}+\ensuremath{\alpha}$ $\ensuremath{\rightarrow}$ ${}^{18}$O, ${}^{16}\mathrm{O}+\ensuremath{\alpha}$ $\ensuremath{\rightarrow}$ ${}^{20}$Ne, ${}^{18}\mathrm{C}+\ensuremath{\alpha}$ $\ensuremath{\rightarrow}$ ${}^{22}$Ne, and ${}^{20}\mathrm{Ne}+\ensuremath{\alpha}$ $\ensuremath{\rightarrow}$ ${}^{24}$Mg. The spectrum and some $E2$ values are fitted to experiment. Further $E2$ transition values as well as $E1$ and $M1$ transitions are calculated and compared to experiment. In addition, we list the spectroscopic factors of the states listed. These factors are predictions of the model and are of interest in current astrophysical studies.

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