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Nuclear clusters bound to doubly magic nuclei: The case of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Po</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>212</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>
An effective $\ensuremath{\alpha}$-particle equation is derived for cases where an $\ensuremath{\alpha}$ particle is bound to a doubly magic nucleus. As an example, we consider $^{212}\mathrm{Po}$ with the $\ensuremath{\alpha}$ on top of the $^{208}\mathrm{Pb}$ core. We consider the core nucleus infinitely heavy, so that the $\ensuremath{\alpha}$ particle moves with respect to …