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$\alpha$-decay always has enormous impetuses to the development of physicsand chemistry, in particular due to its indispensable role in the research ofnew elements. Although it has been observed in laboratories for more than acentury, it remains a difficult problem to calculate accurately the formationprobability $S_\alpha$ microscopically. To this end, we establish a new model,i.e., multistep model, and the corresponding formation probability $S_\alpha$values of some typical $\alpha$-emitters are calculated without adjustableparameters. The experimental half-lives, in particular their irregular behavioraround a shell closure, are remarkably well reproduced by half-life lawscombined with these $S_\alpha$. In our strategy, the cluster formation is agradual process in heavy nuclei, different from the situation that clusterpre-exists in light nuclei. The present study may pave the way to a fullyunderstanding of $\alpha$-decay from the perspective of nuclear structure.

Alpha-Cluster formation in heavy alpha-emitters within a multistep model