Systematic research on α-decay rates of spherical and deformed nuclei

α decay is of significant interest for the study of nuclear structure and for the synthesis of new superheavy elements. Theoretical approaches in recent α-decay studies are reviewed. After a brief review of the systematic laws of α-decay half-lives, various expressions for the decay width are discussed together with the α preformation factor. These expressions are separately derived within the semiclassical approximation, direct method, distorted wave approach, (modified) two-potential approach, and coupled-channel approach. Within the coupled-channel representation, two techniques to deal with the coupling interaction matrix are discussed for precise descriptions of the α-decay fine structure. Various α-decay calculations within all these different approaches are presented and compared. It is found that both semiclassical and quantum-mechanical calculations well reproduce the experimental α-decay half-lives within a mean factor of about two. However, the semiclassical formalism fails in describing the α transitions to high-lying members of one rotational band, while the coupled-channel approach including enough decay channels gives a precise description of the α-decay fine structure observed in heavy deformed nuclei.