Empirical formulae in alpha and cluster decay studies

In the investigation of heavy elements, the half-lives and their possible decay modes test the ideas developed on the nuclear structure. This has motivated the formulation of empirical relations that provide nuclear information that would have otherwise been difficult to obtain through a complicated microscopic framework. One of these simple formulae is the universal decay law (UDL). This relates the half-life and basic information of the parent nucleus, the daughter nucleus, and the emitted cluster, such as mass and atomic numbers, Q-value, and angular momentum. We formulate a UDL and use it to investigate temperature-dependent decays, the emissions to excited states of the products, and preformation probabilities.