Route to islands of stability of superheavy elements

Problems concerning the existence of hypothetical superheavy elements for which theoretical nuclear models predict high stability with respect to various modes of radioactive decay are discussed. The synthesis of superheavy nuclei and the possibilities for performing experiments aimed at detecting rare events of their production and decay in heavy-ion beams are considered. Experimental results suggesting a considerable increase in the lifetime of nuclei as they approach the closed proton and neutron shells determining the islands of stability of superheavy elements are presented.