We account for the extremely long ($\sim$10${}^{18}$ yr) as well as short ($\sim$10${}^{-4}$ s) lifetimes of $\alpha$ decay in the cases of naturally occurring heavy $\alpha$ emitters with proton number $Z=58$–82 and successfully predict the results via an analytical expression for the decay half-life, developed by using an exactly solvable global potential in the theory of potential scattering.

• Received 21 February 2012

DOI:https://doi.org/10.1103/PhysRevC.85.057601