Modeling Alpha Half-life
Integrating the tunneling barrier
This should be a fairly realistic model of a spherical nucleus. The things it leaves out include the non-spherical nature of many heavy nuclei and the effects of nuclear angular momentum on decay rate. The assumption of a spherical shape is a particular problem for heavy nuclei (A > 230) since they are known to be strongly deformed. This is a serious problem since a 4% change in radius can yield a factor of 5 difference in halflife. Sometimes the measured halflife is used to make implications about the radius instead of vice versa.
Alpha Decay Concepts
Eisberg & Resnick