  Nuclear radial distance is a prerequisite for generating any alpha-decay
half-life formula by taking a suitable effective potential. We study the
emission process of alpha particles from an isolated quasi-bound state
generated by an effective potential to a scattering state. The effective
potential is expressed in terms of Frahn form of potential which is exactly
solvable and an analytical expression for half-life is obtained in terms of
Coulomb function, wave function and the potential. We then derive a closed form
expression for the decay half-life in terms of the parameters of the potential,
Q-value of the system, mass and proton numbers of the nuclei valid for
alpha-decay as well as proton-decay. From the nature of variations of half-life
as a function of radial distance, we trace the radial independence region where
decay time is almost constant. Finally by overviewing our results and picking
that particular radial distance we predict the half-lives of a series of nuclei
by using the closed form expression.
