Analytical expression for α-decay half-life and explanation of extremely large life-times

An analytically solvable composite potential have been developed which can closely reproduce the combined potential of an α+nucleus system consisting of attractive nuclear and repulsive electrostatic potentials. The exact s-wave solution of the Schroedinger equation with the above potential in the interior region and the outside Coulomb wave function are used to give a heuristic expression for the width or half-life of the quasi-bound state at the accurately determined resonance energy called the Q-value of the decaying system