Question

The alpha decay is explained as a quantum mechanical tunneling. Assuming that the alpha particle energy is much smaller than the potential barrier the alpha particle has to penetrate, the transmission coefficient is given by

The integration limits a and b are determined as solutions to the equation U(r) = E, where U(r) is the non-constant Coulomb’s potential energy. Calculate the alpha transmission coefficient and the decay constant λ.

Answer 1

The transmission coefficient is given by

for the Coulomb potential energy between the alpha particle and the residual nucleus at distance of separation r.

If v_in is the velocity of the alpha particle inside the nucleus and R = a is the nuclear radius then the decay constant λ = 1/τ ∼ (v_in/R).e^−G