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Alpha Decay Probability

γ=1r0r12m(VE)dr\gamma = \dfrac{1}{\hbar} \int_{r_0}^{r_1} \sqrt{2m(V-E)}\, dr

Suppose that the charge of a nucleus and the energy EE of particles in the nucleus change in such a way that the equation above is shifted to γln22\gamma - \frac{\ln 2}{2}, where r0r_0 and r1r_1 are the points where the energy EE intersects the potential VV.

By what factor does the probability of alpha decay in a given amount of time (transmission coefficient) change?

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