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

Suppose that the charge of a nucleus and the energy $E$ of particles in the nucleus change in such a way that the equation above is shifted to $\gamma - \frac{\ln 2}{2}$, where $r_0$ and $r_1$ are the points where the energy $E$ intersects the potential $V$.

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

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