# Alpha Decay Probability

**Classical Mechanics**Level pending

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

Suppose that the charge of a nucleus and the energy \(E\) of particles in the nucleus change in such a way so 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?