the number of times per second the alpha particle strikes the barrier wall. For an alpha particle with kinetic energy $\sim 30\,\text{MeV}$ bouncing inside a nucleus of radius $\sim 7\,\text{fm}$: $v \approx \sqrt{2E/m_\alpha} \approx 0.12c$ and $f = v/(2R) \approx 10^{21}\,\text{s}^{-1}$. - $P$ is