An alpha particle lacks escape energy. Why can a nucleus still decay?

Answer: Wavefunction leakage

Nuclear shell crack — A nuclear shell crack is a plausible picture if you imagine the nucleus as a tiny container, but the barrier here is energetic, not a literal wall. OpenStax describes the alpha particle as lacking enough kinetic energy to get over the rim yet escaping by tunnelling. Cracking would not explain the precise half-life pattern.

Outer-electron shove — An outer-electron shove is not the main pusher in ordinary alpha decay. The alpha particle is already inside the heavy nucleus, confined by nuclear attraction and repelled by the daughter nucleus outside. The escape probability comes from the alpha wavefunction penetrating the Coulomb barrier.

Wavefunction leakage ✓ — Correct. The alpha particle's wavefunction does not stop abruptly at the Coulomb barrier; it decays through the forbidden region and has a tiny tail outside. After many attempts, that tiny probability becomes a measurable decay rate. Tunnelling theory explains alpha-decay half-lives spanning about 17 orders of magnitude.