Science fiction physics: without quantum tunnelling

Problem

In the Sun, proton-proton fusion occurs thanks to quantum tunnelling, which allows protons to overcome the Coulomb barrier despite the relatively low thermal energy. What would happen to the Sun if tunnelling were suddenly switched off?

Solution

At the temperature of the solar core ($\sim 1{,}5\cdot 10^7\ \text{K}$) the average kinetic energy of the protons is about a thousand times too small to classically overcome the Coulomb barrier that repels them. Fusion can only occur because the protons “pass through” the barrier via quantum tunnelling.

If tunnelling were switched off, practically no pair of protons would manage to fuse any more: nuclear energy production in the core would stop completely.

With no more energy generated at the centre, the pressure (thermal and radiative) would no longer be able to balance the weight of the outer layers. The core would begin to contract under its own gravity, collapsing towards a degenerate, cold state (a sort of brown/white dwarf). The star would stop shining.

$\ev{\text{no tunnelling}\Rightarrow\text{no fusion}\Rightarrow\text{gravitational contraction of the Sun}}$

Collegamenti

Argomenti: Fisica nucleare Concetti: Fusione nucleare Competenze: Analisi di casi limite e fantafisica