Fusion Due to Gravitation in Bosonic Atoms

[tomgotthefunk]

In a bosonic atom i.e. Hydrogen, why do we never observe quantum tunneling past the coulomb barrier leading to multiple atoms occupying the same area of space thus (due to Newton's law of universal gravitation) accelerating towards each other resulting in nuclear fusion?

 

[mfb]

Gravity is completely negligible compared to the electrostatic repulsion and the nuclear force. The Coulomb barrier is so high and wide that hydrogen atoms do not have a relevant tunnelling probability at room temperature.