1. Quantum Barrier Penetration
1D~exp(r-r0])
3D: ~exp(r-r0])/r
=[U-E]1/2 ~ U1/2.
Gamov factor
EG(pp)=500KeV
Classical suppression
e(-E/U) ~ e-1000.
Quantum suppression
Exp[-(500)1/2]

2. Barrier Penetration
Classical Turning point r1.
E=e2/r1.

3. Thermal Distribution x Gamow Penetration Factor

4. Weak Interactions in pp
S0 factor
Consider time two protons are within 1fm of each other
Compare with n half life of 13 min
S0 is small
Each proton waits 20 Billion years to fuse with another (Astrophysics in a Nutshell, Eq 3.136)
The sun can burn for billions of years at its current luminosity