1. Constraints on Nuclear Fusion Reactions
Binary reactions dominate
Energy Conservation (Energy release)
Charge conservation (d=2H nucleus)
pp  d+e++Energy +??
Angular momentum conservation
Proton, electron spin = (1/2)[h/(2π)]
Deuteron spin = h/(2π)
Neutrino predicted by E.Fermi
pp  d+e++ +Energy
Detected in 1950s by Reines and Cowen next to a nuclear reactors
Weak Interactions (lepton number conservation)
n  p + e+ anti-. Half Life 12,33 year
Weak interactions are Weak  Reaction Rates are slow

2. Light Nuclei, http://www.nndc.bnl.gov/chart/
No stable A=5 nuclei

3. pp chains in Sun
31%
69%
99.7%
(pp I)
0.3%
(pp II)
(pp III)

4. pp chains H+H+H+H4He+2e+2e++2
First Step
pp  D + e+ +  + MeV
Weak interaction process
D=(pn) = nucleus of 2H.
Neutron half life = min
Suppressed by pp Coulomb repulsion
Quantum Tunneling required
Protons are waves
If Kinetic energy = E-U > 0 = h/p
If Kinetic energy = E-U < 0
Wave is exponentially damped exp(-r)  = [U-E]1/2.

5. Billiard Ball model of pp collisions
Proton density , Temperature T
Velocity distribution (Maxwell-Boltzman)
P(v;T) = exp(-mv2/(2KT)) / [2πkT]3/2.
<mv2/2>= <mvx2/2> +<mvy2/2> +<mvz2/2> =3kT/2
vrms ≈ [kT/m]1/2.
Collision rate per unit volume: R.
≈ (10-15m)2.
Rate R ≈ 2v|≈ 2 [kT/m]1/2.
Volume = vt

6. Ballistic Burn Time of Sun
Number density of sun = /MH.
Average = 8 1029 /m3.
Central = 1032 /m3.
Temperature, rms Velocity vrms ≈ [kT/mc2]1/2
Surface kT = 0.5 eV. vrms ≈ 7000 m/s
Central kT = 1KeV. vrms ≈ 3 105 m/s
Proton Mass = 0.9 GeV
Time for all protons to collide / R = /[|v|]
Surface 1/[|v|] ≈ 10-4 s
Center ≈ 30 ns
Crucial role of Coulomb Repulsion and Weak interactions to regulate nuclear fusion rate in sun

7. pp fusion slowed by coulomb repulsion
Kinetic energy required to bring two protons to within 1 fm
e2/(4π0 r) = 1.4 MeV
Center of sun kT ≈ 1 KeV
Maxwell Boltzmann distribution
P(v) = exp{-[mv2/(2kT)]}
P[-(1.4MeV)/(1 KeV)] ≈ exp(-1000)
Classical pp Collision rate in sun ≈ 0
No pp fusion, even worse for heavier elements
Quantum barrier penetration