Proton-Proton Cycle

The thermonuclear reactions in the proton-proton cycle inside the Sun convert four protons into an alpha particle, two positrons, two electron neutrinos, and two photons with the release of 26.7 MeV of energy. First, two protons collide to form a deuteron H-2, then this deuteron collides with a proton to form He-3, then finally two He-3 nuclei must find each other to collide and form an He-4. The overall representation of this proton-proton cycle is:

4H → He-4 + 2e+ + 2ν + 2γ.

The six photons ultimately produced, including the four 0.511 MeV photons from two positron-electron annihilations, take about a million years to reach the Sun’s surface to be emitted eventually as visible photons, which then take about another eight minutes to reach Earth. The two neutrinos carry away about 3 percent of the energy to balance the energy conservation equation and to conserve lepton family number.

Presented as the primary source of our Sun’s energy, this method of burning hydrogen is not the primary method for fusion energy in many stars. Why not? What reaction sequence is the primary candidate?

Answer

The other stars are using the carbon cycle for their fusion energy. The common proton-proton cycle reaction is not the source of fusion energy in many stars burning hydrogen because the first reaction in this sequence has two protons combining to form a deuteron H-2, a very unlikely event that occurs slowly. A more likely sequence of reactions involves having C-12 be a catalyst:

C-12 + p → N-13 + γ

N-13 → C-13 + e+ + ν

C-13 + p → N-14 + γ

N-14 + p → O-15 + γ

O-15 → N-15 + e+ + ν

N-15 + p → C-12 + He-4

Called the carbon cycle, this sequence of reactions occurs much more rapidly than the proton-proton cycle sequence because the C-12 acts as a catalyst, neither being produced nor consumed by the totality of reactions. The net process is still the same: 4 protons → He-4, and the net energy produced is the same, but the rate of energy production is much higher.

The carbon cycle occurs at a higher temperature than the proton-proton cycle because the C and H Coulomb repulsion is greater than the H and H repulsion, so the Sun, with its internal temperature of about 15 × 10⁶ K, is too cool to activate the carbon cycle, which requires about 20 × 10⁶ K.