proton-proton chain

The proton-proton chain is the process of nuclear fusion by which the Sun and other low-mass, main sequence stars generate energy. In essence, the reaction turns four hydrogen nuclei (four protons) into one helium nucleus (an alpha particle). Since the alpha particle has less mass than the four protons individually, the reaction is exoergic, and the excess energy heats the surrounding gas.

The following particles are involved:

• H¹ - proton
• D² - deuteron
• He³ - helium 3
• He⁴ - helium 4
• e^- - electron
• e⁺ - positron (anti-electron)
• Li⁷ - lithium 7
• Be⁷ - beryllium 7
• Be⁸ - beryllium 8
• B⁸ - boron 8
• nu - neutrino
• gamma - photon (gamma ray)

The proton-proton chain actually consists of three related reactions, PPI, PPII, and PPIII. The three reactions (and the net energy released) are as follows:

PPI:

1. H¹ + H¹ -> D² + e⁺ + nu(1) (1.442 MeV)
2. D² + H¹ -> He³ + gamma (5.493 MeV)
3. He³ + He³ -> He⁴ + 2H¹ (12.859 MeV)

PPII:

1. H¹ + H¹ -> D² + e⁺ + nu(1) (1.442 MeV)
2. D² + H¹ -> He³ + gamma (5.493 MeV)
3. He³ + He⁴ -> Be⁷ + gamma (1.586 MeV)
4. Be⁷ + e^- -> Li⁷ + nu(2) (0.861 MeV)
5. Li⁷ + H¹ -> He⁴ + He⁴ (17.347 MeV)

PPIII:

1. H¹ + H¹ -> D² + e⁺ + nu(1) (1.442 MeV)
2. D² + H¹ -> He³ + gamma (5.493 MeV)
3. He³ + He⁴ -> Be⁷ + gamma (1.586 MeV)
4. Be⁷ + H¹ -> B⁸ + gamma (0.135 MeV)
5. B⁸ -> Be⁸ + e⁺ + nu(3) (followed by spontaneous decay...)
6. Be⁸ -> 2He⁴ (18.074 MeV)

Notice that each of the three chains results in the emission of either one (PPI) or two (PPII and III) neutrinos. These neutrinos can be detected (with great difficulty) on Earth. Each neutrino has a different energy spectrum, so the relative strength of the three chains in the Sun can be calibrated (in principle). The mean energy of the three neutrinos are: nu(1) = 0.263 MeV, nu(2) = 0.80 MeV, and nu(3) = 7.2 MeV. Notice also that the PPII and PPIII chains release the same amount of energy, but result in neutrinos with very different energies. Thus PPIII generates less heat in the core.

Most of this was worked out by physicist Hans Bethe in Physical Review, 55:103,434 (1939), for which he won the Nobel Prize in physics in 1967.

It is important to note that the proton-proton chain reactions are strongest only in low-mass stars with hydrogen in the core. More massive stars with higher core temperatures use the CNO cycle.

Source: D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, McGraw Hill, 1968.