University of California, San Diego
Center for Astrophysics & Space Sciences

Gene Smith's Astronomy Tutorial

Nuclear Reactions

Nuclear energy can be produced by either of two types of reactions: fission, the splitting apart of a massive atomic nucleus, or by fusion of lighter nuclei into a heavier nucleus.

Atomic Particles
Particle Symbol Charge Mass
proton p+ +1 1.673 x 10-24 1.00727 baryon
neutron n0 0 1.675 x 10-24 1.00866 baryon
e-/e+ -1/+1 9.109 x 10-28 5.485 x 10-4 lepton
neutrino 0 < 10-32 < 5 x 10-9 lepton
photon 0 0 0 photon

Terrestrial Energy-Releasing Reactions
Energy Source Chemical Fission Fusion
Sample Reaction C + O2 -> CO2 n + U235 -> Ba143 + Kr91 + 2n H2 + H3 -> He4 + n
Typical Inputs (to Power Plant) Bituminous Coal UO2 (3% U235 + 97% U238) Deuterium & Lithium
Typical Reaction Temperature (K) 700 1000 108
Energy Released per kg of Fuel (erg/gm) 3.3 x 1011 2.1 x 1016 3.4 x 1018
Efficiency (E/mc2) 3 x 10-8% 0.002% 0.4%

The Proton-Proton Chain

The Proton-Proton Chain is the principal set of reactions for solar-type stars to transform hydrogen to helium:

The individual nuclear reactions proceed rather slowly, and it is a very small fraction of nuclei in the core of the sun with enough energy to overcome the electrical repulsion. Even so, every second the sun turns 600 million tons of hydrogen into 596 million tons of helium (with 4 million tons transformed into luminous eneryy via E=mc2).

More massive stars burn hydrogen via a catalytic reaction called The CNO CYCLE. Because the initial step in the CNO Cycle requires a Carbon nucleus (6 p+) to react with a proton it requires higher temperatures and is much more temperature sensitive than the P-P Chain (The energy produced is proportional to T20 for the CNO cycle vs T4 for the P-P Chain). Stars of mass greater than about 1.2 M with core temperatures, Tcore > 17 million K, produce most of their energy by the CNO cycle.

The Triple-Alpha Process

The Triple-Alpha Process follows hydrogen burning in both solar-type stars and high-mass stars transforming Helium into Carbon. (n.b. Stars with M < 0.4 M will not reach high enough temperatures for the 3-alpha process.) There are no stable isotopes with Atomic Mass 5 or 8 (i.e. such that reactions like:

may occur). The next stage in energy generation in stars is the Triple-Alpha Process which requires 3 - alpha particles (4He nuclei) to collide simultaneously to form Carbon:

This reaction requires both very high temperatures (T > 100 million K) and very high densities which will occur only after the star has exhausted its store of hydrogen and has a core of nearly pure helium. Only stars with masses greater than about 0.4M will reach temperatures high enough to ignite the Triple-alpha process.

Advanced Nuclear Burning Stages

Following the Triple-alpha process there are a variety of reactions which may occur depending on the mass of the star. Three general principles influence the roles that these nuclear burning stages may play:

  1. Successive nuclear burning stages, involving more massive nuclei with higher charges, will require increasingly high temperatures to overcome the increased electrical repulsion.
  2. The amount of energy released by each successive reaction stage decreases so that later nuclear burning stages become shorter and shorter.
  3. Once fusion reactions have produced an iron core, further fusion reactions no longer produce energy, but absorb energy from the stellar core. As we shall see this may have a catastrophic effect on the star as it nears the end of its life.

In stars like the sun, Carbon produced by helium burning via the Triple-alpha process will react with available helium nuclei to produce oxygen:

with some production of Neon, but the extreme electrical repulsion makes it difficult to produce nuclei more massive than Neon via helium-capture.

In more massive stars with temperatures greater than about 500 million K, Carbon burning will occur. This is just one of a variety of possible reactions:

And above 1 billion K, Oxygen burning may occur; again with a variety of possible reaction products (e.g.Sulfur, as shown, Magnesium, Silicon & Phosphorus):

Finally, at temperatures greater than about 3 billion K, Silicon burning occurs through a series of reactions that produce nuclei near the "iron-peak", that is near 56Fe on the Periodic Table, the element with the most strongly bound nucleus.

The Solar Neutrino "Problem"

Neutrinos were first "invented" by W. Pauli (of Exclusion Principle fame) in order to explain apparent failures in conservation of energy, momentum and leptons in certain nuclear decays. Pauli reasoned that these particles must be chargeless, have a mass much lower than the mass of the electron and interact only very weakly with other matter. He called them "neutrons", but when the massive baryon that we now call the neutron was discovered, it was realized that this could not be Pauli's particle and the name of the hypothetical particle was changed to "neutrino". The existence of the neutrino was confirmed by Reines and Cowan in 1956.

Although astrophysicists have great confidence in their calculations of the structure and evolution of stars like the sun, there is no substitute for experimental confirmation. Because the neutrinos are the only nuclear reaction products that make it out from the solar core, the most direct confirmation of the theories would be to measure the neutrinos emitted by the sun's P-P chain. The first experiment, begun in 1970 used a 100,000 gallon tank of cleaning fluid called perchloroethylene -- C2Cl4 to detect neutrinos from a subsidiary branch of the Proton-Proton Chain via the weak interaction:

37Cl + --> 37Ar + e-

The experiment was placed a mile underground in the Homestake gold mine in Lead, SD to avoid contamination from other particle interactions. The experiment was predicted to create 3 Argon atoms, which could be counted by their radioactivity, every other day, but only about 1/3 that number were detected. The experiment has continued for over 20 years and has recently been joined by other solar neutrino experiments in Japan (Kamiokande), Russia (SAGE = Soviet(sic)-American Gallium Experiment) and Italy (GALLEX), all reporting the same result.

The most promising resolution of this problem lies in the physics of the neutrino itself. There are three flavors of leptons -- electrons (with their associated anti-particle the positron), muons and tau leptons, each with an associated flavor of neutrino, , and . In an extension of the electroweak unified force theory it has been proposed that neutrinos can "oscillate" among these three flavors. If this theory is correct, then the electron neutrinos produced by the solar nuclear fusion reactions may be oscillating among flavors as they travel toward earth, producing the apparent deficit. One implication of this idea is that neutrinos must have a small but non-zero mass. Current limits place the mass of the electron neutrino at less than 1/100000 th the mass of the electron. Recent experimental results appear to confirm this theory.

Some neutrino links:

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Conducted by Gene Smith, CASS/UCSD.
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Prof. H. E. (Gene) Smith
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Last updated: 16 April 1999