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

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 (g)	Mass (amu)	Family
proton	p+	+1	1.673 x 10-24	1.00727	baryon
neutron	n0	0	1.675 x 10-24	1.00866	baryon
electron/ positron	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

• How a nuclear fission reactor works.
• The Virtual Nuclear Tourist has a wealth of nuclear (fission) information, including sections on Chernobyl, Three-Mile Island, and environmental effects.
• Try your hand at controlling a nuclear reactor.
• The High Energy Weapons Archive and Trinity Site are sites with historical and current information about nuclear weapons.
• Two sites on Fusion Power from the Princeton Plasma Physics Laboratory and the Contemporary Physics Education Project
• Highly recommended reference: The Making of the Atomic Bomb" by Richard Rhodes - Pulitzer Prize winning account of the Manhattan Project. Also, "Dark Sun" - not quite as readable account of the development of Fusion Weapons by the same author.

The Proton-Proton Chain

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

• ¹H + ¹H --> ²H + e⁺ + neutrino Two protons (p⁺) react to form Deuterium (²H = 1p⁺ & 1 n) plus a positron (e⁺) and a neutrino. In the highly ionized stellar interior the positron will quickly "annihilate" with an electron (e⁺ + e^- --> 2 gamma-rays); the gamma-rays will be absorbed and re-emitted by the dense matter in the stellar interior, gradually diffusing outward and being "degraded" into photons of lower energy. When the gamma-ray energy reaches the photosphere each gamma-ray will have been transformed into about 200,000 visible photons. The neutrino, which only interacts through the Weak Force streams straight out of the sun.

• ²H + ¹H --> ³He + gamma-ray The Deuterium reacts with another proton to form ³He (2p⁺ & 1n) plus another gamma-ray. The first two reactions must happen twice to form two ³He nuclei.

• ³He + ³He --> ⁴He + 2 ¹H The two ³He nuclei react to form ⁴He (2p⁺ & 2n) giving two protons "change" plus a bit of added kinetic of the product nuclei. Not that the ³He nuclei repel each other more strongly because they contain two positively charged protons. The initial reaction above can occur at temperatures as low as 1 million K, but the last reaction can only occur at temperatures greater than about 10 million K.

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, T_core > 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:

• ⁴He + ¹H --> ⁵X
• ⁴He + ⁴He --> ⁸X

• ⁴He + ⁴He + ⁴He --> ¹²C

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:

• ¹²C + ⁴He --> ¹⁶0 + gamma-ray

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

• ¹⁶0 + ⁴He --> ²⁰Ne + gamma-ray

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:

• ¹²C + ¹²C --> ²⁴Mg + gamma-ray

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):

• ¹⁶0 + ¹⁶0 --> ³²S + gamma-ray

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.

• Nuclear Reactions from the University of Oregon's Electronic Textbook.

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 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:

• In a book entitled Telephone Poles and other Poems, John Updike published a poem about neutrinos called Cosmic Gall
• A comprehensive Neutrino History
• UC Irvine physicists report of detection of neutrino oscillations & mass from Kamiokande.
• Here is an account of the Solar Neutrino Problem relayed by John Bahcall and Ray Davis who have been involved since the beginning.
• Here are links to almost certainly more than you want to know.

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