The proton-proton chain reaction is one of several fusion reactions by which stars convert hydrogen to helium, the primary alternative being the CNO cycle. The proton-proton chain dominates in stars the size of the Sun or smaller. The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing fusion power. ... STAR is an acronym for: Organizations Society of Ticket Agents and Retailers], the self-regulatory body for the entertainment ticket industry in the UK. Society for Telescopy, Astronomy, and Radio, a non-profit New Jersey astronomy club. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Standard atomic weight 4. ... This article does not cite its references or sources. ... The Sun (Latin: Sol) is the star at the center of the Solar System. ...

Overcoming electrostatic repulsion between two hydrogen nuclei requires a large amount of energy, and this reaction takes an average of 10⁹ years to complete at the temperature of the Sun's core. Because of the slowness of this reaction the Sun is still shining; if it were faster, the Sun would have exhausted its hydrogen long ago.

In general, proton-proton fusion can occur only if the temperature (i.e. kinetic energy) of the protons is high enough to overcome their mutual Coulomb repulsion. The theory that proton-proton reactions were the basic principle by which the Sun and other stars burn was advocated by Arthur Stanley Eddington in the 1920s. At the time, the temperature of the Sun was considered too low to overcome the Coulomb barrier. After the development of quantum mechanics, it was discovered that tunneling of the wavefunctions of the protons through the repulsive barrier allows for fusion at a lower temperature than the classical prediction. This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks in-text citations. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... coulomb repulsion is the force acting between two similarly charge particles. ... One of Sir Arthur Stanley Eddingtons papers announced Einsteins theory of general relativity to the English-speaking world. ... The 1920s is a decade that is sometimes referred to as the Jazz Age or the Roaring Twenties, usually applied to America. ... The Coulomb barrier, named after physicist Charles-Augustin de Coulomb (1736—1806), is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo nuclear fusion. ... Fig. ... Quantum tunnelling (or tunneling) is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ... Classical physics is physics based on principles developed before the rise of quantum theory, usually including the special theory of relativity and general theory of relativity. ...

The pp chain reaction

The Proton-proton chain dominates in stars the size of the Sun or smaller.

The first step involves the fusion of two hydrogen nuclei ¹H (protons) into deuterium ²H, releasing a positron and a neutrino as one proton changes into a neutron. Image File history File links FusionintheSun. ... Image File history File links FusionintheSun. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in 6500 of hydrogen (~154 PPM). ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... Neutrinos are elementary particles denoted by the symbol ν. Travelling close to the speed of light, lacking electric charge and able to pass through ordinary matter almost undisturbed, they are extremely difficult to detect. ... This article or section does not adequately cite its references or sources. ...

¹H + ¹H → ²H + e⁺ + ν_e

with the neutrinos released in this step carrying energies up to 0.42 MeV. The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... Neutrinos are elementary particles denoted by the symbol ν. Travelling close to the speed of light, lacking electric charge and able to pass through ordinary matter almost undisturbed, they are extremely difficult to detect. ... The electronvolt (symbol eV, or, rarely and incorrectly, ev) is a unit of energy. ...

This first step is extremely slow, because it depends on an endoergic beta positive decay, which requires energy to be absorbed, to convert one proton into a neutron. In fact this is the limiting step, with a proton waiting an average of 10⁹ years before fusing into deuterium^{[citation needed]}. Positron emission is a type of beta decay, sometimes referred to as beta plus (β+). In beta plus decay, a proton is converted to a neutron via the weak nuclear force and a beta plus particle (a positron) and a neutrino are emitted. ...

The positron immediately annihilates with an electron, and their mass energy is carried off by two gamma ray photons. e- redirects here. ... This article is about electromagnetic radiation. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ...

e⁺ + e⁻ → 2γ + 1.02 MeV

After this, the deuterium produced in the first stage can fuse with another hydrogen to produce a light isotope of helium, ³He: This article is about electromagnetic radiation. ... Isotopes are any of the several different forms of an element each having different atomic mass (mass number). ... General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Standard atomic weight 4. ... Helium-3 is a non-radioactive and light isotope of helium. ...

²H + ¹H → ³He + γ + 5.49 MeV

From here there are three possible paths to generate helium isotope ⁴He. In pp1 helium-4 comes from fusing two of the helium-3 nuclei produced; the pp2 and pp3 branches fuse ³He with a pre-existing ⁴He to make Beryllium. In the Sun, branch pp1 takes place with a frequency of 86%, pp2 with 14% and pp3 with 0.11%. There is also an extremely rare pp4 branch. This article is about electromagnetic radiation. ... Helium-4 is a non-radioactive and light isotope of helium. ...

The pp I branch

³He +³He → ⁴He + ¹H + ¹H + 12.86 MeV

The complete pp I chain reaction releases a net energy of 26.7 MeV. The pp I branch is dominant at temperatures of 10 to 14 megakelvins (MK). Below 10 MK, the PP chain does not produce much ⁴He. The kelvin (symbol: K) is a unit increment of temperature and is one of the seven SI base units. ...

The pp II branch

The pp II branch is dominant at temperatures of 14 to 23 MK. General Name, Symbol, Number beryllium, Be, 4 Chemical series alkaline earth metals Group, Period, Block 2, 2, s Appearance white-gray metallic Standard atomic weight 9. ... This article is about electromagnetic radiation. ... General Name, Symbol, Number lithium, Li, 3 Chemical series alkali metals Group, Period, Block 1, 2, s Appearance silvery white/grey Standard atomic weight 6. ... Neutrinos are elementary particles denoted by the symbol ν. Travelling close to the speed of light, lacking electric charge and able to pass through ordinary matter almost undisturbed, they are extremely difficult to detect. ...

90% of the neutrinos produced in the reaction ⁷Be(e⁻,ν_e)⁷Li* carry an energy of 0.861 MeV, while the remaining 10% carry 0.383 MeV (depending on whether lithium-7 is in the ground state or an excited state, respectively).

The pp III branch

The pp III chain is dominant if the temperature exceeds 23 MK. This article is about electromagnetic radiation. ... General Name, Symbol, Number boron, B, 5 Chemical series metalloids Group, Period, Block 13, 2, p Appearance black/brown Standard atomic weight 10. ... This article is about electromagnetic radiation. ... Neutrinos are elementary particles denoted by the symbol ν. Travelling close to the speed of light, lacking electric charge and able to pass through ordinary matter almost undisturbed, they are extremely difficult to detect. ...

The pp III chain is not a major source of energy in the Sun (only 0.11%), but was very important in the solar neutrino problem because it generates very high energy neutrinos (up to 14.06 MeV). The solar neutrino problem was a major discrepancy between measurements of the neutrinos flowing through the Earth and theoretical models of the solar interior, lasting from the mid-1960s to about 2002. ...

The pp IV or Hep

This reaction is predicted but has never been observed due to its great rarity (about 0.3 parts per million in the Sun). In this reaction, Helium-3 reacts directly with a proton to give helium-4, with an even higher possible neutrino energy (up to 18.8 MeV). Parts per million (ppm) is a measure of concentration that is used where low levels of concentration are significant. ...

³He + ¹H → ⁴He + ν_e + e⁺

Energy release

Comparing the mass of the final helium-4 atom with the masses of the four protons reveals that 0.007 or 0.7% of the mass of the original protons has been lost. This mass has been converted into energy, in the form of gamma rays and neutrinos released during each of the individual reactions. The total energy we get in one whole chain is 26.73 MeV.

Only energy released as gamma rays will interact with electrons and protons and heat the interior of the Sun. This heating supports the Sun and prevents it from collapsing under its own weight.

Neutrinos do not interact significantly with matter and do not help support the Sun against gravitational collapse. The neutrinos in the ppI, ppII and ppIII chains carry away the 2.0%, 4.0% and 28.3% of the energy respectively.^[1]

The pep reaction

Image of Proton-Proton and Electron-Capture Chain reactions in a Star, see at the site of NDM'06 Int'l Conference on Neutrino and Dark Matter, Thursday 07 Sept 2006

Deuterium can also be produced by the rare pep (proton-electron-proton) reaction (electron capture): Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance in the oceans of Earth of approximately one atom in 6500 of hydrogen (~154 PPM). ... Electron capture is a decay mode for isotopes that will occur when there are too many protons in the nucleus of an atom, and there isnt enough energy to emit a positron; however, it continues to be a viable decay mode for radioactive isotopes that can decay by positron...

¹H + e⁻ + ¹H → ²H + ν_e

In the Sun, the frequency of pep reaction versus pp reaction is 1:400. However the neutrinos released are far more energetic: while neutrinos produced in the first step of the pp reaction range in energy up to 0.42 MeV, the neutrinos from the pep reaction produce sharp-energy-line neutrinos of 1.44 MeV.

Both PEP and PP reactions can be seen as two different Feynman representations of the same basic interaction, where the electron passes to the right side of the reaction as an anti-electron. Represented in the figure of Proton-Proton and Electron-Capture Chain reactions in a Star, available at the site of NDM'06 ^[2] Richard Feynman Richard Phillips Feynman (May 11, 1918–February 15, 1988) (surname pronounced FINE-man) was one of the most influential American physicists of the 20th century, expanding greatly the theory of quantum electrodynamics. ...

References

1. ^ Claus E. Rolfs, William S. Rodney: Cauldrons in the Cosmos, The University of Chicago Press, 1988, 354. pp
2. ^ Int'l Conference on Neutrino and Dark Matter, Thursday 07 Sept 2006, http://indico.lal.in2p3.fr/getFile.py/access?contribId=s16t1&sessionId=s16&resId=1&materialId=0&confId=a05162 Session 14

See also

• Triple-alpha process
• CNO cycle