Proton–proton chain reaction

The proton–proton chain reaction is one of two known sets of nuclear fusion reactions by which stars convert hydrogen to helium. It dominates in stars with masses less than or equal to that of the Sun's,[1] whereas the CNO cycle, the other known reaction, is suggested by theoretical models to dominate in stars with masses greater than about 1.3 times that of the Sun's.[2]

In general, proton–proton fusion can occur only if the kinetic energy (i.e. temperature) of the protons is high enough to overcome their mutual electrostatic or Coulomb repulsion.[3]

In the Sun, deuterium-producing events are rare. Diprotons are the much more common result of proton–proton reactions within the star, and diprotons almost immediately decay back into two protons. Since the conversion of hydrogen to helium is slow, the complete conversion of the hydrogen in the core of the Sun is calculated to take more than ten billion years.[4]

Although often called the "proton-proton chain reaction", it is not a chain reaction in the normal sense of the word (at least not Branch I — in Branches II and III helium, which is the product, also serves as a catalyst). It does not produce particles that go on to induce the reaction to continue (such as neutrons given off during fission). In fact, the rate is self-limiting because the heat produced tends toward reducing the density. It is however a chain (like a decay chain) and a reaction, or more accurately a branched chain of reactions starting with two protons coming together and yielding deuterium.

Fusion in the Sun.svg&lang=en
The proton–proton branch I chain reaction dominates in stars the size of the Sun or smaller

History of the theory

The theory that proton–proton reactions are the basic principle by which the Sun and other stars burn was advocated by Arthur Eddington in the 1920s. At the time, the temperature of the Sun was considered to be 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.

Even so, it was unclear how proton–proton fusion might proceed, because the most obvious product, helium-2 (diproton), is unstable and almost instantly dissociates back into two protons. In 1939, Hans Bethe proposed that one of the protons could decay by beta emission into a neutron via the weak interaction during the brief moment of fusion, making deuterium a vital product in the chain.[5] This idea was part of the body of work in stellar nucleosynthesis for which Bethe won the Nobel Prize in Physics in 1967.

The proton–proton chain reaction

The first step involves the fusion of two 1
H
nuclei (protons) into deuterium, releasing a positron and a neutrino as one proton changes into a neutron. It is a two-stage process; first, two protons fuse to form a diproton:

1
1
H
 
1
1
H
 
→  2
2
He
 

followed by the beta-plus decay of the diproton to deuterium:

2
2
He
 
→  2
1
H-
 

e+
 

ν
e

with the overall formula:

1
1
H
 
1
1
H
 
→  2
1
H-
 

e+
 

ν
e
 
0.42 MeV

This second step is extremely slow because the positron emission of the diproton to deuterium is extremely rare (the vast majority of the time, the diproton decays back into two hydrogen-1 unbound protons through proton emission). This is because the emission of the positron is brought about by the weak nuclear force, which is immensely weaker than the strong nuclear force and the electromagnetic force.

The half-life of a proton in the core of the Sun before it is involved in a successful proton–proton fusion is estimated to be about one billion years, even at the extreme pressures and temperatures found there.

The positron emitted by the decay by beta emission usually annihilates immediately with an electron. Their mass-energies plus their kinetic energy is carried off by two gamma rays (photons) with the mass-energy of 511 keV (thousand electron-volts) apiece.


e
 

e+
 
→ 
γ
 
1.022 MeV

After it is formed, the deuterium produced in the first stage can fuse with another proton to produce the light isotope of helium, 3
He
:

2
1
D
 
1
1
H
 
→  3
2
He
 

γ
 
5.49 MeV

This process, mediated by the strong nuclear force rather than the weak force, is extremely fast by comparison to the first step. It is estimated that, under the conditions in the Sun's core, each newly created deuterium nucleus exists for only about four seconds before it is converted to He-3.

In the Sun, each helium-3 nucleus produced in these reactions exists for only about 400 years before it is converted into helium-4.[6] Once the helium-3 has been produced, there are four possible paths to generate 4
He
. In p-p I, helium-4 is produced by fusing two helium-3 nuclei; the p-p II and p-p III branches fuse 3
He
with pre-existing 4
He
to form beryllium-7, which undergoes further reactions to produce two helium-4 nuclei.

In the Sun, 4
He
synthesis via branch p-p I occurs with a frequency of 83.30 percent, p-p II with 16.68 percent, and p-p III with 0.02 percent.[7]

There is also the extremely rare p-p IV branch. Other even rarer reactions may occur. The rate of these reactions is very low due to very small cross-sections, or because the number of reacting particles is so low that any reactions that might happen are statistically insignificant. This is partly why no mass-5 or mass-8 elements are seen. While the reactions that would produce them, such as a proton + helium-4 producing lithium-5, or two helium-4 nuclei coming together to form beryllium-8, may actually happen, these elements are not detected because there are no stable isotopes of atomic masses 5 or 8; the resulting products immediately decay into their initial reactants.

The overall reaction is:

1
1
H
4
He2-
+ 2e+ + 2νe

The P-P I branch

3
2
He
 
3
2
He
 
→  4
2
He
 
1
1
H
 
12.86 MeV

The complete p-p I chain reaction releases a net energy of 26.732 MeV.[8] Two percent of this energy is lost to the neutrinos that are produced.[9] The p-p I branch is dominant at temperatures of 10 to 14 MK. Below 10 MK, the P-P chain does not produce much 4
He
.

The P-P II branch

Proton-Proton II chain reaction
Proton–proton II chain reaction
3
2
He
 
4
2
He
 
→  7
4
Be
 

γ
7
4
Be
 

e
 
→  7
3
Li-
 

ν
e
 
0.861 MeV  0.383 MeV
7
3
Li
 
1
1
H
 
→  4
2
He

The P-P II branch is dominant at temperatures of 14 to 23 MK.

Note that the energies in the equation above are not the energy released by the reaction. Rather, they are the energies of the neutrinos that are produced by the reaction. 90 percent of the neutrinos produced in the reaction of 7
Be
to 7
Li
carry an energy of 0.861 MeV, while the remaining 10 percent carry 0.383 MeV. The difference is whether the lithium-7 produced is in the ground state or an excited (metastable) state, respectively.

The P-P III branch

Proton-Proton III chain reaction
Proton–proton III chain reaction
3
2
He
 
4
2
He
 
→  7
4
Be
 

γ
7
4
Be
 
1
1
H
 
→  8
5
B
 

γ
8
5
B
 
    →  8
4
Be
 

e+
 

ν
e
 
8
4
Be
 
    →  4
2
He

The P-P III chain is dominant if the temperature exceeds 23 MK.

The p-p III chain is not a major source of energy in the Sun (only 0.11 percent), but it was very important in the solar neutrino problem because it generates very high energy neutrinos (up to 14.06 MeV).

The P-P IV (Hep) branch

This reaction is predicted theoretically, but it has never been observed due to its rarity (about 0.3 ppm in the Sun). In this reaction, helium-3 captures a proton directly to give helium-4, with an even higher possible neutrino energy (up to 18.8 MeV).

3
2
He
 
1
1
H
 
→  4
2
He
 

e+
 

ν
e
 
18.8 MeV

Energy release

Comparing the mass of the final helium-4 atom with the masses of the four protons reveals that 0.7 percent 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 yield of one whole chain is 26.73 MeV.

Energy released as gamma rays will interact with electrons and protons and heat the interior of the Sun. Also kinetic energy of fusion products (e.g. of the two protons and the 4
2
He
from the p-p I reaction) increases the temperature of plasma in the Sun. This heating supports the Sun and prevents it from collapsing under its own weight.

Neutrinos do not interact significantly with matter and therefore do not help support the Sun against gravitational collapse. Their energy is lost: the neutrinos in the p-p I, p-p II, and p-p III chains carry away 2.0%, 4.0%, and 28.3% of the energy in those reactions, respectively.[10]

The PEP reaction

Proton proton cycle
Proton–proton and electron-capture chain reactions in a star

Deuterium can also be produced by the rare pep (proton–electron–proton) reaction (electron capture):

1
1
H
 

e
 
1
1
H
 
→  2
1
D+
 

ν
e

In the Sun, the frequency ratio of the pep reaction versus the p-p reaction is 1:400. However, the neutrinos released by the pep reaction are far more energetic: while neutrinos produced in the first step of the p-p reaction range in energy up to 0.42 MeV, the pep reaction produces sharp-energy-line neutrinos of 1.44 MeV. Detection of solar neutrinos from this reaction were reported by the Borexino collaboration in 2012.[11]

Both the pep and p-p 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 a positron. This is represented in the figure of proton–proton and electron-capture chain reactions in a star, available at the NDM'06 web site.[12]

See also

References

  1. ^ "The Proton-Proton Chain". Astronomy 162: Stars, Galaxies, and Cosmology. Archived from the original on 2016-06-20. Retrieved 2018-07-30.
  2. ^ Salaris, Maurizio; Cassisi, Santi (2005). Evolution of Stars and Stellar Populations. John Wiley and Sons. pp. 119–121. ISBN 0-470-09220-3.
  3. ^ Ishfaq Ahmad, The Nucleus, 1: 42, 59, (1971), The Proton type-nuclear fission reaction.
  4. ^ Kenneth S. Krane, Introductory Nuclear Physics, Wiley, 1987, p. 537.
  5. ^ Hans A. Bethe, Physical Review 55:103, 434 (1939); cited in Donald D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, The University of Chicago Press, 1983, p. 366.
  6. ^ This time and the two other times above come from: Byrne, J. Neutrons, Nuclei, and Matter, Dover Publications, Mineola, NY, 2011, ISBN 0486482383, p 8.
  7. ^ Adelberger, Eric G.; et al. (12 April 2011). "Solar fusion cross sections. II. The pp chain and CNO cycles". Reviews of Modern Physics. 83 (1): 201. arXiv:1004.2318. Bibcode:2011RvMP...83..195A. doi:10.1103/RevModPhys.83.195.
  8. ^ LeBlanc, Francis. An Introduction to Stellar Astrophysics.
  9. ^ Burbidge, E.; Burbidge, G.; Fowler, William; Hoyle, F. (1 October 1957). "Synthesis of the Elements in Stars". Reviews of Modern Physics. 29 (4): 547–650. Bibcode:1957RvMP...29..547B. doi:10.1103/RevModPhys.29.547. This value excludes the 2% neutrino energy loss.
  10. ^ Claus E. Rolfs and William S. Rodney, Cauldrons in the Cosmos, The University of Chicago Press, 1988, p. 354.
  11. ^ Bellini, G.; et al. (2 February 2012). "First Evidence of pep Solar Neutrinos by Direct Detection in Borexino". Physical Review Letters. 108 (5): 051302. arXiv:1110.3230. Bibcode:2012PhRvL.108e1302B. doi:10.1103/PhysRevLett.108.051302. PMID 22400925.
  12. ^ Int'l Conference on Neutrino and Dark Matter, Thursday 07 Sept 2006, https://indico.lal.in2p3.fr/getFile.py/access?contribId=s16t1&sessionId=s16&resId=1&materialId=0&confId=a05162 Session 14.
CNO cycle

The CNO cycle (for carbon–nitrogen–oxygen) is one of the two known sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain reaction (pp-chain reaction). Unlike the latter, the CNO cycle is a catalytic cycle. It is dominant in stars that are more than 1.3 times as massive as the Sun.In the CNO cycle, four protons fuse, using carbon, nitrogen, and oxygen isotopes as catalysts, to produce one alpha particle, two positrons and two electron neutrinos. Although there are various paths and catalysts involved in the CNO cycles, all these cycles have the same net result:

4 11H + 2 e− → 42He + 2 e+ + 2 e− + 2 νe + 3 γ + 24.7 MeV → 42He + 2 νe + 3 γ + 26.7 MeVThe positrons will almost instantly annihilate with electrons, releasing energy in the form of gamma rays. The neutrinos escape from the star carrying away some energy. One nucleus goes on to become carbon, nitrogen, and oxygen isotopes through a number of transformations in an endless loop.

The proton–proton chain is more prominent in stars the mass of the Sun or less. This difference stems from temperature dependency differences between the two reactions; pp-chain reaction starts at temperatures around 4×106 K (4 megakelvin), making it the dominant energy source in smaller stars. A self-maintaining CNO chain starts at approximately 15×106 K, but its energy output rises much more rapidly with increasing temperatures so that it becomes the dominant source of energy at approximately 17×106 K.

The Sun has a core temperature of around 15.7×106 K, and only 1.7% of 4He nuclei produced in the Sun are

born in the CNO cycle. The CNO-I process was independently proposed by Carl von Weizsäcker and Hans Bethe in the late 1930s.

Carbon-burning process

The carbon-burning process or carbon fusion is a set of nuclear fusion reactions that take place in the cores of massive stars (at least 8 M ⊙ {\displaystyle {\begin{smallmatrix}M_{\odot }\end{smallmatrix}}} at birth) that combines carbon into other elements. It requires high temperatures (> 5×108 K or 50 keV) and densities (> 3×109 kg/m3).

These figures for temperature and density are only a guide. More massive stars burn their nuclear fuel more quickly, since they have to offset greater gravitational forces to stay in (approximate) hydrostatic equilibrium. That generally means higher temperatures, although lower densities, than for less massive stars. To get the right figures for a particular mass, and a particular stage of evolution, it is necessary to use a numerical stellar model computed with computer algorithms. Such models are continually being refined based on nuclear physics experiments (which measure nuclear reaction rates) and astronomical observations (which include direct observation of mass loss, detection of nuclear products from spectrum observations after convection zones develop from the surface to fusion-burning regions – known as dredge-up events – and so bring nuclear products to the surface, and many other observations relevant to models).

Cosmological lithium problem

In astronomy, the lithium problem, lithium discrepancy or lithium gap refers to the discrepancy between the observed abundance of lithium produced in Big Bang nucleosynthesis and the amount that should theoretically exist. Namely, the most widely-accepted models of the Big Bang suggest that three times as much primordial lithium, in particular lithium-7, should exist. This contrasts with the observed abundance of isotopes of hydrogen (1H and 2H) and helium (3He and 4He) that are consistent with predictions.

Deuterium fusion

Deuterium fusion, also called deuterium burning, is a nuclear fusion reaction that occurs in stars and some substellar objects, in which a deuterium nucleus and a proton combine to form a helium-3 nucleus. It occurs as the second stage of the proton–proton chain reaction, in which a deuterium nucleus formed from two protons fuses with another proton, but can also proceed from primordial deuterium.

Ettore Fiorini

Ettore Fiorini is an Italian experimental particle physicist. He is professor emeritus of nuclear and subnuclear physics at the University of Milano-Bicocca.

Fuel

A fuel is any material that can be made to react with other substances so that it releases energy as heat energy or to be used for work. The concept was originally applied solely to those materials capable of releasing chemical energy but has since also been applied to other sources of heat energy such as nuclear energy (via nuclear fission and nuclear fusion).

The heat energy released by reactions of fuels is converted into mechanical energy via a vishal engine. Other times the heat itself is valued for warmth, cooking, or industrial processes, as well as the illumination that comes with combustion. Fuels are also used in the cells of organisms in a process known as cellular respiration, where organic molecules are oxidized to release usable energy. Hydrocarbons and related oxygen-containing molecules are by far the most common source of fuel used by humans, but other substances, including radioactive metals, are also utilized.

Fuels are contrasted with other substances or devices storing potential energy, such as those that directly release electrical energy (such as batteries and capacitors) or mechanical energy (such as flywheels, springs, compressed air, or water in a reservoir).

GALLEX

GALLEX or Gallium Experiment was a radiochemical neutrino detection experiment that ran between 1991 and 1997 at the Laboratori Nazionali del Gran Sasso (LNGS). This project was performed by an international collaboration of French, German, Italian, Israeli, Polish and American scientists led by the Max-Planck-Institut für Kernphysik Heidelberg. After brief interruption, the experiment was continued under a new name GNO (Gallium Neutrino Observatory) from May 1998 to April 2003.

It was designed to detect solar neutrinos and prove theories related to the Sun's energy creation mechanism. Before this experiment (and the SAGE experiment that ran concurrently), there had been no observation of low energy solar neutrinos.

Helion (chemistry)

A helion is a short name for the naked nucleus of helium, a doubly positively charged helium ion. In practice, helion refers specifically to the nucleus of the helium-3 isotope, consisting of two protons and one neutron. The nucleus of the other stable isotope of helium, helium-4 isotope, which consists of two protons and two neutrons, is specifically called an alpha particle.

This particle is emitted in the decay of tritium, an isotope of hydrogen:

According to CODATA, the mass of a helion particle is 5.006 412 700(62) × 10−27 kg.

Helions are intermediate products in the proton-proton chain reaction in stellar fusion.

Isotopes of helium

Although there are nine known isotopes of helium (2He) (standard atomic weight: 4.002602(2)), only helium-3 (3He) and helium-4 (4He) are stable. All radioisotopes are short-lived, the longest-lived being 6He with a half-life of 806.7 milliseconds. The least stable is 5He, with a half-life of 7.6×10−22 s, although it is possible that 2He has an even shorter half-life.

In the Earth's atmosphere, there is one 3He atom for every million 4He atoms. However, helium is unusual in that its isotopic abundance varies greatly depending on its origin. In the interstellar medium, the proportion of 3He is around a hundred times higher. Rocks from the Earth's crust have isotope ratios varying by as much as a factor of ten; this is used in geology to investigate the origin of rocks and the composition of the Earth's mantle. The different formation processes of the two stable isotopes of helium produce the differing isotope abundances.

Equal mixtures of liquid 3He and 4He below 0.8 K will separate into two immiscible phases due to their dissimilarity (they follow different quantum statistics: 4He atoms are bosons while 3He atoms are fermions). Dilution refrigerators take advantage of the immiscibility of these two isotopes to achieve temperatures of a few millikelvins.

Nuclear chain reaction

A nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, this leading to the possibility of a self-propagating series of these reactions. The specific nuclear reaction may be the fission of heavy isotopes (e.g., uranium-235, 235U). The nuclear chain reaction releases several million times more energy per reaction than any chemical reaction.

Pp1

PP1 may refer to:

Proton–proton chain reaction

Protein phosphatase 1

Constituency PP-1 (Rawalpindi-I) a Constituency of Provincial Assembly of Punjab

Ribonuclease PP1

Roles of chemical elements

This table is designed to show the role(s) performed by each chemical element, in nature and in technology.

Z = Atomic number Sym. = Symbol Per. = Period Gr. = Group

Solar core

The core of the Sun is considered to extend from the center to about 0.2 to 0.25 of

solar radius. It is the hottest part of the Sun and of the Solar System. It has a density of 150 g/cm3 (150 times the density of liquid water) at the center, and a temperature of 15 million kelvins (15 million degrees Celsius, 27 million degrees Fahrenheit). The core is made of hot, dense plasma (ions and electrons), at a pressure estimated at 265 billion bar (3.84 trillion psi or 26.5 petapascals (PPa)) at the center. Due to fusion, the composition of the solar plasma drops from 68-70% hydrogen by mass at the outer core, to 33% hydrogen at the core/Sun center.

The core inside 0.20 of the solar radius contains 34% of the Sun's mass, but only 3.4% of the Sun's volume. Inside 0.24 solar radius, the core generates 99% of the fusion power of the Sun. There are two distinct reactions in which four hydrogen nuclei may eventually result in one helium nucleus: the proton-proton chain reaction – which is responsible for most of the Sun's released energy – and the CNO cycle.

Solar neutrino

Electron neutrinos are produced in the Sun as a product of nuclear fusion. Solar neutrinos constitute by far the largest flux of neutrinos from natural sources observed on Earth, as compared with e.g. atmospheric neutrinos or the diffuse supernova neutrino background.

Stellar core

A stellar core is the extremely hot, dense region at the center of a star. For an ordinary main sequence star, the core region is the volume where the temperature and pressure conditions allow for energy production through thermonuclear fusion of hydrogen into helium. This energy in turn counterbalances the mass of the star pressing inward; a process that self-maintains the conditions in thermal and hydrostatic equilibrium. The minimum temperature required for stellar hydrogen fusion exceeds 107 K (10 MK), while the density at the core of the Sun is over 100 g cm−3. The core is surrounded by the stellar envelope, which transports energy from the core to the stellar atmosphere where it is radiated away into space.

Stellar nucleosynthesis

Stellar nucleosynthesis is the theory explaining the creation (nucleosynthesis) of chemical elements by nuclear fusion reactions between atoms within stars. Stellar nucleosynthesis has occurred continuously since the original creation of hydrogen, helium and lithium during the Big Bang. It is a highly predictive theory that today yields excellent agreement between calculations based upon it and the observed abundances of the elements. It explains why the observed abundances of elements in the universe grow over time and why some elements and their isotopes are much more abundant than others. The theory was initially proposed by Fred Hoyle in 1946, who later refined it in 1954. Further advances were made, especially to nucleosynthesis by neutron capture of the elements heavier than iron, by Margaret Burbidge, Geoffrey Burbidge, William Alfred Fowler and Hoyle in their famous 1957 B2FH paper, which became one of the most heavily cited papers in astrophysics history.

Stars evolve because of changes in their composition (the abundance of their constituent elements) over their lifespans, first by burning hydrogen (main sequence star), then helium (red giant star), and progressively burning higher elements. However, this does not by itself significantly alter the abundances of elements in the universe as the elements are contained within the star. Later in its life, a low-mass star will slowly eject its atmosphere via stellar wind, forming a planetary nebula, while a higher–mass star will eject mass via a sudden catastrophic event called a supernova. The term supernova nucleosynthesis is used to describe the creation of elements during the evolution and explosion of a pre-supernova massive star (12–35 times the mass of the sun). Those massive stars are the most prolific source of new isotopes from carbon (Z = 6) to nickel (Z = 28).

The advanced sequence of burning fuels is driven by gravitational collapse and its associated heating, resulting in the subsequent burning of carbon, oxygen and silicon. However, most of the nucleosynthesis in the mass range A = 28–56 (from silicon to nickel) is actually caused by the upper layers of the star collapsing onto the core, creating a compressional shock wave rebounding outward. The shock front briefly raises temperatures by roughly 50%, thereby causing furious burning for about a second. This final burning in massive stars, called explosive nucleosynthesis or supernova nucleosynthesis, is the final epoch of stellar nucleosynthesis.

A stimulus to the development of the theory of nucleosynthesis was the discovery of variations in the abundances of elements found in the universe. The need for a physical description was already inspired by the relative abundances of isotopes of the chemical elements in the solar system. Those abundances, when plotted on a graph as a function of atomic number of the element, have a jagged sawtooth shape that varies by factors of tens of millions (see history of nucleosynthesis theory). This suggested a natural process that is not random. A second stimulus to understanding the processes of stellar nucleosynthesis occurred during the 20th century, when it was realized that the energy released from nuclear fusion reactions accounted for the longevity of the Sun as a source of heat and light.

Triple-alpha process

The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon.

Turnoff point

The turnoff point for a star refers to the point on the Hertzsprung-Russell diagram where it leaves the main sequence after the exhaustion of its main fuel. It is often referred to as the main sequence turnoff.

By plotting the turnoff point of the stars in star clusters, one can estimate the cluster's age.

Radioactive
decay
Stellar
nucleosynthesis
Other
processes

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