Proton-proton reaction

Schematic sequence of the proton-proton I chain

The proton-proton reaction ( pp reaction , proton-proton chain ) is one of two fusion reactions of the so-called hydrogen burning , through which hydrogen is converted into helium in stars .

In stars with masses up to about 1.5 solar masses ( M _☉ ), the proton-proton reaction plays a more important role in energy conversion than the CNO cycle . They generate more than 98% of the sun's luminosity .

The strongly exothermic character of the fusion stems from the fact that the end product helium has a mass about 0.7% less than the hydrogen particles that entered the reaction ( mass defect ). The difference is released as energy due to the equivalence of mass and energy ( ) . ${\displaystyle E=mc^{2}}$

The proton-proton reaction has the lowest temperature requirements of all fusion reactions occurring in stars. ( Fusion reactions take place in brown dwarfs even below this limit, but they are not stars.) It can take place in stars with a core temperature of more than 3 million Kelvin . At these temperatures, all the atomic nuclei involved are completely ionized , i. H. without electron shell .

In the proton-proton reaction, the fusion rate is proportional to the 4th power of the temperature. Thus, an increase in temperature by 5% causes an increase in energy release of 22%.

Start reactions

The first step of the proton-proton reaction: two protons fuse to form a deuterium nucleus. At the same time a positron and an electron neutrino are emitted.

The second step of the proton-proton reaction: a proton and a deuterium nucleus fuse to form a helium nucleus ³ He while at the same time releasing a gamma quantum.

The third step in the proton-proton I chain: two ³ He nuclei fuse to form ⁴ He and in the process release two protons.

First merge two hydrogen nuclei ¹ H ( proton ) to a deuterium core ² H, wherein by converting a proton to a neutron , a positron e ⁺ and an electron-neutrino ν _e are free:

${\displaystyle \mathrm {{}^{1}H+{}^{1}H\to {}^{2}H+e^{+}+\nu _{e}+0{,}42\;MeV} }$

The nuclear reaction rate is very small and thus determines the rate of the overall reaction. The reason is that the electrostatic repulsion usually keeps the positively charged protons at a distance, there is no bound state for the diproton and the creation of the neutron as a process of weak interaction is only possible at very small distances. Even according to the Maxwell-Boltzmann distribution, very rare, particularly high-energy impacts are not sufficient according to the classical theory. Only through the quantum mechanical tunnel effect do the protons come close enough, but with a very low probability: In the sun it takes an average of 1.4 · 10 ¹⁰  years for a certain proton to react with another, which is why the sun has a long lifespan .

The neutrino carries an average of 0.267 MeV from the relatively low energy release of the reaction. Since these light particles can leave the stellar matter almost unhindered, this amount of energy is lost to the star.

The resulting positron annihilates immediately with an electron e ^- , i.e. that is, they react with each other and are completely converted into energy. The mass of both partners is released as energy in the form of two gamma quanta γ.

${\displaystyle \mathrm {e^{+}+e^{-}\to 2\gamma +1{,}022\;MeV} }$

The resulting deuterium can then react with another proton, creating the light helium isotope ³ He :

${\displaystyle \mathrm {{}^{2}H+{}^{1}H\to {}^{3}He+\gamma +5{,}493\;MeV} }$

This process does not depend on the weak interaction, and the binding energy is large. The reaction rate is therefore much higher: in the sun, the deuterium produced by the initial reaction only lives for about 1.4 seconds. The deuterium present in star formation can already react in much smaller celestial bodies, from a size of around 12 Jupiter's masses. This marks the lower limit for a brown dwarf.

Main follow-up reactions

There are now essentially three different reaction chains in which the helium isotope ⁴ He (which predominates in nature) is finally generated. They set in at different temperatures. The reactions described below occur with varying frequency in the sun:

• Proton-Proton I chain: 83.30%
• Proton-Proton II chain: 16.68%
• Proton-Proton III chain: 0.02%

Proton-Proton I chain

After an average of 10 ⁶  years, two helium nuclei fuse ³ He to ⁴ He ( α-particles ), releasing two protons. They are available for further reaction steps.

${\displaystyle \mathrm {{}^{3}He+{}^{3}He\to {}^{4}He+2\,{}^{1}H+12{,}86\;MeV} }$

The complete reaction chain up to this point, in which the reactions listed under start reaction are run through twice in order to create the necessary ³ He particles for the last fusion, sets a net energy - that is, minus the neutrino energy - of

${\displaystyle \mathrm {2\cdot (0{,}42\;MeV+1{,}022\;MeV+5{,}493\;MeV-0{,}267\;MeV)+12{,}86\;MeV=\mathbf {26{,}196\;MeV} } }$

free (≈ 4.20 · 10 ⁻¹²  J ). The proton-proton I chain prevails at temperatures of 10-14 million Kelvin. Very little ⁴ He is produced below this temperature .

Proton-Proton II chain

Proton-Proton II chain

In the proton-proton II chain, a previously generated helium nucleus ⁴ He serves as a catalyst to produce another from ³ He.

${\displaystyle {\begin{aligned}{\rm {{}^{3}He+{}^{4}He}}&\to {\rm {{}^{7}Be+\gamma +1{,}59\;MeV}}\\{\rm {{}^{7}Be+e^{-}}}&\to {\rm {{}^{7}Li+\nu _{e}}}\\{\rm {{}^{7}Li+{}^{1}H}}&\to {\rm {2\,{}^{4}He+17{,}35\;MeV}}\end{aligned}}}$

The proton-proton II chain runs primarily at temperatures of 14-23 million Kelvin.

89.7% of the neutrinos that are generated in the sun by the second reaction have an energy of around 0.863 MeV, while the remaining 10.3% have around 0.386 MeV, depending on whether the lithium produced is ⁷ Li is in the ground state or in the excited state.

The third reaction step can also take place without the first two reactions with lithium , which the star noticed when it was formed ( lithium burning ). As a result, the lithium concentration in stars decreases.

Proton-Proton III chain

Proton-Proton III chain

Here, too, a helium core ⁴ He acts as a catalyst.

${\displaystyle {\begin{aligned}{\rm {{}^{3}He+{}^{4}He}}&\to {\rm {{}^{7}Be+\gamma +1{,}59\;MeV}}\\{\rm {{}^{7}Be+{}^{1}H}}&\to {\rm {{}^{8}B+\gamma +0{,}14\;MeV}}\\{\rm {{}^{8}B}}&\to {\rm {{}^{8}Be+e^{+}+\nu _{e}+18\;MeV}}\\{\rm {{}^{8}Be}}&\leftrightarrow {\rm {2\,{}^{4}He}}\end{aligned}}}$

The proton-proton III chain is predominant at temperatures above 23 million Kelvin.

Although this reaction is not the sun's main source of energy, the temperature of which is not high enough for it, it does play an important role in explaining the solar neutrino problem, as it generates neutrinos with relatively high energies of up to 14.06 MeV (about 6.735 on average MeV), the so-called ⁸ B neutrinos. Such neutrinos can be detected more easily in terrestrial neutrino detectors than the low-energy ones .

More reactions

In addition to the three reactions mentioned above, there are two more rare reactions.

Proton-electron-proton reaction

In the proton-electron-proton reaction, or pep reaction for short, two protons and one electron fuse to form a deuterium nucleus.

${\displaystyle \mathrm {{}^{1}H+e^{-}+{}^{1}H\to {}^{2}H+\nu _{e}} }$

This is why the reaction occurs so rarely - in the sun the competing reaction ¹ H + ¹ H → ² H + e ⁺ + ν _e takes place about 400 times as often - because here three particles have to meet almost simultaneously. The energy of the generated neutrinos is, however, significantly higher at around 1.445 MeV.

Helium-proton reaction

The helium-proton reaction (Hep reaction for short) occurs even more rarely, the direct fusion of helium ³ He with a proton to form ⁴ He.

${\displaystyle \mathrm {{}^{3}He+{}^{1}H\to {}^{4}He+\nu _{e}+e^{+}+18{,}77\;MeV} }$

The neutrinos emitted during this reaction can have an energy of up to 18.778 MeV; on average they have an energy of 9.628 MeV.

ash

The "ash" of the hydrogen burning is helium ⁴ He, which can serve as a starting material for the helium burning that may start later .

See also

• Nucleosynthesis

Web links

Commons : Proton-Proton Reaction  - collection of pictures, videos, and audio files

• tim-thompson.com: Solar Fusion & Neutrinos

Individual evidence

1. ^ G. Bellini et al .: First Evidence of pep Solar Neutrinos by Direct Detection in Borexino . In: Physical Review Letters . tape 108 , no. 5 , 2012, p. 051302-2 , doi : 10.1103 / PhysRevLett.108.051302 .
2. ^ John N. Bahcall, MH Pinsonneault, Sarbani Basu: Solar Models: Current Epoch and Time Dependences, Neutrinos, and Helioseismological Properties . In: Astrophysical Journal . tape 555 , no. 2 , 2001, p. 990-1012, here: 995 , doi : 10.1086 / 321493 .
3. ^ Alfred Weigert , Heinrich Johannes Wendker , Lutz Wisotzki: Astronomy and astrophysics: a basic course . 5th, updated and exp. Edition. Wiley-VCH, Weinheim 2009, ISBN 978-3-527-40793-4 , pp. 215 .
4. ↑ Eric G. Adelberger et al .: Solar fusion cross sections. II. The pp chain and CNO cycles . In: Reviews of Modern Physics . tape 83 , no. 1 , 2011, p. 195–245, here: 226 , doi : 10.1103 / RevModPhys.83.195 .
5. ↑ ^{a b c d e} John N. Bahcall: Gallium solar neutrino experiments: Absorption cross sections, neutrino spectra, and predicted event rates. In: Physical Review C . Volume 56, No. 6, 1997, pp. 3391-3409, doi : 10.1103 / PhysRevC.56.3391 .
6. ↑ ^{a b} Eric G. Adelberger et al .: Solar fusion cross sections. II. The pp chain and CNO cycles . In: Reviews of Modern Physics . tape 83 , no. 1 , 2011, p. 195–245, here: 201 , doi : 10.1103 / RevModPhys.83.195 .