Alpha process

 ( Nuclear Fusion ) 

The alpha process, also known as alpha capture or the alpha ladder, is one of two classes of nuclear fusion reactions by which stars convert helium into heavier chemical element. The other class is a cycle of reactions called the triple-alpha process, which consumes only helium, and produces carbon.

The alpha process most commonly occurs in massive stars and during Supernova.

Both processes are preceded by hydrogen fusion, which produces the helium that fuels both the triple-alpha process and the alpha ladder processes. After the triple-alpha process has produced enough carbon, the alpha-ladder begins and fusion reactions of increasingly heavy elements take place, in the order listed below. Each step only consumes the product of the previous reaction and helium. The later-stage reactions which are able to begin in any particular star, do so while the prior stage reactions are still under way in outer layers of the star.

$\backslash begin\{array\}\{ll\}$

\ce{ ~{}_6^{12}C\ ~~+ {}_2^4He\ -> ~{}_{8}^{16}O\ \ ~+ \gamma~,}& E=\mathsf{7.16\ MeV} \\ \ce{ ~{}_8^{16}O\ ~~+ {}_2^4He\ -> {}_{10}^{20}Ne\ \ + \gamma~,}& E=\mathsf{4.73\ MeV} \\ \ce{ {}_{10}^{20}Ne\ ~+ {}_2^4He\ -> {}_{12}^{24}Mg\ + \gamma~,}& E=\mathsf{9.32\ MeV} \\ \ce{ {}_{12}^{24}Mg\ + {}_2^4He\ -> {}_{14}^{28}Si\ ~~+ \gamma~,}& E=\mathsf{9.98\ MeV} \\ \ce{ {}_{14}^{28}Si\ ~~+ {}_2^4He\ -> {}_{16}^{32}S\ \ ~~~+ \gamma~,}& E=\mathsf{6.95\ MeV} \\ \ce{ {}_{16}^{32}S\ ~~~+ {}_2^4He\ -> {}_{18}^{36}Ar\ ~\ + \gamma~,}& E=\mathsf{6.64\ MeV} \\ \ce{ {}_{18}^{36}Ar\ ~+ {}_2^4He\ -> {}_{20}^{40}Ca\ \ + \gamma~,}& E=\mathsf{7.04\ MeV} \\ \ce{ {}_{20}^{40}Ca\ + {}_2^4He\ -> {}_{22}^{44}Ti\ ~~+ \gamma~,}& E=\mathsf{5.13\ MeV} \\ \ce{ {}_{22}^{44}Ti\ ~+ {}_2^4He\ -> {}_{24}^{48}Cr\ ~+ \gamma~,}& E=\mathsf{7.70\ MeV} \\ \ce{ {}_{24}^{48}Cr\ + {}_2^4He\ -> {}_{26}^{52}Fe\ ~\ + \gamma~,}& E=\mathsf{7.94\ MeV} \\ \ce{ {}_{26}^{52}Fe\ + {}_2^4He\ -> {}_{28}^{56}Ni\ ~\ + \gamma~,}& E=\mathsf{8.00\ MeV} \end{array} The energy produced by each reaction, , is mainly in the form of (), with a small amount taken by the By-product element, as added momentum. It is a common misconception that the above sequence ends at $\backslash ,\; \{\}\_\{28\}^\{56\}\backslash mathrm\{Ni\}\; \backslash ,$ (or $\backslash ,\; \{\}\_\{26\}^\{56\}\backslash mathrm\{Fe\}\; \backslash ,$, which is a decay product of $\backslash ,\; \{\}\_\{28\}^\{56\}\backslash mathrm\{Ni\}\; \backslash ,$) because it is the most tightly bound nuclide – i.e., the nuclide with the highest nuclear binding energy per nucleon – and production of heavier nuclei would consume energy (be endothermic) instead of release it (exothermic). $\backslash ,\; \{\}\_\{28\}^\{62\}\backslash mathrm\{Ni\}\; \backslash ,$ (Nickel-62) is actually the most tightly bound nuclide in terms of binding energy (though $\{\}^\{56\}\backslash textrm\{Fe\}$ has a lower energy or mass per nucleon). The reaction $\{\}^\{56\}\backslash textrm\{Fe\}+\{\}^\{4\}\backslash textrm\{He\}\backslash rightarrow\; \{\}^\{60\}\backslash textrm\{Ni\}$ is actually exothermic, and indeed adding alphas continues to be exothermic all the way to $\backslash \; \{\}\_\{50\}^\{100\}\backslash mathrm\{Sn\}\backslash$, but nonetheless the sequence does effectively end at iron. The sequence stops before producing elements heavier than nickel because conditions in stellar interiors cause the competition between photodisintegration and the alpha process to favor photodisintegration around iron. This leads to more $\backslash ,\; \{\}\_\{28\}^\{56\}\backslash mathrm\{Ni\}\; \backslash ,$ being produced than $\backslash ,\; \{\}\_\{28\}^\{62\}\backslash mathrm\{Ni\}\; ~.$

All these reactions have a very low rate at the temperatures and densities in stars and therefore do not contribute significant energy to a star's total output. They occur even less easily with elements heavier than neon () due to the increasing Coulomb barrier.

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Alpha process elements

Alpha process elements (or alpha elements) are so-called since their most abundant isotopes are integer multiples of four – the mass of the helium nucleus (the alpha particle). These isotopes are called .

• The stable alpha elements are: carbon, oxygen, neon, magnesium, silicon, and sulfur.
• The elements argon and calcium are "observationally stable". They are synthesized by alpha capture prior to the silicon fusing stage, that leads to
• silicon and calcium are purely alpha process elements.
• magnesium can be separately consumed by proton capture reactions.

The status of oxygen (oxygen) is contested – some authors

Houjun Mo (2025). 9780521857932, Cambridge University Press. ISBN 9780521857932

consider it an alpha element, while others do not. oxygen is surely an alpha element in low-metallicity Population II stars: It is produced in Type II supernovae, and its enhancement is well correlated with an enhancement of other alpha process elements.

Sometimes carbon and nitrogen are considered alpha process elements since, like oxygen, they are synthesized in nuclear alpha-capture reactions, but their status is ambiguous: Each of the three elements is produced (and consumed) by the CNO cycle, which can proceed at temperatures far lower than those where the alpha-ladder processes start producing significant amounts of alpha elements (including carbon, nitrogen, & oxygen). So just the presence of carbon, nitrogen, or oxygen in a star does not a clearly indicate that the alpha process is actually underway – hence reluctance of some astronomers to (unconditionally) call these three "alpha elements".

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Production in stars The alpha process generally occurs in large quantities only if the star is sufficiently massive – more massive than about 10 . These stars contract as they age, increasing core temperature and density to high enough levels to enable the alpha process. Requirements increase with atomic mass, especially in later stages – sometimes referred to as silicon burning – and thus most commonly occur in supernovae. Type II supernovae mainly synthesize oxygen and the alpha-elements (neon, magnesium, silicon, sulfur, argon, calcium, and titanium) while Type Ia supernovae mainly produce elements of the iron peak (titanium, vanadium, chromium, manganese, iron, cobalt, and nickel). Sufficiently massive stars can synthesize elements up to and including the iron peak solely from the hydrogen and helium that initially comprises the star.

Typically, the first stage of the alpha process (or alpha-capture) follows from the helium-burning stage of the star once helium becomes depleted; at this point, free $\{\}\_6^\{12\}\backslash textrm\{C\}$ capture helium to produce $\{\}\_\{8\}^\{16\}\backslash textrm\{O\}$.

Donald D. Clayton (1983). 9780226109534, University of Chicago Press. ISBN 9780226109534

This process continues after the core finishes the helium burning phase as a shell around the core will continue burning helium and Convection into the core. The second stage (neon burning) starts as helium is freed by the photodisintegration of one $\{\}\_\{10\}^\{20\}\backslash textrm\{Ne\}$ atom, allowing another to continue up the alpha ladder. Silicon burning is then later initiated through the photodisintegration of $\{\}\_\{14\}^\{28\}\backslash textrm\{Si\}$ in a similar fashion; after this point, the $\backslash ,\; \{\}\_\{28\}^\{56\}\backslash mathrm\{Ni\}\; \backslash ,$peak discussed previously is reached. The supernova shock wave produced by stellar collapse provides ideal conditions for these processes to briefly occur.

During this terminal heating involving photodisintegration and rearrangement, nuclear particles are converted to their most stable forms during the supernova and subsequent ejection through, in part, alpha processes. Starting at $\{\}\_\{22\}^\{44\}\backslash textrm\{Ti\}$ and above, all the product elements are radioactive and will therefore decay into a more stable isotope; for instance, $\backslash ,\; \{\}\_\{28\}^\{56\}\backslash mathrm\{Ni\}\; \backslash ,$ is formed and decays into $\{\}\_\{26\}^\{56\}\backslash textrm\{Fe\}$.

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Special notation for relative abundance

The abundance of total alpha elements in stars is usually expressed in terms of , with astronomers customarily using a square bracket notation:

$\backslash left\; ~\backslash equiv~\; \backslash log\_\{10\}\{\backslash left(\backslash ,\; \backslash frac\{\; N\_\{\backslash mathrm\{E\}\backslash alpha\}\; \}\{\backslash ,\; N\_\backslash ce\{Fe\}\; \backslash ,\}\; \backslash ,\backslash right)\_\backslash mathsf\{Star\}\}\; -\; \backslash log\_\{10\}\{\backslash left(\backslash frac\{\; N\_\{\backslash mathrm\{E\}\backslash alpha\}\; \}\{\backslash ,\; N\_\backslash ce\{Fe\}\; \backslash ,\}\backslash ,\backslash right)\_\backslash mathsf\{Sun\}\; \}\; ~,$

where $\backslash ,\; N\_\{\backslash mathrm\{E\}\backslash alpha\}\; \backslash ,$ is the number of alpha elements per unit volume, and $\backslash ,\; N\_\backslash ce\{Fe\}\; \backslash ,$ is the number of iron nuclei per unit volume. It is for the purpose of calculating the number $\backslash ,\; N\_\{\backslash mathrm\{E\}\backslash alpha\}\; \backslash ,$ that which elements are to be considered "alpha elements" becomes contentious. Theoretical galactic evolution models predict that early in the universe there were more alpha elements relative to iron.

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Further reading

Categories: Nuclear Fusion, Nucleosynthesis

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