Creation of elements beyond carbon through alpha process

The alpha process, also known as the alpha ladder, is one of two classes of nuclear fusion reactions by which stars convert helium into heavier elements, the other being the triple-alpha process.[1]

The triple-alpha process consumes only helium, and produces carbon. After enough carbon has accumulated, further reactions below take place, listed below. Each step only consumes helium and the product of the previous reaction.

${\displaystyle {\begin{array}{ll}{\ce {~{}_{6}^{12}C\ ~~+{}_{2}^{4}He\ ->~{}_{8}^{16}O\ \ ~+\gamma ~,))&E={\mathsf {7.16\ MeV))\\{\ce {~{}_{8}^{16}O\ ~~+{}_{2}^{4}He\ ->{}_{10}^{20}Ne\ \ +\gamma ~,))&E={\mathsf {4.73\ MeV))\\{\ce ((}_{10}^{20}Ne\ ~+{}_{2}^{4}He\ ->{}_{12}^{24}Mg\ +\gamma ~,))&E={\mathsf {9.32\ MeV))\\{\ce ((}_{12}^{24}Mg\ +{}_{2}^{4}He\ ->{}_{14}^{28}Si\ ~~+\gamma ~,))&E={\mathsf {9.98\ MeV))\\{\ce ((}_{14}^{28}Si\ ~~+{}_{2}^{4}He\ ->{}_{16}^{32}S\ \ ~~~+\gamma ~,))&E={\mathsf {6.95\ MeV))\\{\ce ((}_{16}^{32}S\ ~~~+{}_{2}^{4}He\ ->{}_{18}^{36}Ar\ ~\ +\gamma ~,))&E={\mathsf {6.64\ MeV))\\{\ce ((}_{18}^{36}Ar\ ~+{}_{2}^{4}He\ ->{}_{20}^{40}Ca\ \ +\gamma ~,))&E={\mathsf {7.04\ MeV))\\{\ce ((}_{20}^{40}Ca\ +{}_{2}^{4}He\ ->{}_{22}^{44}Ti\ ~~+\gamma ~,))&E={\mathsf {5.13\ MeV))\\{\ce ((}_{22}^{44}Ti\ ~+{}_{2}^{4}He\ ->{}_{24}^{48}Cr\ ~+\gamma ~,))&E={\mathsf {7.70\ MeV))\\{\ce ((}_{24}^{48}Cr\ +{}_{2}^{4}He\ ->{}_{26}^{52}Fe\ ~\ +\gamma ~,))&E={\mathsf {7.94\ MeV))\\{\ce ((}_{26}^{52}Fe\ +{}_{2}^{4}He\ ->{}_{28}^{56}Ni\ ~\ +\gamma ~,))&E={\mathsf {8.00\ MeV))\end{array))}$

The energy produced each the reaction, E , is primarily in the gamma ray (γ), with a small amount taken by the byproduct element, as added momentum.

It is a common misconception that the above sequence ends at ${\displaystyle \,{}_{28}^{56}\mathrm {Ni} \,}$ (or ${\displaystyle \,{}_{26}^{56}\mathrm {Fe} \,}$, which is a decay product of ${\displaystyle \,{}_{28}^{56}\mathrm {Ni} \,}$[2]) because it is the most tightly bound nuclide - i.e., having the highest nuclear binding energy per nucleon, and production of heavier nuclei would require energy (be endothermic) instead of releasing it (exothermic). ${\displaystyle \,{}_{28}^{62}\mathrm {Ni} \,}$ (Nickel-62) is actually the most tightly bound nuclide in terms of binding energy[3] (though 56Fe has a lower energy or mass per nucleon). The reaction 56Fe + 4He → 60Ni   is actually exothermic, but nonetheless the sequence does effectively end at iron. The sequence stops before producing ${\displaystyle \,{}_{28}^{56}\mathrm {Ni} \,}$ because conditions in stellar interiors cause the competition between photodisintegration and the alpha process to favor photodisintegration around iron.[2][4] This leads to more ${\displaystyle \,{}_{28}^{56}\mathrm {Ni} \,}$ being produced than ${\displaystyle \,{}_{28}^{62}\mathrm {Ni} ~.}$

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 (atomic number N > 10 ), due to the increasing Coulomb barrier.

## 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 alpha nuclides.

Logarithm of the relative energy output (ε) of proton–proton (p-p), CNO, and triple-α fusion processes at different temperatures (T). The dashed line shows the combined energy generation of the p-p and CNO processes within a star.

The status of oxygen (O) is contested – some authors[which?] consider it an alpha element, while others do not. O is surely an alpha element in low-metallicity Population II stars: It is produced in Type II supernovas, and its enhancement is well correlated with an enhancement of other alpha process elements.

Sometimes C and N are considered alpha process elements since, like O, 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 process starts producing significant amounts of alpha elements (including C, N, & O). So just the presence of C, N, or O 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".

### Special notation for relative abundance

The abundance of total alpha elements in stars is usually expressed in a logarithmic manner, with a square bracket notation:

${\displaystyle \left[{\frac {\alpha }{\,{\ce {Fe))\,))\right]~\equiv ~\log _{10}{\left(\,{\frac {N_{\mathrm {E} \alpha )){\,N_((\ce {Fe))}\,))\,\right)_{\mathsf {Star))}-\log _{10}{\left({\frac {N_{\mathrm {E} \alpha )){\,N_((\ce {Fe))}\,))\,\right)_{\mathsf {Sun))}~,}$

where ${\displaystyle \,N_{\mathrm {E} \alpha }\,}$ is the number of alpha elements per unit volume, and ${\displaystyle \,N_((\ce {Fe))}\,}$ is the number of iron nuclei per unit volume. It is for the purpose of calculating the number ${\displaystyle \,N_{\mathrm {E} \alpha }\,}$ 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. Type II supernovae mainly synthesize oxygen and the alpha-elements (Ne, Mg, Si, S, Ar, Ca, and Ti) while Type Ia supernovae mainly produce elements of the iron peak (Ti, V, Cr, Mn, Fe, Co, and Ni), but also alpha-elements.

## References

1. ^ Narlikar, Jayant V. (1995). From Black Clouds to Black Holes. World Scientific. p. 94. ISBN 978-9810220334.
2. ^ a b Fewell, M.P. (1995-07-01). "The atomic nuclide with the highest mean binding energy". American Journal of Physics. 63 (7): 653–658. Bibcode:1995AmJPh..63..653F. doi:10.1119/1.17828. ISSN 0002-9505.
3. ^ Nave, Carl R. (c. 2017) [c. 2001]. "The most tightly bound nuclei". Physics and Astronomy. hyperphysics.phy-astr.gsu.edu. HyperPhysics pages. Georgia State University. Retrieved 2019-02-21.
4. ^ Burbidge, E. Margaret; Burbidge, G.R.; Fowler, William A.; Hoyle, F. (1957-10-01). "Synthesis of the elements in stars". Reviews of Modern Physics. 29 (4): 547–650. Bibcode:1957RvMP...29..547B. doi:10.1103/RevModPhys.29.547.