There are numerous discrete processes involved in stellar nucleosynthesis:

--Proton-proton chain
--Carbon-nitrogen-oxygen (CNO) cycle
--Triple-alpha process
--Alpha process
--Carbon fusion
--Oxygen fusion

Fusion of hydrogen into helium in low-mass stars (less than about 1.5 solar masses) occurs mainly through the proton-proton chain. Two hydrogen nuclei fuse to form a deuterium nucleus plus a positron. The deuterium fuses with another hydrogen nucleus to form helium-3, and two helium-3 nuclei then fuse to form a helium-4 nucleus plus two hydrogen nuclei.

In heavier stars, helium is formed via the CNO cycle. A single carbon-12 nucleus undergoes a series of fusion reactions with hydrogen nuclei, producing nitrogen and oxygen before a final fusion reaction yields a carbon-12 nucleus (completing the cycle) plus a helium-4 nucleus.

The triple-alpha process fuses helium into carbon. Two helium-4 nuclei fuse to form beryllium-8, which in turn fuses with another helium-4 nucleus to form carbon-12.

In the alpha process, carbon-12 fuses with helium-4 to form oxygen-16, which then fuses with another helium-4 nucleus to form neon-20. Successive helium-4 fusions produce magnesium-24, silicon-28, and so on up to nickel-56 (which is unstable and decays into iron-56).

Elements heavier than helium can also fuse directly. Two carbon-12 nuclei can fuse, with a variety of possible products including neon-20, sodium-23, magnesium-23, and magnesium-24. Two oxygen-16 nuclei can fuse to form various isotopes of magnesium, silicon, phosphorus, and sulfur.

Additional processes take place in supernova explosions:

--R-process
--Rp-process

In supernova explosions, heavier elements are formed through the successive capture of neutrons (via the R-process) and protons (Rp-process) by iron nuclei and their heavier successors. There are no specific reaction chains, and the final mix of heavy elements can be variable.

Note that there is yet another fusion process, the S-process of neutron capture, which is believed to operate in the cores of stars on the asymptotic giant branch (AGB stars) of the H-R diagram. S-process fusion absorbs energy rather than releasing it; however, the process is slow, and the energy loss is not enough to cause a core collapse (as occurs in supernovae when fusion reactions stop releasing enough energy to support the star against gravity).
Source(s):
http://www.absoluteastronomy.com/topics/Stellar_nucleosynthesis
http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html
http://www.absoluteastronomy.com/topics/CNO_cycle
http://www.absoluteastronomy.com/topics/Triple-alpha_process
http://en.wikipedia.org/wiki/Carbon_burning_process
http://en.wikipedia.org/wiki/Neon_burning_process
http://en.wikipedia.org/wiki/Oxygen_burning_process
http://www.absoluteastronomy.com/topics/Supernova_nucleosynthesis

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