Nucleosynthesis is the process of creating new atomic nuclei from preexisting nucleons (protons and neutrons). The primordial nucleons themselves were formed from the quark-gluon plasma of the Big Bang as it cooled below ten million degrees. A few minutes afterward, starting with only protons and neutrons, nuclei up to lithium and beryllium (both with mass number 7) were formed but only in relatively small amounts. This first process of primordial nucleosynthesis may also be called nucleogenesis. The subsequent nucleosynthesis of the elements (including all carbon, all oxygen, etc.) occurs primarily in stars either by nuclear fusion or nuclear fission.
The first ideas were that the chemical elements were created at the beginnings of the universe, but no successful picture could be found. Arthur Stanley Eddington first suggested in 1920 that stars obtain their energy by fusing hydrogen to helium, but this idea was not generally accepted because it lacked nuclear mechanisms. In the years immediately before World War II Hans Bethe first provided those nuclear mechanisms by which hydrogen is fused into helium. However, neither of these early works on stellar power addressed the origin of the elements heavier than helium. Fred Hoyle's original work on nucleosynthesis of heavier elements in stars occurred just after World War II (see Ref. list). This work attributed production of heavier elements from hydrogen in stars during the nuclear evolution of their compositions. Hoyle's work explained how the abundances of the elements increased with time as the galaxy aged. Subsequently, Hoyle's picture was expanded during the 1960s by creative contributions by William A. Fowler, Alistair G. W. Cameron, and Donald D. Clayton, and then by many others. The creative 1957 review paper by E. M. Burbidge, G. R. Burbidge, Fowler and Hoyle (see Ref. list) is a well-known summary of the state of the field in 1957. That paper defined new processes for changing one heavy nucleus into others within individual stars, processes that could be documented by astronomers.
There are a number of astrophysical processes which are believed to be responsible for nucleosynthesis in the universe. The majority of these occur within the hot matter inside stars. The successive nuclear fusion processes which occur inside stars are known as hydrogen burning (via the proton-proton chain or the CNO cycle), helium burning, carbon burning, neon burning, oxygen burning and silicon burning. These processes are able to create elements up to iron and nickel, the region of the isotopes having the highest binding energy per nucleon. Heavier elements can be assembled within stars by a neutron capture process known as the s process or in explosive environments, such as supernovae, by a number of processes. Some of the more important of these include the r process which involves rapid neutron captures, the rp process which involves rapid proton captures and the p process (sometimes known as the gamma process) which involves photodisintegration of existing nuclei.
The four major types of nucleosynthesis
Big Bang nucleosynthesis
Big Bang nucleosynthesis occurred within the first three minutes of the universe and is responsible for much of the abundance ratios of 1H (protium), 2H (deuterium), 3He (helium-3), and 4He (helium-4), in the universe . Although 4He continues to be produced by other mechanisms (such as stellar fusion and alpha decay) and trace amounts of 1H continue to be produced by spallation and certain types of radioactive decay (proton emission and neutron emission), most of the mass of these isotopes in the universe, and all but the insignificant traces of the 3He and deuterium in the universe produced by rare processes such as cluster decay, are thought to have been produced in the Big Bang. The nuclei of these elements, along with some 7Li, and 7Be are believed to have been formed when the universe was between 100 and 300 seconds old, after the primordial quark-gluon plasma froze out to form protons and neutrons. Because of the very short period in which Big Bang nucleosynthesis occurred before being stopped by expansion and cooling, no elements heavier than lithium could be formed. (Elements formed during this time were in the plasma state, and did not cool to the state of neutral atoms until much later).
Stellar nucleosynthesisStellar nucleosynthesis occurs in stars during the process of stellar evolution. It is responsible for generation of elements from carbon to calcium by nuclear fusion processes. Stars are the nuclear furnaces in which H and He are fused into heavier nuclei, a process which occurs by proton-proton chain in stars cooler than the Sun, and by the CNO cycle in stars hotter than the Sun.
Of particular importance is carbon, because its formation from He is a bottleneck in the entire process. Carbon is produced by the triple-alpha process in all stars. Carbon is also the main element used in the production of free neutrons within the stars, giving rise to the s process which involves the slow absorption of neutrons to produce elements heavier than iron and nickel (57Fe and 62Ni). Carbon and other elements formed by this process are also fundamental to life.<p> The products of stellar nucleosynthesis are generally distributed into the universe as planetary nebulae, or through the solar wind.<p>The first direct proof that nucleosynthesis occurs in stars was the detection of technetium in the atmosphere of a red giant in the early 1950s. Because technetium is radioactive, with halflife much less than the age of the star, its abundance must reflect its creation within that star during its lifetime. Less dramatic, but equally convincing evidence is of large overabundances of specific stable elements in a stellar atmosphere. An historically important case was observation of barium abundances some 20-50 times greater than in unevolved stars, which is evidence of the operation of the s process within that star. Many modern proofs appear in the isotopic composition of Stardust, solid grains that condensed from the gases of individual stars and which have been extracted from meteorites. Stardust is one component of cosmic dust. The measured isotopic compositions demonstrate many aspects of nucleosynthesis within the stars from which the stardust grains condensed 
This includes supernova nucleosynthesis, and produces the elements heavier than iron by an intense burst of nuclear reactions that typically last but seconds during the explosion of the supernova core. In explosive environments of supernovae, the elements between silicon and nickel are synthesized by fast fusion. Also in supernovae further nucleosynthesis processes can occur, such as the r process , in which the most neutron-rich isotopes of elements heavier than nickel are produced by rapid absorption of free neutrons released during the explosions. It is responsible for our natural cohort of radioactive elements, such as uranium and thorium, as well as the most neutron-rich isotopes of each heavy element. <p> The rp process involves the rapid absorption of free protons as well as neutrons, but its role is less certain. <p> Explosive nucleosynthesis occurs too rapidly for radioactive decay to increase the number of neutrons, so that many abundant isotopes having equal even numbers of protons and neutrons are synthesized. These include 44Ti , 48Cr , 52Fe , and 56Ni , all of which decay after the explosion to create abundant stable isobars at each atomic weight. Many such decays are accompanied by emission of gamma-ray lines capable of identifying the isotope that has just been created in the explosion. <p> The most convincing proof of explosive nucleosynthesis in supernovae occurred in 1987 when gamma-ray lines were detected emerging from supernova 1987A. Gamma ray lines identifying 56Co and 57Co , whose radioactive halflives limit their age to about a year, proved that 56Fe and 57Fe were created by radioactive parents. This nuclear astronomy was predicted in 1969  as a way to confirm explosive nucleosynthesis of the elements, and that prediction played an important role in the planning for NASA's successful Compton Gamma-Ray Observatory. Other proofs of explosive nucleosynthesis are found within the stardust grains that condensed within the interiors of supernovae as they expanded and cooled. Stardust grains are one component of cosmic dust. In particular, radioactive 44Ti was measured to be very abundant within supernova stardust grains at the time they condensed during the supernova expansion , confirming a 1975 prediction for identifying supernova stardust. Other unusual isotopic ratios within those grains reveal specific aspects of explosive nucleosynthesis.
Cosmic ray spallation
Cosmic ray spallation produces some of the lightest elements present in the universe (though not significant deuterium). Most notably spallation is believed to be responsible for the generation of almost all of 3He and the elements lithium, beryllium and boron (some lithium-7 and beryllium-7 are thought to have been produced in the Big Bang). The spallation process results from the impact of cosmic rays (mostly fast protons) against the interstellar medium. These impacts fragment carbon, nitrogen and oxygen nuclei present in the cosmic rays, and also these elements being struck by protons in cosmic rays. <p> Beryllium and boron are not significantly produced in stellar fusion processes, because the instability of any 8Be formed from two 4He nuclei prevents simple 2-particle reaction building-up of these elements.
Theories of nucleosynthesis are tested by calculating isotope abundances and comparing with observed results. Isotope abundances are typically calculated by calculating the transition rates between isotopes in a network. Often these calculations can be simplified as a few key reactions control the rate of other reactions.
-  Big Bang Java Calculator v1.1, Craig Hogan, Luis Mendoza
- S. Paul W. Merrill (1952). "Spectroscopic Observations of Stars of Class". THE ASTROPHYSICAL JOURNAL. 116: 21.
- D. D. Clayton and L. R. Nittler (2004). "Astrophysics with Presolar Stardust". ANNUAL REVIEW OF ASTRONOMY AND ASTROPHYSICS. 42: 39–78. doi:10.1146/annurev.astro.42.053102.134022.
- D. D. Clayton, S.A. Colgate, G.J. Fishman (1969). "Gamma ray lines from young supernova remnants". THE ASTROPHYSICAL JOURNAL. 155: 75–82. doi:10.1086/149849.
- D. D. Clayton, L. R.Nittler (2004). "Astrophysics with Presolar stardust". ANNUAL REVIEWS OF ASTRONOMY AND ASTROPHYSICS. 42: 39–78. doi:10.1146/annurev.astro.42.053102.134022.
- E. M. Burbidge, G. R. Burbidge, W. A. Fowler, F. Hoyle, Synthesis of the Elements in Stars, Rev. Mod. Phys. 29 (1957) 547 (article at the Physical Review Online Archive (subscription required)).
- F. Hoyle, Monthly Notices Roy. Astron. Soc. 106, 366 (1946)
- F. Hoyle, Astrophys. J. Suppl. 1, 121 (1954)
- D. D. Clayton, "Principles of Stellar Evolution and Nucleosynthesis", McGraw-Hill, 1968; University of Chicago Press, 1983, ISBN 0-226-10952-6
- C. E. Rolfs, W. S. Rodney, Cauldrons in the Cosmos, Univ. of Chicago Press, 1988, ISBN 0-226-72457-3.
- D. D. Clayton, "Handbook of Isotopes in the Cosmos", Cambridge University Press, 2003, ISBN 0 521 823811.