Nuclear transmutation is the conversion of one chemical element or an isotope into another chemical element. Because any element (or isotope of one) is defined by its number of protons (and neutrons) in its atoms, i.e. in the atomic nucleus, nuclear transmutation occurs in any process where the number of protons or neutrons in the nucleus is changed.
Natural transmutation by stellar nucleosynthesis in the past created most of the heavier chemical elements in the known existing universe, and continues to take place to this day, creating the vast majority of the most common elements in the universe, including helium, oxygen and carbon. Most stars carry out transmutation through fusion reactions involving hydrogen and helium, while much larger stars are also capable of fusing heavier elements up to iron late in their evolution.
Elements heavier than iron, such as gold or lead, are created through elemental transmutations that can only naturally occur in supernovae. As stars begin to fuse heavier elements, substantially less energy is released from each fusion reaction. Reactions that produce elements heavier than iron are endothermic and unable to generate the energy required to maintain stable fusion inside the star.
One type of natural transmutation observable in the present occurs when certain radioactive elements present in nature spontaneously decay by a process that causes transmutation, such as alpha or beta decay. An example is the natural decay of potassium-40 to argon-40, which forms most of the argon in the air. Also on Earth, natural transmutations from the different mechanisms of natural nuclear reactions occur, due to cosmic ray bombardment of elements (for example, to form carbon-14), and also occasionally from natural neutron bombardment (for example, see natural nuclear fission reactor).
Artificial transmutation may occur in machinery that has enough energy to cause changes in the nuclear structure of the elements. Such machines include particle accelerators and tokamak reactors. Conventional fission power reactors also cause artificial transmutation, not from the power of the machine, but by exposing elements to neutrons produced by fission from an artificially produced nuclear chain reaction. For instance, when a uranium atom is bombarded with slow neutrons, fission takes place. This releases, on average, 3 neutrons and a large amount of energy. The released neutrons then cause fission of other uranium atoms, until all of the available uranium is exhausted. This is called a chain reaction.
The term transmutation dates back to alchemy. Alchemists pursued the philosopher's stone, capable of chrysopoeia – the transformation of base metals into gold. While alchemists often understood chrysopoeia as a metaphor for a mystical, or religious process, some practitioners adopted a literal interpretation, and tried to make gold through physical experiment. The impossibility of the metallic transmutation had been debated amongst alchemists, philosophers and scientists since the Middle Ages. Pseudo-alchemical transmutation was outlawed and publicly mocked beginning in the fourteenth century. Alchemists like Michael Maier and Heinrich Khunrath wrote tracts exposing fraudulent claims of gold making. By the 1720s, there were no longer any respectable figures pursuing the physical transmutation of substances into gold.Antoine Lavoisier, in the 18th century, replaced the alchemical theory of elements with the modern theory of chemical elements, and John Dalton further developed the notion of atoms (from the alchemical theory of corpuscles) to explain various chemical processes. The disintegration of atoms is a distinct process involving much greater energies than could be achieved by alchemists.
It was first consciously applied to modern physics by Frederick Soddy when he, along with Ernest Rutherford, discovered that radioactive thorium was converting itself into radium in 1901. At the moment of realization, Soddy later recalled, he shouted out: "Rutherford, this is transmutation!" Rutherford snapped back, "For Christ's sake, Soddy, don't call it transmutation. They'll have our heads off as alchemists."
Rutherford and Soddy were observing natural transmutation as a part of radioactive decay of the alpha decay type. The first artificial transmutation was accomplished in 1925 by Patrick Blackett, a research fellow working under Rutherford, with the transmutation of nitrogen into oxygen, using alpha particles directed at nitrogen 14N + ? -> 17O + p.  Rutherford had shown in 1919 that a proton (he called it a hydrogen atom) was emitted from alpha bombardment experiments but he had no information about the residual nucleus. Blackett's 1921-1924 experiments provided the first experimental evidence of an artificial nuclear transmutation reaction. Blackett correctly identified the underlying integration process and the identity of the residual nucleus. In 1932, a fully artificial nuclear reaction and nuclear transmutation was achieved by Rutherford's colleagues John Cockcroft and Ernest Walton, who used artificially accelerated protons against lithium-7 to split the nucleus into two alpha particles. The feat was popularly known as "splitting the atom," although it was not the modern nuclear fission reaction discovered in 1938 by Otto Hahn, Lise Meitner and their assistant Fritz Strassmann in heavy elements.
Later in the twentieth century the transmutation of elements within stars was elaborated, accounting for the relative abundance of heavier elements in the universe. Save for the first five elements, which were produced in the Big Bang and other cosmic ray processes, stellar nucleosynthesis accounted for the abundance of all elements heavier than boron. In their 1957 paper Synthesis of the Elements in Stars,William Alfred Fowler, Margaret Burbidge, Geoffrey Burbidge, and Fred Hoyle explained how the abundances of essentially all but the lightest chemical elements could be explained by the process of nucleosynthesis in stars.
It transpired that, under true nuclear transmutation, it is far easier to turn gold into lead than the reverse reaction, which was the one the alchemists had ardently pursued. Nuclear experiments have successfully transmuted lead into gold, but the expense far exceeds any gain. It would be easier to convert lead into gold via neutron capture and beta decay by leaving lead in a nuclear reactor for a long period of time.
Glenn Seaborg produced several thousand atoms of gold from bismuth, but at a net loss.
More information on gold synthesis, see Synthesis of precious metals.
The Big Bang is thought to be the origin of the hydrogen (including all deuterium) and helium in the universe. Hydrogen and helium together account for 98% of the mass of ordinary matter in the universe, while the other 2% makes up everything else. The Big Bang also produced small amounts of lithium, beryllium and perhaps boron. More lithium, beryllium and boron were produced later, in a natural nuclear reaction, cosmic ray spallation.
Stellar nucleosynthesis is responsible for all of the other elements occurring naturally in the universe as stable isotopes and primordial nuclide, from carbon to uranium. These occurred after the Big Bang, during star formation. Some lighter elements from carbon to iron were formed in stars and released into space by asymptotic giant branch (AGB) stars. These are a type of red giant that "puffs" off its outer atmosphere, containing some elements from carbon to nickel and iron. All elements with atomic weight greater than 64 atomic mass units are produced in supernova stars by means of neutron capture, which sub-divides into two processes: r-process and s-process.
The Solar System is thought to have condensed approximately 4.6 billion years before the present, from a cloud of hydrogen and helium containing heavier elements in dust grains formed previously by a large number of such stars. These grains contained the heavier elements formed by transmutation earlier in the history of the universe.
All of these natural processes of transmutation in stars are continuing today, in our own galaxy and in others. Stars fuse hydrogen and helium into heavier and heavier elements in order to produce energy. For example, the observed light curves of supernova stars such as SN 1987A show them blasting large amounts (comparable to the mass of Earth) of radioactive nickel and cobalt into space. However, little of this material reaches Earth. Most natural transmutation on the Earth today is mediated by cosmic rays (such as production of carbon-14) and by the radioactive decay of radioactive primordial nuclides left over from the initial formation of the solar system (such as potassium-40, uranium and thorium), plus the radioactive decay of products of these nuclides (radium, radon, polonium, etc.). See decay chain.
Transmutation of transuranium elements (TRUs, i.e. actinides minus actinium to uranium) such as the isotopes of plutonium (about 1wt% in the Light Water Reactors' used nuclear fuel (UNF)) or the minor actinides (MAs, i.e. neptunium, americium, and curium, about 0.1wt% each in LWRs' UNF) has the potential to help solve some problems posed by the management of radioactive waste by reducing the proportion of long-lived isotopes it contains. (This does not rule out the need for a Deep Geological Repository (DGR) for High radioactive Level Waste (HLW).) When irradiated with fast neutrons in a nuclear reactor, these isotopes can undergo nuclear fission, destroying the original actinide isotope and producing a spectrum of radioactive and nonradioactive fission products.
Ceramic targets containing actinides can be bombarded with neutrons to induce transmutation reactions to remove the most difficult long-lived species. These can consist of actinide-containing solid solutions such as (Am,Zr)N, (Am,Y)N, (Zr,Cm)O2, (Zr,Cm,Am)O2, (Zr,Am,Y)O2 or just actinide phases such as AmO2, NpO2, NpN, AmN mixed with some inert phases such as MgO, MgAl2O4, (Zr,Y)O2, TiN and ZrN. The role of non-radioactive inert phases is mainly to provide stable mechanical behaviour to the target under neutron irradiation.
There are issues with this P&T (partitioning and transmutation) strategy however:
The new study led by Satoshi Chiba at Tokyo Tech (called "Method to Reduce Long-lived Fission Products by Nuclear Transmutations with Fast Spectrum Reactors") shows that effective transmutation of LLFPs can be achieved in fast spectrum reactors without the need for isotope separation. This can be achieved by adding a yttrium deuteride (YD2) moderator.
For instance, plutonium can be reprocessed into MOX fuels and transmuted in standard reactors. The heavier elements could be transmuted in fast reactors, but probably more effectively in a subcritical reactor which is sometimes known as an energy amplifier and which was devised by Carlo Rubbia. Fusion neutron sources have also been proposed as well suited.
There are several fuels that can incorporate plutonium in their initial composition at beginning of cycle (BOC) and have a smaller amount of this element at the end of cycle (EOC). During the cycle, plutonium can be burnt in a power reactor, generating electricity. This process is not only interesting from a power generation standpoint, but also due to its capability of consuming the surplus weapons grade plutonium from the weapons program and plutonium resulting of reprocessing UNF.
Mixed oxide fuel (MOX) is one of these. Its blend of oxides of plutonium and uranium constitutes an alternative to the low enriched uranium (LEU) fuel predominantly used in LWRs. Since uranium is present in MOX, although plutonium will be burnt, second generation plutonium will be produced through the radiative capture of U-238 and the two subsequent beta minus decays.
Fuels with plutonium and thorium are also an option. In these, the neutrons released in the fission of plutonium are captured by Th-232. After this radiative capture, Th-232 becomes Th-233, which undergoes two beta minus decays resulting in the production of the fissile isotope U-233. The radiative capture cross section for Th-232 is more than three times that of U-238, yielding a higher conversion to fissile fuel than that from U-238. Due to the absence of uranium in the fuel, there is no second generation plutonium produced, and the amount of plutonium burnt will be higher than in MOX fuels. However, U-233, which is fissile, will be present in the UNF. Weapons-grade and reactor-grade plutonium can be used in plutonium-thorium fuels, with weapons-grade plutonium being the one that shows a bigger reduction in the amount of Pu-239.
Isotopes of plutonium and other actinides tend to be long-lived with half-lives of many thousands of years, whereas radioactive fission products tend to be shorter-lived (most with half-lives of 30 years or less). From a waste management viewpoint, transmutation (or "burning" or "incineration") of actinides eliminates a very long-term radioactive hazard and replaces it with a much shorter-term one.
It is important to understand that the threat posed by a radioisotope is influenced by many factors including the physical (e.g. heat -infrared photon radiation-, which is an advantage for the storage or disposal af radioactive waste), chemical and biological properties of the element. For instance caesium has a relatively short biological half-life (1 to 4 months) while strontium and radium both have very long biological half-lives. As a result, strontium-90 and radium are much more able to cause harm than caesium-137 when a given activity is ingested. 
Many of the actinides are very radiotoxic because they have long biological half-lives and are alpha emitters. In transmutation the intention is to convert the actinides into fission products. The fission products are very radioactive, but the majority of the activity will decay away within a short time. The most worrying short-lived fission products are those that accumulate in the body, such as iodine-131 which accumulates in the thyroid gland, but it is hoped[by whom?] that by good design of the nuclear fuel and transmutation plant that such fission products can be isolated from humans and their environment and allowed to decay. In the medium term the fission products of highest concern are strontium-90 and caesium-137; both have a half-life of about 30 years. The caesium-137 is responsible for the majority of the external gamma dose experienced by workers in nuclear reprocessing plants and, in 2005, to workers at the Chernobyl site. When these medium-lived isotopes have decayed almost completely (usually after 10 half-lives) the remaining isotopes will pose a much smaller threat.
Some radioactive fission products can be converted into shorter-lived radioisotopes by transmutation. Transmutation of all fission products with half-life greater than one year is studied in Grenoble, with varying results.
Sr-90 and Cs-137, with half-lives of about 30 years, are the largest radiation (including heat) emitters in used nuclear fuel on a scale of decades to ~305 years (Sn-121m is insignificant because of the low yield), and are not easily transmuted because they have low neutron absorption cross sections. Instead, they should simply be stored until they decay. Given that this length of storage is necessary, the fission products with shorter half-lives can also be stored until they decay.
The next longer-lived fission product is Sm-151, which has a half-life of 90 years, and is such a good neutron absorber that most of it is transmuted while the nuclear fuel is still being used; however, effectively transmuting the remaining Sm-151 in nuclear waste would require separation from other isotopes of samarium. Given the smaller quantities and its low-energy radioactivity, Sm-151 is less dangerous than Sr-90 and Cs-137 and can also be left to decay for ~970 years.
Finally, there are 7 long-lived fission products. They have much longer half-lives in the range 211,000 years to 15.7 million years. Two of them, Tc-99 and I-129, are mobile enough in the environment to be potential dangers, are free or mostly free of mixture with stable isotopes of the same element, and have neutron cross sections that are small but adequate to support transmutation. Also, Tc-99 can substitute for U-238 in supplying Doppler broadening for negative feedback for reactor stability. Most studies of proposed transmutation schemes have assumed 99Tc, 129I, and TRUs as the targets for transmutation, with other fission products, activation products, and possibly reprocessed uranium remaining as waste.
Of the remaining 5 long-lived fission products, Se-79, Sn-126 and Pd-107 are produced only in small quantities (at least in today's thermal neutron, U-235-burning light water reactors) and the last two should be relatively inert. The other two, Zr-93 and Cs-135, are produced in larger quantities, but also not highly mobile in the environment. They are also mixed with larger quantities of other isotopes of the same element.