The s-process or slow-neutron-capture-process is a nucleosynthesis process that occurs at relatively low neutron density and intermediate temperature conditions in stars. Under these conditions heavier nuclei are created by neutron capture, increasing the atomic weight of the nucleus by one. A neutron in the new nucleus decays by beta-minus decay to a proton, creating a nucleus of higher atomic number. The rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay, hence the name. This process produces stable isotopes by moving along the valley of beta-decay stable isobars in the chart of isotopes. The S-process produces approximately half of the isotopes of the elements heavier than iron, and therefore plays an important role in the galactic chemical evolution. The more rapid R-process differs from the S-process by its faster rate of neutron capture of more than one neutron before beta-decay takes place.
The S-process was seen to be needed from the relative abundances of isotopes of heavy elements and from a newly published table of abundances by Hans Suess and Harold Urey in 1956. Among other things, these data showed abundance peaks for strontium, barium, and lead, which, according to quantum mechanics and the nuclear shell model, are particularly stable nuclei, much like the noble gases are chemically inert. This implied that some abundant nuclei must be created by slow neutron capture, and it was only a matter of determining how other nuclei could be accounted for by such a process. A table apportioning the heavy isotopes between S-process and R-process was published in the famous B2FH review paper in 1957. There it was also argued that the S-process occurs in red giant stars. In a particularly illustrative case, the element technetium, whose longest half-life is 4.2 million years, had been discovered in S-, M-, and N-type stars in 1952. Since these stars were thought to be billions of years old, the presence of technetium in their outer atmospheres was taken as evidence of its recent creation there, probably unconnected with the nuclear fusion in the deep interior of the star that provides its power.
A calculable model for creating the heavy isotopes from iron seed nuclei in a time-dependent manner was not provided until 1961. That work showed that the large overabundances of barium observed by astronomers in certain red-giant stars could be created from iron seed nuclei if the total fluence (number of neutrons per unit area) of neutrons was appropriate. It also showed that no one single value for the fluence could account for the observed S-process abundances, but that a wide range of fluences is required. The numbers of iron seed nuclei that were exposed to a given fluence must decrease as the fluence becomes stronger. This work also showed that the curve of the product of neutron-capture cross section times abundance is not a smoothly falling curve, as B2FH had sketched, but rather has a ledge-precipice structure. A series of papers in the 1970s by Donald D. Clayton based on the assumption of an exponentially declining neutron fluence as a function of the number of iron seed so exposed became the standard model of the S-process and remained so until the details of AGB-star nucleosynthesis became advanced enough that they became a standard model based on the stellar structure models. Important series of measurements of neutron-capture cross sections were reported from Oak Ridge National Lab in 1965 and by Karlsruhe Nuclear Physics Center in 1982 and subsequently. These placed the S-process on the firm quantitative basis that it enjoys today.
The S-process in stars 
The S-process is believed to occur mostly in asymptotic giant branch stars. In contrast to the R-process which is believed to occur over time scales of seconds in explosive environments, the S-process is believed to occur over time scales of thousands of years, passing decades between neutron captures. The extent to which the s-process moves up the elements in the chart of isotopes to higher mass numbers is essentially determined by the degree to which the star in question is able to produce neutrons. The quantitative yield is also proportional to the amount of iron in the star's initial abundance distribution. Iron is the "starting material" (or seed) for this neutron capture – beta-minus decay sequence of synthesizing new elements.
The main neutron source reactions are:
One distinguishes the main and the weak s-process component. The main component produces heavy elements beyond Sr and Y, and up to Pb in the lowest metallicity stars. The production sites of the main component are low-mass Asymptotic Giant Branch stars. The main component relies on the 13C neutron source above. The weak component of the S-process, on the other hand, synthesizes S-process isotopes of elements from iron group seed nuclei to 58Fe on up to Sr and Y, and takes place at the end of helium- and Carbon-burning in massive stars. It employs primarily the 22Ne neutron source. These stars will become supernovae at their demise and spew those s isotopes into interstellar gas.
The S-process is sometimes approximated over a small mass region using the so-called "local approximation", by which the ratio of abundances is inversely proportional to the ratio of neutron-capture cross-sections for nearby isotopes on the s-process path. This approximation is – as the name indicates – only valid locally, meaning for isotopes of nearby mass numbers, but it is invalid at magic numbers where the ledge-precipice structure dominates.
Because of the relatively low neutron fluxes expected to occur during the S-process (on the order of 105 to 1011 neutrons per cm2 per second), this process does not have the ability to produce any of the heavy radioactive isotopes such as thorium or uranium. The cycle that terminates the S-process is:
The process thus terminates in bismuth, the heaviest "stable" element. (Bismuth is actually slightly radioactive, but with a half-life so long—a billion times the present age of the universe—that it is effectively stable over the lifetime of any existing star.)
The S-process measured in stardust 
Stardust is one component of cosmic dust. Individual solid grains from various long-dead stars that existed before the solar system are found in meteorites, where they have been preserved. Meteoriticists usually refer to them as Presolar grains. The origin of these grains is demonstrated by laboratory measurements of extremely unusual isotopic abundance ratios within the grain. The results give new insight into astrophysics. Silicon-carbide (SiC) grains condense in the atmospheres of AGB stars and thus trap the isotopes of that star. Because the AGB stars are the main site of the S-process in the galaxy, the heavy elements in the SiC grains are virtually pure S-process isotopes. This fact has been demonstrated repeatedly by sputtering-ion mass spectrometer studies of these presolar grains. Several surprising results have shown that the ratio of S-process and R-process abundances is somewhat different from that which was previously assumed. It has also been shown with trapped isotopes of krypton and xenon that the S-process abundances in the stellar atmospheres change with time or from star to star, presumably with the strength of neutron fluence or perhaps the temperature. This is a frontier of S-process studies today.
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