S-process

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 the rate of neutron capture by atomic nuclei is slow relative to the rate of radioactive beta-minus decay. A stable isotope captures another neutron; but a radioactive isotope decays to its stable daughter before the next neutron is captured. This process produces stable isotopes by moving along the valley of beta stability 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 S-process differs from the more rapid R-process of neutron-capture by its slow rate of neutron captures.

History
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, this 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 what 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. But 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 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, but rather has a ledge-precipice structure. A series of papers in the 1970s by 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. 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, and by 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:


 * {| border="0"


 * align="right" | 13C + 4He
 * &rarr;
 * 16O + n
 * align="right" | 22Ne + 4He
 * &rarr;
 * 25Mg + n
 * }
 * 25Mg + n
 * }



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 site of the main component are low-mass Asymptotic Giant Branch stars. An excellent short discussion and illuminating figure of how both neutron sources operate in complicated pulsation cycles within the AGB stars can be found in Science magazine. The weak component of the S-process, on the other hand, synthesizes S-process isotopes of elements from the iron group up to Sr and Y, and takes place at the end of He- and C-burning in massive stars. These stars will become supernovae at their demise and spew those s isotopes into interstellar space.

The S-process is often mathematically treated using the so-called local approximation, which gives a theoretical model of elemental abundances based on the assumption of constant neutron flux in a star, so that the ratio of abundances is inversely proportional to the ratio of neutron-capture cross-sections for different isotopes. This approximation is - as the name indicates - only valid locally, meaning for isotopes of similar mass number.

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:

209Bi captures a neutron, producing 210Bi, which decays to 210Po by &beta;- decay. 210Po in turn decays to 206Pb by &alpha; decay.


 * $$\mathrm{{}^2{}^{09}_{83}Bi} + n^0 \rightarrow \mathrm{{}^2{}^{10}_{83}Bi} + \gamma$$
 * $$\mathrm{{}^2{}^{10}_{83}Bi}      \rightarrow \mathrm{{}^2{}^{10}_{84}Po} + e^- + \bar{\nu}_e\,$$
 * $$\mathrm{{}^2{}^{10}_{84}Po}      \rightarrow \mathrm{{}^2{}^{06}_{82}Pb} + \mathrm{^{4}_{2}He}$$

206Pb then captures three neutrons, producing 209Pb, which decays to 209Bi by &beta;- decay, restarting the cycle.


 * $$\mathrm{{}^2{}^{06}_{82}Pb} + 3n^0 \rightarrow \mathrm{{}^2{}^{09}_{82}Pb}$$
 * $$\mathrm{{}^2{}^{09}_{82}Pb}       \rightarrow \mathrm{{}^2{}^{09}_{83}Bi} + e^- + \bar{\nu}_e\,$$

The net result of this cycle therefore is that 4 neutrons are converted into one alpha particle, two electrons, two anti-electron neutrinos and gamma radiation:


 * $$4n^0 \rightarrow \mathrm{^{4}_{2}He} + 2e^- + 2\bar{\nu}_e\, + \gamma$$

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. 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 than 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.