View source for S-process

{{Short description|Nucleosynthesis pathway}}
{{DISPLAYTITLE:''s''-process}}
{{nuclear physics}}
The '''slow neutron-capture process''', or '''''s''-process''', is a series of [[nuclear reactions|reactions]] in [[nuclear astrophysics]] that occur in stars, particularly [[asymptotic giant branch stars]]. The ''s''-process is responsible for the creation ([[nucleosynthesis]]) of approximately half the [[Atomic nucleus|atomic nuclei]] [[Heavy metal (chemical element)|heavier than iron]].

In the ''s''-process, a [[seed nucleus]] undergoes [[neutron capture]] to form an [[isotope]] with one higher [[atomic mass]]. If the new isotope is [[stable nuclide|stable]], a series of increases in mass can occur, but if it is [[unstable nucleus|unstable]], then [[beta decay]] will occur, producing an element of the next higher [[atomic number]]. The process is ''slow'' (hence the name) in the sense that there is sufficient time for this [[radioactive decay]] to occur before another neutron is captured. A series of these reactions produces stable isotopes by moving along the [[valley of stability|valley]] of [[beta-decay stable isobars]] in the [[table of nuclides]].

A range of elements and isotopes can be produced by the ''s''-process, because of the intervention of [[alpha decay]] steps along the reaction chain. The relative abundances of elements and isotopes produced depends on the source of the neutrons and how their flux changes over time. Each branch of the ''s''-process reaction chain eventually terminates at a cycle involving [[lead]], [[bismuth]], and [[polonium]].

The ''s''-process contrasts with the [[r-process|''r''-process]], in which successive neutron captures are ''rapid'': they happen more quickly than the beta decay can occur. The ''r''-process dominates in environments with higher fluxes of [[free neutron]]s; it produces heavier elements and more neutron-rich isotopes than the ''s''-process. Together the two processes account for most of the relative [[abundance of chemical elements]] heavier than iron.

==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 [[Abundance of the chemical elements|abundances]] by [[Hans Suess]] and [[Harold Urey]] in 1956.<ref>{{cite journal |last1=Suess |first1=H. E. |last2=Urey |first2=H. C. |year=1956 |title=Abundances of the Elements |journal=[[Reviews of Modern Physics]] |volume=28 |issue=1 |pages=53–74 |bibcode=1956RvMP...28...53S |doi=10.1103/RevModPhys.28.53}}</ref> 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 gas]]es are chemically [[Inert gas|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|''r''-process]] was published in the famous [[B2FH paper|B<sup>2</sup>FH review paper]] in 1957.<ref name="Synthesis of the Elements in Stars">
{{cite journal
 |last1=Burbidge |first1=E. M.
 |last2=Burbidge |first2=G. R.
 |last3=Fowler |first3=W. A.
 |last4=Hoyle |first4=F.
 |date=1957
 |title=Synthesis of the Elements in Stars
 |journal=[[Reviews of Modern Physics]]
 |volume=29 |issue=4 |pages=547–650
 |bibcode=1957RvMP...29..547B
 |doi=10.1103/RevModPhys.29.547 |doi-access=free
}}</ref> There it was also argued that the ''s''-process occurs in [[red giant]] stars. In a striking confirmation, the element [[technetium]], with no isotope having a half-life longer than 4.2 million years, had been discovered in [[S-type star|S-type]] and [[carbon stars]] in 1952 by [[Paul W. Merrill]].<ref>{{cite journal|author=Merrill, P. W.|year=1952|title=Technetium in the stars|journal=Science|volume=115|issue=2992|page=484|doi=10.1126/science.115.2992.479 |pmid=17792758 |bibcode=1952Sci...115..479M }}</ref><ref>{{cite web|title=An Introduction to the Evidence for Stellar Nucleosynthesis|author=George Sivulka|date=8 March 2017|access-date=3 May 2018|publisher=Stanford University|url=http://large.stanford.edu/courses/2017/ph241/sivulka1/}}</ref> Since these stars were thought to be billions of years old, the presence of technetium in their outer atmospheres was evidence of its recent creation, with no necessary connection to the nuclear fusion in the deep interior of the star that provides its power.

[[File:Nucleosynthesis periodic table.svg|thumb|500px|Periodic table showing the cosmogenic origin of each element. The elements heavier than iron with origins in ''dying low-mass stars'' are typically those produced by the ''s''-process, which is characterized by slow neutron diffusion and capture over long periods in such stars.]]

A calculable model for creating the heavy isotopes from iron seed nuclei in a time-dependent manner was not provided until 1961.<ref>
{{cite journal
 |last1=Clayton |first1=D. D.
 |last2=Fowler |first2=W. A.
 |last3=Hull |first3=T. E.
 |last4=Zimmerman |first4=B. A.
 |year=1961
 |title=Neutron capture chains in heavy element synthesis
 |journal=[[Annals of Physics]]
 |volume=12 |issue=3 |pages=331–408
 |bibcode=1961AnPhy..12..331C
 |doi=10.1016/0003-4916(61)90067-7
}}</ref> 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 neutron flux (number of neutrons per unit area) was appropriate. It also showed that no one single value for neutron flux could account for the observed ''s''-process abundances, but that a wide range is required. The numbers of iron seed nuclei that were exposed to a given flux must decrease as the flux 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|B<sup>2</sup>FH]] had sketched, but rather has a ''ledge-precipice structure''. A series of papers<ref>
{{cite journal
 |last1=Clayton |first1=D. D.
 |last2=Rassbach |first2=M. E.
 |year=1967
 |title=Termination of the ''s''-process
 |journal=[[The Astrophysical Journal]]
 |volume=148 |page=69
 |bibcode=1967ApJ...148...69C |bibcode-access=free
 |doi=10.1086/149128 |doi-access=free
}}</ref><ref>
{{cite book
 |last=Clayton |first=D. D.
 |year=1968
 |chapter=Distribution of neutron-source strengths for the ''s''-process
 |editor1-last=Arnett |editor1-first=W. D.
 |editor2-last=Hansen |editor2-first=C. J.
 |editor3-last=Truran |editor3-first=J. W.
 |editor4-last=Cameron  |editor4-first=A. G. W.
 |title=Nucleosynthesis
 |pages=225–240
 |publisher=[[Gordon and Breach]]
}}</ref><ref>
{{cite journal
 |last1=Peters |first1=J. G.
 |last2=Fowler |first2=W. A.
 |last3=Clayton |first3=D. D.
 |year=1972
 |title=Weak ''s''-process Irradiations
 |journal=[[The Astrophysical Journal]]
 |volume=173 |page=637
 |bibcode=1972ApJ...173..637P |bibcode-access=free
 |doi=10.1086/151450 |doi-access=free
}}</ref><ref>
{{cite journal
 |last1=Clayton |first1=D. D.
 |last2=Newman |first2=M. J.
 |year=1974
 |title=''s''-process Studies: Exact Solution to a Chain Having Two Distinct Cross-Section Values
 |journal=[[The Astrophysical Journal]]
 |volume=192 |page=501
 |bibcode=1974ApJ...192..501C |bibcode-access=free
 |doi=10.1086/153082 |doi-access=free
}}</ref><ref>
{{cite journal
 |last1=Clayton |first1=D. D.
 |last2=Ward |first2=R. A.
 |year=1974
 |title=''s''-process Studies: Exact Evaluation of an Exponential Distribution of Exposures
 |journal=[[The Astrophysical Journal]]
 |volume=193 |page=397
 |bibcode=1974ApJ...193..397C |bibcode-access=free
 |doi=10.1086/153175 |doi-access=free
}}</ref><ref>
{{cite journal
 |last1=Ward |first1=R. A.
 |last2=Newman |first2=M. J.
 |last3=Clayton |first3=D. D.
 |year=1976
 |title=''s''-process Studies: Branching and the Time Scale
 |journal=[[The Astrophysical Journal Supplement Series]]
 |volume=31 |page=33
 |bibcode=1976ApJS...31...33W |bibcode-access=free
 |doi=10.1086/190373 |doi-access=free
}}</ref> in the 1970s by [[Donald D. Clayton]] utilizing an exponentially declining neutron flux as a function of the number of iron nuclei exposed became the standard model of the ''s''-process and remained so until the details of [[Asymptotic Giant Branch|AGB-star]] nucleosynthesis became sufficiently advanced that they became a standard model for ''s''-process element formation based on stellar structure models. Important series of measurements of neutron-capture cross sections were reported from [[Oak Ridge National Lab]] in 1965<ref>
{{cite journal
 |last1=Macklin |first1=R. L.
 |last2=Gibbons |first2=J. H.
 |year=1965
 |title=Neutron Capture Data at Stellar Temperatures
 |journal=[[Reviews of Modern Physics]]
 |volume=37 |issue=1 |pages=166–176
 |bibcode=1965RvMP...37..166M
 |doi=10.1103/RevModPhys.37.166
}}</ref> and by [[Karlsruhe Institute of Technology]]'s Nuclear Physics Center in 1982<ref>
{{cite journal
 |last1=Kaeppeler |first1=F.
 |last2=Beer |first2=H. 
 |last3=Wisshak |first3=K.
 |last4=Clayton |first4=D. D.
 |last5=Macklin |first5=R. L.
 |last6=Ward |first6=R. A.
 |year=1982
 |title=''s''-process studies in the light of new experimental cross sections
 |journal=[[The Astrophysical Journal]]
 |volume=257 |pages=821–846
 |bibcode=1982ApJ...257..821K |bibcode-access=free
 |doi=10.1086/160033 |doi-access=free
}}</ref> and subsequently, these placed the ''s''-process on the firm quantitative basis that it enjoys today.{{cn|date=October 2019}}

==In stars==

The ''s''-process is believed to occur mostly in [[asymptotic giant branch]] stars, seeded by iron nuclei left by a supernova during a previous generation of 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 number]]s is essentially determined by the degree to which the star in question is able to produce [[neutron]]s. The quantitative yield is also proportional to the amount of iron in the star's initial abundance distribution.{{dubious|The number of neutrons produced should not be proportional to this.|date=August 2025}} [[Iron]] is the "starting material" (or seed) for this neutron capture-beta minus decay sequence of synthesizing new elements.<ref name=Reifarth2010>{{cite journal |last=Reifarth |first=R. |title=The s-process – overview and selected developments |journal=Journal of Physics: Conference Series |volume=202 |date=2010 |number=12022 |article-number=012022 |doi=10.1088/1742-6596/202/1/012022|doi-access=free |bibcode=2010JPhCS.202a2022R }}</ref>

The main [[neutron source]] reactions are:

<!-- Autogenerated using Phykiformulae 0.12 [[User:SkyLined#Phykiformulae]]
C-13 + He-4 -> O-16 + n
Ne-22 + He-4 -> Mg-25 + n
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|{{nuclide|link=yes|carbon|13}}&nbsp;||+&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||→&nbsp;||{{nuclide|link=yes|oxygen|16}}&nbsp;||+&nbsp;||{{SubatomicParticle|link=yes|Neutron}}
|- style="height:2em;"
|{{nuclide|link=yes|neon|22}}&nbsp;||+&nbsp;||{{nuclide|link=yes|helium|4}}&nbsp;||→&nbsp;||{{nuclide|link=yes|magnesium|25}}&nbsp;||+&nbsp;||{{SubatomicParticle|link=yes|Neutron}}
|}

[[Image:S-process-elem-Ag-to-Sb.svg|thumb|right|400 px|The ''s''-process acting in the range from [[silver|Ag]] to [[antimony|Sb]]]]

One distinguishes the main and the weak ''s''-process component. The main component produces heavy elements beyond [[Strontium|Sr]] and [[Yttrium|Y]], and up to [[Lead|Pb]] in the lowest metallicity stars. The production sites of the main component are low-mass asymptotic giant branch stars.<ref>
{{cite journal
 |last=Boothroyd |first=A. I.
 |year=2006 
 |title=Heavy elements in stars
 |journal=[[Science (journal)|Science]]
 |volume=314 |issue=5806 |pages=1690–1691
 |doi=10.1126/science.1136842
 |pmid=17170281
|s2cid=116938510
 }}</ref> The main component relies on the <sup>13</sup>C neutron source above.<ref>
{{cite journal
 |last1=Busso |first1=M.
 |last2=Gallino |first2=R.
 |last3=Wasserburg |first3=G. J.
 |year=1999
 |title=Nucleosynthesis in Asymptotic Giant Branch Stars: Relevance for Galactic Enrichment and Solar System Formation
 |journal=[[Annual Review of Astronomy and Astrophysics]]
 |volume=37 |issue=1 |pages=239–309
 |bibcode=1999ARA&A..37..239B
 |doi=10.1146/annurev.astro.37.1.239
|url=https://authors.library.caltech.edu/1194/1/BUSaraa99.pdf
 }}</ref> The weak component of the ''s''-process, on the other hand, synthesizes ''s''-process isotopes of elements from iron group seed nuclei to <sup>58</sup>Fe on up to Sr and Y, and takes place at the end of [[helium fusion|helium]]- and [[carbon-burning process|carbon-burning]] in massive stars. It employs primarily the <sup>22</sup>Ne neutron source. These stars will become supernovae at their demise and spew those ''s''-process 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.

==Termination of the s-process==

[[File:S-R-processes-atomic-mass-201-to-210.svg|thumb|right|250px|Chart representing the final part of the ''s''-process. Red horizontal lines with a circle in their right ends represent [[neutron capture]]s; blue arrows pointing up-left represent [[beta decay]]s; green arrows pointing down-left represent [[alpha decay]]s; cyan/light-green arrows pointing down-right represent [[electron capture]]s.]]
Because of the relatively low [[neutron flux]]es expected to occur during the ''s''-process (on the order of 10<sup>5</sup> to 10<sup>11</sup> neutrons per cm<sup>2</sup> 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 includes the stable isotopes Pb-206,207,208 and Bi-209; when the last captures another neutron, it becomes Po-210 (or Bi-210m) then alpha decays back to mass 206. Should another neutron be captured, alpha decay from 211 to 207 is faster yet. The net result of the cycle is that 4 [[neutron]]s are fused into one [[alpha particle]] with two [[beta decays]].

In fact, this cycle does not reach equilibrium because the neutron cross section of the doubly magic [[lead-208|<sup>208</sup>Pb]] is so small that that isotope will accumulate, and very little bismuth is produced in the s-process, as the chart above indicates.

The other magic numbers can behave similarly: the stable nuclei passed through between iron and lead with a magic number of neutrons are Sr-Zr (N = 50) and Ba-Nd (N = 82) and those isotopes all are unusually abundant and the most abundant of their element (the only for the odd elements, except for the extremely rare radioactive [[lanthanum-138]]).

==In stardust==

Stardust is one component of [[cosmic dust]]. Stardust is individual solid grains that condensed during mass loss from various long-dead stars. Stardust existed throughout interstellar gas before the birth of the Solar System and was trapped in meteorites when they assembled from interstellar matter contained in the planetary accretion disk in early Solar System. Today they are found in meteorites, where they have been preserved. Meteoriticists habitually refer to them as [[presolar grains]]. The ''s''-process enriched grains are mostly [[silicon carbide]] (SiC). The origin of these grains is demonstrated by laboratory measurements of extremely unusual isotopic abundance ratios within the grain. First experimental detection of ''s''-process xenon isotopes was made in 1978,<ref>
{{cite journal
 |last1=Srinivasan |first1=B.
 |last2=Anders |first2=E.
 |year=1978
 |title=Noble Gases in the Murchison Meteorite: Possible Relics of ''s''-process Nucleosynthesis
 |journal=[[Science (journal)|Science]]
 |volume=201 |issue=4350 |pages=51–56
 |bibcode=1978Sci...201...51S
 |doi=10.1126/science.201.4350.51
|pmid=17777755
 |s2cid=21175338
 }}</ref> confirming earlier predictions that ''s''-process isotopes would be enriched, nearly pure, in stardust from red giant stars.<ref>
{{cite journal
 |last1=Clayton |first1=D. D.
 |last2=Ward |first2=R. A.
 |year=1978
 |title=''s''-process studies: Xenon and krypton isotopic abundances
 |journal=[[The Astrophysical Journal]]
 |volume=224 |page=1000
 |bibcode=1978ApJ...224.1000C |bibcode-access=free
 |doi=10.1086/156449 |doi-access=free
|url=http://tigerprints.clemson.edu/cgi/viewcontent.cgi?article=1338&context=physastro_pubs|url-access=subscription}}</ref> These discoveries launched new insight into astrophysics and into the origin of meteorites in the Solar System.<ref name="Clayton2004">
{{cite journal
 |last1=Clayton |first1=D. D.
 |last2=Nittler |first2=L. R.
 |year=2004
 |title=Astrophysics with Presolar Stardust
 |journal=[[Annual Review of Astronomy and Astrophysics]]
 |volume=42 |issue=1 |pages=39–78
 |bibcode=2004ARA&A..42...39C
 |doi=10.1146/annurev.astro.42.053102.134022
|s2cid=96456868
 |url=https://pdfs.semanticscholar.org/a254/39a457245a227a7e010c2033cac8e17e8306.pdf |archive-url=https://web.archive.org/web/20200219012701/https://pdfs.semanticscholar.org/a254/39a457245a227a7e010c2033cac8e17e8306.pdf |archive-date=2020-02-19 }}</ref> Silicon carbide (SiC) grains condense in the atmospheres of [[Asymptotic Giant Branch|AGB stars]] and thus trap isotopic abundance ratios as they existed in that star. Because the AGB stars are the main site of the ''s''-process in the galaxy, the heavy elements in the SiC grains contain almost pure ''s''-process isotopes in elements heavier than iron. This fact has been demonstrated repeatedly by sputtering-ion mass spectrometer studies of these stardust [[presolar grains]].<ref name="Clayton2004"/> Several surprising results have shown that within them 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 AGB-star atmospheres changed with time or from star to star, presumably with the strength of neutron flux in that star or perhaps the temperature. This is a frontier of ''s''-process studies in the 2000s.

==See also==
{{Portal|Astronomy|Physics}}
*[[Nucleosynthesis]]
*[[r-process]]
*[[p-process]]

==References==
{{Reflist}}

{{Nuclear processes|state=uncollapsed}}
{{Star}}

[[Category:Nuclear physics]]
[[Category:Neutron]]
[[Category:Astrophysics]]
[[Category:Nucleosynthesis]]