Editing CNO cycle (section)

=== CNO-I ===
The first proposed catalytic cycle for the conversion of hydrogen into helium was initially called the carbon–nitrogen cycle (CN-cycle), also referred to as the Bethe–Weizsäcker cycle in honor of the independent work of [[Carl Friedrich von Weizsäcker|Carl Friedrich von&nbsp;Weizsäcker]] in 1937–38<ref name = vonWeizsäcker-1/><ref name = vonWeizsäcker-2/> and [[Hans Bethe]]. Bethe's 1939 papers on the CN-cycle<ref name = Bethe-1939-a/><ref name = Bethe-1939-b>{{cite journal
 |last = Bethe |first = Hans A. |author-link = Hans Bethe
 |year = 1939
 |title = Energy production in stars
 |journal = [[Physical Review]]
 |volume = 55 |issue = 5 |pages = 434–456
 |doi = 10.1103/PhysRev.55.434 |doi-access = free
 |pmid = 17835673 |bibcode = 1939PhRv...55..434B
}}</ref> drew on three earlier papers written in collaboration with [[Robert Bacher]] and [[Milton Stanley Livingston]]<ref>{{cite journal
 |last1 = Bethe  |first1 = Hans A. |author1-link = Hans Bethe
 |last2 = Bacher |first2 = Robert  |author2-link = Robert Bacher
 |year = 1936
 |title = Nuclear Physics, A: Stationary states of nuclei
 |journal = [[Reviews of Modern Physics]]
 |volume = 8 |issue = 2 |pages = 82–229
 |doi = 10.1103/RevModPhys.8.82
 |bibcode = 1936RvMP....8...82B
 |url = https://authors.library.caltech.edu/51288/1/RevModPhys.8.82.pdf
}}</ref><ref>{{cite journal
 |last = Bethe |first = Hans A. |author-link = Hans Bethe
 |year = 1937
 |title = Nuclear Physics, B: Nuclear dynamics, theoretical
 |journal = [[Reviews of Modern Physics]]
 |volume = 9 |issue = 2 |pages = 69–244
 |doi= 10.1103/RevModPhys.9.69 |bibcode = 1937RvMP....9...69B
}}</ref><ref>{{cite journal
 |last1 = Bethe      |first1 = Hans A.   |author1-link = Hans Bethe
 |last2 = Livingston |first2 = Milton S. |author2-link = Milton Stanley Livingston
 |year = 1937
 |title = Nuclear Physics, C: Nuclear Dynamics, Experimental
 |journal = [[Reviews of Modern Physics]]
 |volume = 9 |issue = 2 |pages = 245–390
 |doi = 10.1103/RevModPhys.9.245 |bibcode = 1937RvMP....9..245L
}}</ref> and which came to be known informally as ''Bethe's Bible''. It was considered the standard work on nuclear physics for many years and was a significant factor in his being awarded the [[List of Nobel laureates in Physics|1967 Nobel Prize in Physics]].<ref>{{cite magazine
 |first = Jason Socrates  |last = Bardi
 |date = 23 January 2008
 |title = Landmarks: What makes the stars shine?
 |magazine = [[Physical Review Focus]]
 |volume = 21 |issue = 3
 |doi = 10.1103/physrevfocus.21.3
 |url = https://physics.aps.org/story/v21/st3
 |access-date = 26 November 2018
}}</ref> Bethe's original calculations suggested the CN-cycle was the Sun's primary source of energy.<ref name = Bethe-1939-a/><ref name = Bethe-1939-b/> This conclusion arose from a belief that is now known to be mistaken, that the [[abundance of the chemical elements|abundance of nitrogen in the sun]] is approximately 10%; it is actually less than half a percent.<ref name="Krane"/> The CN-cycle, named as it contains no stable isotope of oxygen, involves the following cycle of transformations:<ref name="Krane">
{{Cite book
 |last=Krane |first=Kenneth S.
 |year=1988
 |title=Introductory Nuclear Physics
 |page=[https://archive.org/details/introductorynucl00kran/page/n559 537]
 |publisher=[[John Wiley & Sons]]
 |isbn=0-471-80553-X
 |url=https://archive.org/details/introductorynucl00kran
 |url-access=limited
}}</ref>
: {{nuclide|carbon|12|link=yes}} &nbsp; → &nbsp;{{nuclide|nitrogen|13|link=yes}} &nbsp; → &nbsp;{{nuclide|carbon|13|link=yes}} &nbsp; → &nbsp; {{nuclide|nitrogen|14|link=yes}} &nbsp; → &nbsp; {{nuclide|oxygen|15|link=yes}} &nbsp; → &nbsp; {{nuclide|nitrogen|15|link=yes}} &nbsp; → &nbsp; {{nuclide|carbon|12}}

This cycle is now understood as being the first part of a larger process, the CNO-cycle, and the main reactions in this part of the cycle (CNO-I) are:<ref name="Krane" /> 
<!-- Autogenerated using Phykiformulae 0.12 [[User:SkyLined#Phykiformulae]] corrected by [[User:DAID]]
 C-12 + H -> N-13 + y  _ _  + 1.95 MeV
 N-13 _ _ -> C-13 + e+ + ve + 1.20 MeV 
 C-13 + H -> N-14 + y  _ _  + 7.54 MeV
 N-14 + H -> O-15 + y  _ _  + 7.35 MeV
 O-15 _ _ -> N-15 + e+ + ve + 2.75 MeV 
 N-15 + H -> C-12 + He _ _  + 4.96 MeV
-->
:{| border="0"
|- style="height:2em;"
|{{nuclide|carbon|12}}&nbsp;||+&nbsp;||{{nuclide|hydrogen|1}}&nbsp;||→&nbsp;||{{nuclide|nitrogen|13}}&nbsp;||+&nbsp;||{{math|{{SubatomicParticle|link=yes|Gamma}}}}&nbsp;||&nbsp;||&nbsp;||+&nbsp;||{{val|1.95|ul=MeV}}
|- style="height:2em;"
|{{nuclide|nitrogen|13}}&nbsp;||&nbsp;||&nbsp;||→&nbsp;||{{nuclide|carbon|13}}&nbsp;||+&nbsp;||{{SubatomicParticle|link=yes|Positron}}&nbsp;||+&nbsp;||{{math|{{SubatomicParticle|link=yes|Electron Neutrino}}}}&nbsp;||+&nbsp;||{{val|1.20|u=MeV}} ||([[half-life]] of 9.965 minutes<ref name="half-life-cn">{{cite book
 |first = Alak  |last = Ray
 |year = 2010
 |chapter = Massive stars as thermonuclear reactors and their explosions following core collapse
 |editor1-first = Aruna    |editor1-last = Goswami
 |editor2-first = B. Eswar |editor2-last = Reddy
 |title = Principles and Perspectives in Cosmochemistry
 |page = 233
 |publisher = [[Springer Science & Business Media]]
 |isbn = 9783642103681
 |chapter-url = https://books.google.com/books?id=gCr9WVH0utwC&pg=PA233
}}</ref>)
|- style="height:2em;"
|{{nuclide|carbon|13}}&nbsp;||+&nbsp;||{{nuclide|hydrogen|1}}&nbsp;||→&nbsp;||{{nuclide|nitrogen|14}}&nbsp;||+&nbsp;||{{math|{{SubatomicParticle|Gamma}}}}&nbsp;||&nbsp;||&nbsp;||+&nbsp;||{{val|7.54|u=MeV}}
|- style="height:2em;"
|{{nuclide|nitrogen|14}}&nbsp;||+&nbsp;||{{nuclide|hydrogen|1}}&nbsp;||→&nbsp;||{{nuclide|oxygen|15}}&nbsp;||+&nbsp;||{{math|{{SubatomicParticle|Gamma}}}}&nbsp;||&nbsp;||&nbsp;||+&nbsp;||{{val|7.35|u=MeV}}
|- style="height:2em;"
|{{nuclide|oxygen|15}}&nbsp;||&nbsp;||&nbsp;||→&nbsp;||{{nuclide|nitrogen|15}}&nbsp;||+&nbsp;||{{SubatomicParticle|Positron}}&nbsp;||+&nbsp;||{{math|{{SubatomicParticle|Electron Neutrino}}}}&nbsp;||+&nbsp;||{{val|1.73|u=MeV}}||(half-life of 122.24 seconds<ref name="half-life-cn"/>)
|- style="height:2em;"
|{{nuclide|nitrogen|15}}&nbsp;||+&nbsp;||{{nuclide|hydrogen|1}}&nbsp;||→&nbsp;||{{nuclide|carbon|12}}&nbsp;||+&nbsp;||{{nuclide|helium|4}}&nbsp;||&nbsp;||&nbsp;||+&nbsp;||{{val|4.96|u=MeV}}
|}
where the carbon-12 nucleus used in the first reaction is regenerated in the last reaction. After the two [[positron emission|positrons emitted]] [[annihilation|annihilate]] with two ambient electrons producing an additional {{val|2.04|u=MeV}}, the total energy released in one cycle is 26.73&nbsp;MeV; in some texts, authors are erroneously including the positron annihilation energy in with the [[Beta decay|beta-decay]] [[Q value (nuclear science)|Q-value]] and then neglecting the equal amount of energy released by annihilation, leading to possible confusion. All values are calculated with reference to the Atomic Mass Evaluation 2003.<ref>{{cite web
 |last1=Wapstra
 |first1=Aaldert
 |last2=Audi
 |first2=Georges
 |date=18 November 2003
 |title=The 2003 Atomic Mass Evaluation
 |publisher=Atomic Mass Data Center
 |url=http://amdc.in2p3.fr/web/masseval.html
 |access-date=25 October 2011
 |archive-date=28 September 2011
 |archive-url=https://web.archive.org/web/20110928003450/http://amdc.in2p3.fr/web/masseval.html
 |url-status=dead
 }}</ref>

The limiting (slowest) reaction in the CNO-I cycle is the [[proton capture]] on {{nuclide|nitrogen|14}}. In 2006 it was experimentally measured down to stellar energies, revising the calculated age of [[globular cluster]]s by around 1 billion years.<ref>
{{cite journal
 | collaboration=LUNA Collaboration
 | last1=Lemut          | first1=A.   | last2=Bemmerer   | first2=D. 
 | last3=Confortola     | first3=F.   | last4=Bonetti    | first4=R. 
 | last5=Broggini       |first5=C.    | last6=Corvisiero | first6=P. 
 | last7=Costantini     |first7=H.    | last8=Cruz       | first8=J. 
 | last9=Formicola      |first9=A.    | last10=Fülöp     | first10=Zs. 
 | last11=Gervino     | first11=G. | last12=Guglielmetti | first12=A. 
 | last13=Gustavino     | first13=C.  | last14=Gyürky    | first14=Gy. 
 | last15=Imbriani      | first15=G.  | last16=Jesus A.  | first16=P. 
 | last17=Junker        | first17=M.  | last18=Limata    | first18=B. 
 | last19=Menegazzo     | first19=R.  | last20=Prati     | first20=P. 
 | last21=Roca          | first21=V.  | last22=Rogalla   | first22=D. 
 | last23=Rolfs         | first23=C.  | last24=Romano    | first24=M. 
 | last25=Rossi Alvarez | first25=C.  | last26=Schümann  | first26=F. 
 | last27=Somorjai      | first27=E.  | last28=Straniero | first28=O. 
 | last29=Strieder      | first29=F.  | last30=Terrasi   | first30=F. 
 | last31=Trautvetter   | first31=H.P.       | display-authors=6
 | year=2006
 | title=First measurement of the {{sup|14}}N(p,γ){{sup|15}}O cross section down to 70&nbsp;keV
 | journal=[[Physics Letters B]]
 | volume=634 | issue=5–6 | pages=483–487
 | bibcode=2006PhLB..634..483L | arxiv = nucl-ex/0602012
 | s2cid=16875233  | doi=10.1016/j.physletb.2006.02.021
}}</ref>

The [[neutrino]]s emitted in beta decay will have a spectrum of energy ranges, because although [[Conservation of momentum#Conservation of linear momentum|momentum is conserved]], the momentum can be shared in any way between the positron and neutrino, with either emitted at rest and the other taking away the full energy, or anything in between, so long as all the energy from the Q-value is used. The total [[momentum]] received by the positron and the neutrino is not great enough to cause a significant recoil of the much [[invariant mass|heavier]] daughter nucleus{{efn| Note: It is not important how invariant masses of e and ν are small, because they are already small enough to become relativistic. What is important is that the daughter nucleus is heavy compared to {{frac|''p''|''c''}}&thinsp;.}} and hence, its contribution to kinetic energy of the products, for the precision of values given here, can be neglected.  Thus the neutrino emitted during the decay of nitrogen-13 can have an energy from zero up to {{val|1.20|u=MeV}}, and the neutrino emitted during the decay of oxygen-15 can have an energy from zero up to {{val|1.73|u=MeV}}. On average, about 1.7&nbsp;MeV of the total energy output is taken away by neutrinos for each loop of the cycle, leaving about {{val|25|u=MeV}} available for producing [[luminosity]].<ref>
{{cite book
 | last1 = Scheffler | first1 = Helmut
 | last2 = Elsässer  | first2 = Hans
 | year = 1990
 | title = Die Physik der Sterne und der Sonne
 | trans-title = The Physics of the Stars and the Sun
 | publisher = [[Bibliographisches Institut]] (Mannheim, Wien, Zürich)
 | isbn = 3-411-14172-7
}}</ref>