19 62ApJ. . .135. .779R 12 16 20 12 part ofthisdiscussioncanbecarriedout,andwillsummarizedlaterinpaper. nuclei haverecentlybeencarriedoutwiththeChalkRiverTandemaccelerator(Alm- prior totheadventofChalkRiverresults(Hayashietal.1958;Cameron1959a). clear reactionrateswhichareofimportancefortheunderstandingstellarevolution. an analysisofthepropertiesthesereactionsappearstobecomplicated,itmightstill qvist, Bromley,andKuehner1960;Kuehner,Almqvist1960).Although vance ofthesereactionsandthesubsequentprocessesisdiscussedbriefly. the rateofthermonuclearreactionsinvolvingcarbon,oxygen,andneonnuclei.Theastrophysicalrele- the upperandlowerlimit.Sincepresentestimatefallsinbetweentheselimits,a evaluated, andthesubsequentdiscussionhadbeenextensiveenoughtoencompassboth tion outputofthestar.Inthispaperwewanttocomputethermonuclearrate core, composedmainlyofcarbonandoxygen,willcontractuntilitreachestemperatures branches. Itisexpected,forinstance,that,followingthehelium-burningstage,stellar be possibletoextractfromthedataatleastsomecrudeestimatesofcertainthermonu- portance ofthisreactionatlowCenergycanbe dismissed onfairlygeneraltheoretical more probable.Alphascouldalsocomefromthe O +2abreakup.However,theim- first statesinNecouldalwaysbedetected,and,because ofthelargeenergygapbetween of thetotalnumberaandpemittedisanuncertain point.Theagoingtothetwo reaction. Althoughtherelativeaccuracybetweenvariousneighboringpointsofthese Rather indirectmethodshadthenbeenusedtoevaluatetherates.Inoneofthesepapers energy generationfromisotopesofcarbon,oxygen,andneon. that arehighenoughtoguaranteethenuclearreactionratecorrespondingradia- grounds, aswillbediscussedinalaterparagraph. Argumentssimilartothosegivenfor at 27°,andofneutronsallenergies30°.Thegammaradiationis90°.Whether The dataofAlmqvist(1960)representtheyieldforalphasmorethan7.5Mevlab. the absolutevaluesandrelativeaccuracybetweendistantpointsarequestionable. curves isexcellent(theuncertaintylessthanthewidthsofline),accuracy these levelsandthenexthigherlevels,breakup totheselow-energystatesismuch the aandpmissedbecauseofbiasondetection systemrepresentalargefraction Such reactionsareexpectedtoprovidetheenergysourcesforstarsinredgiant (Reeves andSalpeter1959)anupperalowerlimittotheratesofC+hadbeen (due tothethresholdsofcounters)at42°(c.m.),protonsmorethan6Mev CARBON, OXYGEN,ANDNEONTHERMONUCLEARREACTIONRATES 121416 12 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Extensive measurementsofthenuclearreactionsbetweenC,NandOheavier Recent experimentalresultsobtainedwiththeChalkRiverTandemacceleratorareusedtocalculate In Figure1areshownthecross-sectionsforvariousoutcomesofC+ * DuringastayatTheoreticalPhysics,A.E.C.L.,ChalkRiver. Several papershavebeenwrittenonthecarbonandoxygenthermonuclearreactions, Département dePhysique,UniversitéMontréal,P.Q. Received October7>1961;revisedNovember20,1961 Hubert Reeves* I. INTRODUCTION 12 a) C+ ABSTRACT II. DATA 779 19 62ApJ. . .135. .779R 2023 low-energy extrapolation.TheresultsaregiveninTable1.numbersfor 780 fined tothebackground-curve itself. physical role,andconsequently theywereleftoutofthepicture.Theanalysis wascon- rarer andmuchmorewidelyspacedthanathigh energies.Further,atenergiesbelow techniques andatseveralanglesweretaken,inordertoimprovethereliabilityof the publicationofAlmqvistetal.(1960),alatersetmeasurementswithimproved two reasons,itwasfeltthatsuchresonanceswere unlikelytoplayanimportantastro- 6 or7Mev,theyneverrisebymorethanafactor of2abovethebackground.Forthese the sumofalphaandprotoncross-sectionsintegratedoverangles.(Theneutron at ratherlowenergies(andmightbepresentvery lowenergies),theyseemedtobecome form justpriortothecoalescenceofnuclei. Althoughtheseresonancesareseen and McManus(1960)intermsofthemolecularstates ofthecarbonnuclei,whichwould qvist assignedavalueof50percenttopossibleexperimentalerrors. cross-section wasknownfromFig.1tobemuchsmaller.)InaprivatediscussionE.Alm- in theexcitation-curve.Theseresonanceshavebeen givenalikelyexplanationbyVogt a andthelowlevelsofNewouldholdtrueforprotonstwoloweststatesNa. 12 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem However, theoreticalargumentsmustalwaysbetreatedwithmuchsuspicion.After The cross-sectionforinteraction betweentwochargedparticles(Aand B) atlow The mostremarkablefeatureoftheC+reactions isthepresenceofresonances 5 72 5 58 angles Theerroronthesevaluesislessthan50percent(EAlmqvist, privatecommunication) * Thenumbersgivenarethecombinedvaluesofalphaandproton cross-sectionsintegratedover E (Mev) c m i212 Experimental Cross-SectionsfortheCReaction 12 Fig. 1.—Experimentalcross-sectionsfortheC+reactions 1113 ^a+pC!) 52 25 6 0 5 88 HUBERT REEVES E (Mev) c m TABLE 1* (Ta+p(mb) 32 60 6 12 7 5 E (Mev) c m a-a+p (mb) 235 50 19 62ApJ. . .135. .779R f r -13 17 cross-section (randomvariationsoflessthan40per centforallexperimentalpointsbelow found thatifwereplacethetermdofequation(3) byanewphenomenologicalvariable the lowestenergies. relative velocityisusuallyfoundtobemainlygovernedbyCoulombeffects.Infact, g’ andifwemakeg=0.50(insteadof0.32,as calculatedford'),wegetavalueS mation ofequation(1)or(2)reallyrepresentsonlythel=0partialwave, factors. Thisbehaviorisnotunexpected,sincewedealwithcollisionsbetweencomplex fermis), theSfactorisnotreallyconstantbutvariesoverenergyrangebysmall properly. We,ineffect,findthat,withd'=0.32(ascomputedfromeq.[3]i?6 it isusuallypossibletofitthelow-energyexcitation-curvebyaformulaofform. tential wells)maylosesomeoftheirphysicalmeaning.Furthermore,theusualapproxi- nuclei forwhichtheusualconceptsofnuclearphysics(suchasinteractionradiiorpo- rather complicated,anditwillprobablytakequitealongtimebeforeisunderstood exponential terminwhichdappearsisaslowlyvaryingfunctionofenergy,thewhole becomes ofimportance,namely, one mustincludeintheexpressionofCoulombeffectsasecondterm,whichthen incident energyisnotsoverysmallascomparedwiththeCoulombbarrierenergy,then in thecenter-of-masssystem;andZbareelectricchargesofparticles.When while thecollisionoftwocarbonnucleiinvolvespartial wavesupto/=6or8,evenat result wouldberatherinsensitivetothevalueofRchosen.Onecanthenexpectfind center-of-mass system,isinMev.ThefactorScanthenbecalculatedbyputtingthe of interactioninfermis(1fermi=10cm);E,therelativeenergyAandB where exponential termisthefirstinexpansionoffunctionwhichrepresents where 5isaconstantfactorinwhichallthenucleareffectshavebeenlumpedand that thefactorSisindependentofenergy. experimental valuesofaand,inequation(3),atleastcrudeestimateR.Sincethe 7.5 Mev).Thisismuchsmallerthantheexperimental errors.Wehave M isthereducedmassoftwoparticlesinatomicunit,andRradius Coulomb effects;Eistherelativeenergyandvvelocityoftwoparticles (=7 X10Mevbarns),independentoftheenergy overallthelow-energypartof © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A moreempiricalapproachseemsappropriateto the presentsituation.Indeed,itis In theparticularcaseofC+C,asmentionedearlier,situationseemedtobe p c/ " -(!)“[~Ti' oc+c =7;10-V(^)- i/2 0.9890, c= d =0.122 37 = (-^ÿ—)10-< barns(£ inMev). E THERMONUCLEAR REACTIONRATES \ZZ) ’ AB eX E P (-2tZZ ab 121/2 c'/ =0.4295ZM, ab d' —0.0530 V 2/MWYv,2 2 3 \eZh/ AlB \Z~Z~) ’ AB 781 (1) (2) (4) (5) (3) 19 62ApJ. . .135. .779R experimentally. Thetotalcross-sectionwasestimatedtobeabouttwiceaslarge(assuminga50percent branching ratioforprotonemission).Thegamma-rayyield-curvewasadjustedtofitthelow-energy part ofneutron about halfandinthelow-energyrange.Thisisagreementwithintuitivefeeling. nuclei. Suchatheoryisstilltocome. In words,g'representsanexperimentalcorrectiontothepureGamowcurve.Thecorrect (which againshouldhaveafairlysimilarbranching ratio).Wecountonthegammayield 2 Mev),thenegativeQvaluewillstopneutronproductionalmostentirely. a 782 16 16 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Here onlythealphacross-sectionat27°andgamma yieldareavailable.Wehave We mustconsider,however, thattheadditionismadeatenergieswhichcorrespond Fig. 2.—Cross-sectionfortheO-freaction.Thecross-sectionalphareactionwasmeasured The branchingratiobetweenprotonsandalphasisseenfromtheexperimenttobe No attempthasbeenmadetodetectthepossiblebreakupintoO+2a.However, HUBERT REEVES 16 b) O+ 19 62ApJ. . .135. .779R 1 -1 f 12 32 present conclusion. We wouldthenget This upperlimithasbeenfoundbyassumingthatT takesthefullsingleparticlewidth— an unlikelyhighupperlimit.Abetterlimitfor Fwouldbeone-tenthofthiswidth. A newlevel(1—)hasbeendiscoveredat5.80Mev, with an activeone.Theproduct acter. Theenergyofthenextlevelhasbeenre-evaluated(5.64Mev).Itisa(3—),hence (2/+i)rr/r Spin, parity y Ty/T. a ficient forthepurposeofastrophysicaldiscussion. none ofthesecross-sectionswouldbelargerthanexpected.Thisinformationwillsuf- would theradiusofinteractionbelargerthan6.5fermis.Fromthis,onecouldseethat 2. The4.97-Mevlevelisinactiveforlow-energyalphaprocessesbecauseofits(2—)char- cleared bytheChalkRiverworkers(Gove1961).TheirresultsaresummarizedinTable of interactionfromtheslopeatlowenergies.Itwasfoundthatinnonethesecases range 7-10Mev.Then 0.70 Mev(seeeqs.[2]and[4]),thefactorSvariedbylessthan60percentin 7a varying functionoftheenergy,atanyratefarsmootherthanGamowfactor.Apro- section. Itwasfoundthat,byreplacingd(/M).34here,withR=7.5fermis)g' cedure similartotheonedescribedinC-hwasusedfitexperimentalcross- nuclei. Itisrathersafetoassume,then,thatthemultiplicityis,inthisrange,aslowly to denselypopulatedregionsofthecompoundnucleus5orvariousdaughter 1 14 20 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Aroughestimateoftheabsolute valueofN+at8Mevwaslateravailable.Itsustained the * SeeReeves(1960) The importantsubjectofthepropertieslow-lyinglevelsinNehasfinallybeen Here onlythegamma-rayyieldsareknown.Thebestwecandoistoextractradius a = 20 Properties ofLevelsNeWhichCouldBeActivein THERMONUCLEAR REACTIONRATES 1216u c) C+O,andN (2;+1)1^:= 0.003+0.002ev. (7) Photodisintegration Process* 1 0-(7775/^/æ+ote)(^ibarns,EinMev). n (21+ l)r<0.015ev. (9) 7 (inactive) 4 97 (21+ l)r<0.15ev. (8) 7 TABLE 2 d) Ne™ 0 003+0002ev 0 07(±001) 3— (active) 5 64 Level Estimated: 0015ev 0.003 (±0003) 1— (active) Upper limit:015ev 5 80 783 (6) 19 62ApJ. . .135. .779R 12 3 73 1/23/23 l/zl,z 3 28 mann distribution),onecanstillusethefamiliartechniqueofintegrationthermonu- experimental cross-sectionislinearintheenergy(justliketermofBoltz- of reactionspersecondnucleustypeBinagascontainingnucleiÀ, clear reactionrates(see,forinstance,Salpeter1952).Onethenobtains,thenumber 784 Mev“, andTinBK. where pisthedensityingm/cm,xfractionalofspeciesA;Mmass for theO+Oreaction, of Ainatomicmassunits,Sdefinedequation(4)isMev-barns,g'andgare At thehighdensitiespossiblyencounteredinredgiantstars(upto10gm/cm), effect ofelectronscreeningonthethermonuclearreactionratesisnomorenegligible. for O+O.Thecriterionweakdensitiesis[(—Uo/kT)<1].Forhigherdensities, the weakscreeningisaccountedforbyascribinganadditionalpotentiali/oatcenter It hasbeenevaluated,usingthetechniqueofSalpeter(1954).Fornottoohighdensities, incorporated inTable3,wheretheratesaretabulatedasfunctionsoftemperature of thenucleusandbymultiplyingreactionrateexp{—Uo/kT).Here(—£/o/ Aa kT) ^exp[12.6(p/r)]ingm/cm;TMK*)forC+C,and[25 instance, theseratescouldhavebeencalculatedbythemethodsordinarilyusedin at variousdensities.Itisnoteasytoevaluatethepossibleerrorsontheserates.For we usea(i//^r)=3.5p/TforC+and6.2O+O.Thecorrectionswere nucleon-nuclei scattering(i.e.,byneglectingtheenergy dependenceofS).Theratesob- of themethodusedtoextrapolatedata. for O+inthelowestpartoftemperaturerange, bothlevelingoffasthetempera- tained wouldhavebeenaboutfourtimessmallerfor C+C,andaboutsixtimessmaller here. cross-section (therebyincludingtheresonancesinC+ C curve)andtheextrapolationsofequations ture increases.Hencethebiggestuncertaintyin calculationisattachedtothechoice mations usedpreviously.Theagreementwaswellwithinthe experimentaluncertainties Al. Hegivesanupperlimit to thisrateHisupperlimitisabouttentimeslargerthan therategiven (5) and(6)Theresultsobtainedshowedonlyveryminordeviations fromthoseobtainedbytheapproxi- 0 1614 29 06 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 3 Because ofthefactthattermaddedinexponentequationtofit We obtain,fortheC+reaction, This ratehasrecentlybeenstudiedbyW.Cartledge(1962) byananalysisoftheO(N,2p) 1 BKequals10K.,andMK°K. Aprogramhasbeensetuptointegratetheratenumerically fromtheexperimentalvaluesof e=(gkT) =(0.198gT), pA+R _ px A iog ”G£) ios “(i) 8 4.34 X10 III. THERMONUCLEARREACTIONRATES 27.0 40.5 \MaXMbJMa \ZaZbJ (Ma+M\ 1f b HUBERT REEVES 13 36.55(l +0.ir)V3 59.02(1 +0.14D/ r =4.248 3 3 TV TV 2 . M+„) ■z\mm\^_ a abtU3 l/s Sie-<+‘) T f logioT. logio T; (10 (ii) (12) 19 62ApJ. . .135. .779R 3 3 of the5.64-Mevlevel, with TandE,inMev/BK. for captureoftheseconstituents. gm/cm tion ABperunitnucleusB,cm,sec;xisthefractionaldensityofA;andpmaterialin probability ofphotodisintegration.Werecallthatr isidenticalwithr,thepartialwidth where /andare,respectively,thespinsofexcited stateandofthegroundstate; the relativedepopulationofthatstatebecausepossibilityphotodisintegration: of astatisticalfactortimesMaxwellianwhichtakesintoaccount 0 8 r(£*) istheprobabilityofde-excitationthrough gammaemission;andTd(E*)isthe this state.Inagasinthermalequilibriumwithitsradiation,p(E*)isthentheproduct Q oftheconstituentparts,mostphotodisintegrationratewillbecontributedby has anexcitationenergy£*. times theprobability[T(E*)/h}thatnucleuswillphotodisintegrate,givenit A the relativeprobabilityP(E*)thatnucleuswillbefoundexcitedatanenergy£*, dc 7 d 9 0 (1 BK=IOK) 20 1816 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem For theNe,usingparameters quotedinTable2,onegets,forthecontribution The resonantphotodisintegrationratePdbecomes The numbersinthetablearelogarithmtobase10ofPa+bforvariouspx>andOprobabilityreac- The probabilityPdthatanexcitednucleuswillphotodisintegratecanbeequatedto If thenucleushasanexcitedstateatE*,abovebutclosetoseparationenergy A T inBK 1212620 Thermonuclear ReactionRatesforC-f,O+Ne7->a logio Pd=21.15— + + - 16 -12 0 -14 5 105 4 0 2 7 3 7 1 0 THERMONUCLEAR REACTIONRATES 4 9 90 7 P(E*) IV. PHOTODISINTEGRATIONRATES LOG 10Pc+c 1 + 50 + 37 + 20 -05 -26 - 4 - 8 - 5 - 7 -10 -13 (sec“) 106 (2/+1) rv+Tá (2/+1) Ty TABLE 3 2/+i Ar/ 2/+i \/r+r\ 7c 7c + 49 + 32 + 61 + 07 107 11 3 4 9 6 7 1 3 ç —E*/kT 105 10 11 13 14 16 17 0 8 2 8 9 5 +0+E* LOG 10j>0+0 -1 + 0 - 1 - 7 -10 6 - 4 - 8 - 9 -11 8 -14 8 -13 2 -16 6 (sec) T 106 + -13 -15 - 81 107 10 12 0 9 785 (14) (13) 19 62ApJ. . .135. .779R 0 8 one, whichisimportantonlyforP>2BKAlthoughtheupperandlowerlimitsdifferbyquitelargefactors,estimated also anupperlimitbutamorerealisticone.Thelastcolumnsarethecombinedeffectsofthesetwolevelsplusnexthigher particle limit,mostcertainlyanoverestimate.The“estimate”columnassumesrtobeabout01ofthislimitThisisprobably value hasmostprobablyamuchsmallerrangeofuncertainty by usingequations(15)and(17).Theerrorontheestimateismuchlessthanonewould or one-tenthofthisvalue, of thelifetimeagainstphotodisintegration.Thedensities usedrepresentthelikelysitua- get byusingtheupperandlowerlimit.Itisprobablylessthanafactorof4eachway. In Table4theseratesaretabulated,givinganupperlimit,alowerandestimate 1 1 0 After thestarhasburned mostoftheheliumitscore,itproceedstofurther contrac- tions insidetheredgiantswherethesereactionsare expectedtooccur. atom (B)forvariousvaluesofthefractionaldensities ofatoms(^4),andforNeinterms ture range{T<2BK). 1 2 and, forthe5.80level,usingmaximumF, 1 8. of carbonandoxygen(new data[Gove1961]seemtoallowtheformation of verysmall tion, inordertokeepup withitsradiationoutput.Thecoreisthenmainly composed 786 a 9 a (1 BK=10°K) 20 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem * Forthelastone,onecangiveonlyanupperlimit.Thislimitassumesthatalphawidthrisequaltosingle- The nextlevelinNe(6.74Mev)makesnoappreciable contributioninthistempera- The setofreactionsdiscussedhereisrelevanttoa certainchapterinthelifeofastar. In Figure3thesereactionsareplotted—forCand O intermsofthelifetimeagiven a T INBK 203 P istheProbabilityofPhotodisintegrationNeperCm Ne Errors + LOG10PNe 5 64-Mev -15 7 -22 8 - 15 - 31 -92 ^11 0 -50 -76 -13 1 per SecthroughtheTwoLevels5.64and5.80Mev Level + 02 ogP(5.64) =(is) -0 5 10d (17) logP(5.81) <14.40--^-,(16) 10d ogioPd(5.81) <13.40—* v. astrophysicaldiscussion -12 -14 -22 -10 0 Upper Limit 5 81-MevLevel HUBERT REEVES -f-LOGlO Pe N a) Energetics TABLE 4* Estimate -23 -15 -13 11 0 Estimate -f 4 -22 -15 - 7 - 8 -10 -12 - 1 - 2 - 4 29 3 29 3 All Levels +LOG 10Pe N -22 2 -65 - 81 -10 0 -12 2 -14 9 -02 - 19 -39 Upper Limit -16 -23 - 2 - 8 - 9 -11 -13 - 3 - 5 Lower Limit 19 62ApJ. . .135. .779R 24252627 28 2 12 12 20 58 be morethansufficientto producemostoftheheavyelementsinlargeoverabundance. computed, withtheneutroncross-sectionsmeasured byMacklin(unpublished),that sections, theywerenotexpected toplayanyimportantastrophysicalrole. Indeed,at about 50-60neutronswouldbeabsorbedbyeach metalatom.Suchanamountwould following setofreactions: Mg; then,indecreasingorder,,*Al Si (^1percent),andmuchsmaller density ofnucleiA.) amounts ofthefollowingstableisotopes. would occurintheregion0.6-0.7BK. is tabulatedforafewtemperaturesanddensities.Itappearsthatthecarbon-burning tabulated inTable3(withelectron-screeningcorrection).In4theratioe/(x) 6.5 MevforeachC,or13percollision. loss throughneutrinoemissionisveryhighandmustbetakenintoaccount.Thesubject where thep’saredefinedinequation(10)(withoutelectron-screeningcorrection)and will befurtherdiscussedinaforthcomingpaper.TheC+reactionreleasesabout calculations byChiu(privatecommunication)haveshownthatinthisrangetheenergy amounts ofNeinthehelium-burningstage).Thecontractionwillbepursueduntil bill, butroughestimateswouldplaceitsomewherearound10-10ergs/gmsec.Recent by thestellartemperaturegradient.Nodetailedcalculationsareasyetavailableforthis ’•ate ofenergyproductionfromcarbonisotopesishighenoughtofootthebillpresented c 1214 1614 12 2023 121620 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Unless theC+N, +O,andNreactionshaveextremelylarge cross- If smallamountsofmetals(50<^462)werepresent originallyinthegas,itwas The mostremarkablepointistheproductionoflarge fluxesofneutronsthroughthe The mostabundantisotopesproducedbytheCburning reactionareNe,Naand Fig. 3.—LifetimeofC,OandNeasafunctiondensitytemperature.(pxisthefractiona A The energygeneratedpersecondgram(e)isgivenby THERMONUCLEAR REACTIONRATES 1213+16 C(¿, 7)N0)Ca,n)0. 9 TEMPERATURE INBK(I=I0°K) 17 72 € =10(Xc)p+c, c 787 19 62ApJ. . .135. .779R 20 16 202416 17 13 20 burning stagewouldmostlyhaveburnedit,withoutproducinganynewsupplyofit. remain inthestar.SomenitrogencouldfromC-N-0cyclebuthelium- rather onthesmallside—wecansafelyleavethemoutofastrophysicalpicture. As itindeedturnsoutthatthesecross-sectionsarequitetheexpectedones—infact,being temperatures largerthan0.8BK,extremelysmallamountsofcarbonareexpectedto 788 least intheearlierpartsofNeburning,mostimportantsetreactionsis: the cross-sectionfora+Oinrelevantrangeoftemperature.Consequently,at hence 2Ne—*Mg+Owith4.5Mevforeachphotodisintegration,yieldinge= (10)(¿Ne)0%e). Ne isexhausted. is nottoostrong.Atthistemperaturetheenergy generationfromO+isitselfnon- enough tostopthestellarcontractionagain,atleast incaseswheretheneutrinoemission negligible andwillbethedominantsourceofenergy afteranappreciablefractionofthe with 19.6MevineachcollisionofO+O, 20 20 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 84 The nextsourceofenergywouldcomefromtheNephotodisintegration. The cross-sectionfora+Neisatleastoneortwoordersofmagnitudelargerthan The mostimportantsetofreactionswillthenbe From Table5weseethat,atT=1.3BK,10 - ergs/gmsec,whichisprobably Nuclear EnergyProduction(e)inErgsperGramSecond 1628 2428 2016 O +->Sia, 2024 a +Mg—>Si7, HUBERT REEVES Ne +7Oa, 172 a +Ne->Mgy; 60 =10*Poo(xo). + TABLE 5 19 62ApJ. . .135. .779R 28 2526 24 24 20 28 The mainoutcomewouldbetheisotopesinrange24-32,withprobablyapeakaround Si. more abundantthanMgor.Theneon-burning,ontheotherhand,wouldbean is ratherledtotheconclusionthatisotopesfromH=20^427weremostlypro- hardly beproducedinthehelium-burning,asimpliedbyBurbidgeetal.(1957).One important sourceofMg,mostlikelythedominantone.Theoxygen-burningisresponsi- its preponderanceoverneighbors,butitisdoubtfulwhetherMgwouldbemuch duced bytheC+burningstage.DetailedcalculationsindicatethatNewouldretain ble fortheisotopesinrangeA=25-32,withastrongpeakatSi,mostlikely for isotopes36-46butmaynotbethemainsourceof24,28,and32. enough tomakeitpreponderantoverthebackgroundofisotope-curve. nism forheavy-nucleibuilding. numerical calculations. .1959Ô,ibid.,p.895. Almqvist, E.,Bromley,D.A.,andKuehner,J.A.1960,Phys.Rev.LeUers4,515. sions. IwanttothankMessrs.GaétanMarchandandYvonGirouxfortheirhelpinthe Institute forSpaceStudiesgrouptheirhospitalityandsomeverystimulatingdiscus- Bromley, D.A.,Kuehner,J.andAlmqvist,E.1960,Phys.Rev.Letters,4,365. large amountsofmetalsinoverabundance.Suchaprocesscouldbeanimportantmecha- Hayashi, C.,Nishida,M.,Ohyama,N.,andTsuda,H.1958,Progr.Theoret.Phys.,20,110. Reeves, H.,andSalpeter,E.1959,Phys.Rev.,116,1505. Reeves, H.February,1960,Cornellthesis. Burbidge, E.M.,G.R.,Fowler,W.A.,andHoyle,F.1957.Rev.Mod.Phys.,29,547. Cameron, A.1959a,Ap.J.,130,429. .1954,AustralianJ.Phys.,7,473. Cartledge, W.A.1962,Cañad.J.Phys.,40,139. Vogt, E.,andMcManus,H.1960,Phys.Rev.Letters,4,518. Salpeter, E.1952,Phys.Rev.,88,547. Gove, H.,June,1961,ChalkRiverRept.P.D,p.317. y 20 28 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The newresultsontheNenuclearstructureseemtoimplythatthisisotopecan The nextstepwouldbethephotodisintegrationofSi,whichweshallnotstudyhere. From Table5weseethattherange1.4-1.5BKshouldmostofoxygen-burning. It doesseem,then,thatthealphaprocessofBurbidgeetal.(1957)couldberesponsible The carbon-burninggivesrisetoaneutronfluxwhichisstrongenoughproduce I amindebtedtotheChalkRivergroupfortheirco-operation.wantthank THERMONUCLEAR REACTIONRATES b) Nucleosynthesis REFERENCES 789