<<

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,,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 , 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- 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 of