197 8ApJS. . .36. .2 85W 138 23 /7-process arelistedinTable1alongwiththeir even numbersofneutrons andprotons.Thosefew thought ofasdesignating thefactthatthesenuclei term “/7-nuclei”toreferthissetofspecies(regard- species withoddneutron and protonnumber(La are proton-richrelativeto other stableisotopesofthe less oftheirsynthesismechanism).The“p”maybe understood mechanismthatprobablyoccursin same element. are alsonoted.Inallthatfollows,weshallemploythe progenitors ofthe/?-nucleithroughanasyetpoorly these muchmoreabundantspeciessomehowserveas isotope. Consequentlyallknowledgeofabundance element hasasadominantconstituent/7-process they aretherarestofallstablenuclei.Infact,nosingle chains (r-and¿-processes)thatareresponsiblefor lie ontheproton-richsideofvalleybeta- The AstrophysicalJournalSupplementSeries,36:285-304,1978February odd-particle nuclei.Possible¿-processcontributions designations astowhethertheyareeven,odd,or abundances bymassfractioninthesolarsystemand supernovae. adjacent /7-nuclei,anditisgenerallyacceptedthat abundances thatare10totimeslargerthan r- and¿-processnucleiinthesolarsystemhave producing thebulkofheavyelements.Asagroup solar-system measurements(Cameron1973).Typically, systematics forthesespeciesisbasedentirelyupon stability andarebypassedbytheneutroncapture stable nuclearisotopeswithmassnumberA>1Athat © 1978.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. It isreadilyapparentthatmost ofthesenucleihave Those isotopestraditionallyattributedtothe The “/?-process”isotopesor“/7-nuclei”arethose © American Astronomical Society •Provided by theNASA Astrophysics DataSystem 9 produces anabundancepatternthatdisplaysstrikingsimilaritiestoofthe/7-processnuclei characterized bypeaktemperaturesintherange2.0to3.0x10K.Atthesea is examined.Aparticularlyinterestingcontextforthissynthesisfoundtobeexplosiveevents that haveexperiencedheliumandperhapscarbonburningpriortoexplosion.Implicationsfor in thesolarsystem.Thelargeprotondensitiesusuallyrequiredforsuchsynthesisarenotneeded. series ofphotodisintegrationreactionsoperatinguponadistributionr-and¿-processseeds discussion ofothercurrent/7-processmodelsispresented. Subject headings:nucleosynthesis—stars:abundancessupernovae supernova structure,presupernovaevolution,andcosmochronologyarediscussedacritical Requisite conditionsforthismodelareexpectedtooccurnaturallyinthosezonesofsupernovae Lick Observatory,BoardofStudiesinAstronomyandAstrophysics,UniversityCalifornia,SantaCruz The nucleosyntheticoriginoftherareproton-richisotopes,usuallycalled“^-process” I. INTRODUCTION University ofCalifornia,LawrenceLivermoreLaboratory,Livermore,California Received 1976December27;accepted1977August12 THE ^-PROCESSINSUPERNOVAE W. M.Howard S. E.WOOSLEY ABSTRACT AND 2 92112144 13 180 2 112 16492144 115 -3 /7-nuclei wereassembledhavebeenasubjectof /?-process areevennuclei,afactwhichpresumably Audouze 1970;Hainebach, Schramm,andBlake (/?, y)and(y,n)reactionsoperatingonapreexisting conversion ofheavyelements into/7-nuclei,including local hydrodynamictimescale(10-100s).Since and Brihaye1969;Joukoff 1969;Agnese,LaCamera, (Cameron 1959;Reevesand Stewart1965;Arnould that areshieldedfromproductionbyneutroncapture. 2.5 billiondegrees,andprotondensitiesofroughly and suggestedthatfortemperaturesontheorderof reactions, BFHnamedthesethe“/7-processnuclei” layers oftypeIIsupernovae.Thereacombination that thesenucleiareproducedinthehydrogen-rich controversy foralmost20years.Cameron(1957)and relative abundancepeaksatMo,Sn,m,and where thesynthesisoccurs.Thissensitivitytonuclear reflects thedecreasedstabilityofanucleuswith that allnucleiproducedinsizableamountsbythe the only/7-nucleiwithoddmassnumbers(Inand spallation reactions(Frank-Kamenetskii 1961; Because ofthedominantroleplayedbyproton binding energyisfurtherreflectedintheexistenceof and Ta)areofconsiderablysmallerabundance, set ofr-and¿-processseedscanproduceanuclei Burbidge etal.(1957,henceforthBFH)proposed shells, andSnhasaclosedprotonshell. an unpairedprotonorneutronintheenvironment Er. ThenucleiMoandSmhaveclosedneutron Sn) maybemadebythe¿-process.Thusitappears 1976); positroncapture and photo-betaprocesses 1957 manymechanismshavebeenstudiedforthe 100 gcm,suchconversioncouldtakeplaceona The astrophysicalcircumstancesunderwhichthe 197 8ApJS. . .36. .2 85W 7 114115 113116 1076 936 196 184 180 174 168 164 158 166 144 138 162 138 132 136 130 126 124 116 108 106 120 114 112 102 113 figurations. Onewouldexpect theproductnucleo- objection tothistypeofsynthesis isthatatthehigh nucleus thanisreflectedin Table1.Anothersevere functions ofindividual nuclear excited-statecon- O* y)>(p,(y,«),p\anda)(Ito1961;Frank- synthesis tovarymuchmore sharplyfromnucleusto would proceedatratesthat areextremelysensitive interactions inducedbythehigh-temperaturephoton candidates for/7-nucleosynthesis.Suchreactions and positronbathsalsoappeartobeveryunlikely vironments spallationreactionsproveineffectivein AT; Arnould1976).Forrealisticastrophysicalen- accounting forallbuttherarestof/7-nuclei.Weak Truran 1973;Audouzeand1975,henceforth Kamenetskii 1961;Malkiel1963;AmietandZeh and Wataghin1969);thethermonuclearreactions beta-decay. neutron capturesonCdthatleaveinitsgroundstate. the isomericstateofCd.AlsoSnisformedby5% 1967, 1968;Macklin1970;TruranandCameron1972; on Pdismuchlessthan7x10yr. Zr ismuchlessthan1.5x10yr. Hg... 98 96 190p^ 94 92 Os ...' 180^ 84 Ta... Hf... 78 74 Yb... Er ! 162p Dy... Dy... Sm... La... Gd§.. Ce... Ba... Ce... Ba... Xe... Xe... Snt.. Cdt.. Cd... Te Snt.. Sn... Pd... 286 Int... r Ru... Ru... Mo*. Mo. Sr..., 151 Kr... Se. . The /»-ProcessNuclei(AbundancesfromCameron1973) § On5-branchsinceasignificantfractionofSmwill t Some5-processcontributionifabranchproceedsthrough t Bypassedby5-processiftimescaleforneutroncapture * Bypassedby5-processiftimescaleforneutroncaptureon © American Astronomical Society •Provided by theNASA Astrophysics DataSystem Nucleus Odd particle Odd particle Designation TABLE 1 Particle Even Even Even Even Odd Even Even Even Even Even Even Even Even Even Even Odd Even Even Even Even Even Even Even Even Even Even Even Even Even Even Even Even Even Mass Fraction Solar System 2.76 (-12) 6.00 (-13) 8.17 (-13) 9.39 (-13) 2.18 (-12) 1.12 (-14) 7.12 (-13) 2.43 (-11) 1.60 (-12) 1.18 (-12) 9.83 (-12) 2.03 (-11) 2.18 (—11) WOOSLEY ANDHOWARD 1.39 (-11) 1.20 (-12) 7.49 (-12) 1.24 (-12) 3.50 (-11) 4.61 (-11) 1.37 (-12) 6.55 (-11) 9.36 (-11) 1.49 (-11) 1.52 (—11) 3.39 (-11) 8.40 (-11) 2.43 (-10) 1.88 (-11) 3.08 (-11) 1.65 (-11) 8.22 (-10) 3.06 (-10) 3.13 (-10) 1.41 (-9) 1.04 (-9) 2 144 208 n 2 helium, andprobablycarbon. Intheirsimplestform our resultsareindependent oftheexactcomposition of atypeIIsupernovathat haveexhaustedhydrogen, the /7-nucleiasoccurringmost naturallyinthosezones fact, weviewtherequisite conditions forsynthesizing usually requiredforthe/7-process donotappear.In reactions playnorole.Thusthelargeprotondensities those ofAT,BHF,andothersinthat(p,y)(/?,n) example, cananddoesaffecttheproductionoflighter species likeSm.Ourcalculationsalsodifferfrom In ourcalculationstheseedabundanceofPb,for nuclear chargeZsolelyfromseedhaving< . the y-processdoesnotformaproductnucleusof though theygaveverylittlequantitativedetail.Unlike other scenariosforthe/7-processthatutilizeprotons, products. AmietandZeh(1967,1968)described a similar mechanismforproducingthe/7-nuclei,al- (y> \p\and(y,a)reactionsthatacttostripdown nuclei. Thetransformationoccursviaaseriesof resembles closelythesolarabundancepatternof/7- or “photodisintegrate”theseednucleiintolighter roughly 1sintoadistributionofelementsthat degrees) willbetransformedonatimescaleof having radiationtemperaturesintherange2.1< Tq <3.2(whereTistemperatureinbillionsof called the“y-process.”itisshownthatadistribution the synthesisof/7-nucleiwhichismoreproperly of heavyelementssubjectedtoahotphotonbath these modelsmaybeunjustified.Thisisatopicwe p shall discussingreaterdetailthenextsection. mathematically successful,mayrequirephysicalcon- Furthermore, severaloftheassumptionsinherentin ditions thatcannoteasilyberealizedinnature. ever, itisourcontentionthatthesemodels,while features oftheabundancepattern/7-nuclei.How- important role.Inparticular,thesuccessofATis hydrogen-rich regionswhere(/?,y)reactionsplayan far moststudiesofthissorthavefollowedthelead quite impressiveinreproducingthequahtative candidates fortheproductionof/7-nuclei.Thus BFH andCameron(1957)inlimitingthemselvesto nucleosyntheses insupernovaeappearmoreattractive reprocessing. ejected intotheinterstellarmediumwithoutsignificant likely thattheproductsofthisevolutioncanbe ways allpreviousattemptstomakethe/7-nuclei by Arnould(1976)ofthe/7-processduringhydrostatic This sameobjectionalsoappliestoarecenttreatment within astar.Anyexplosionsignificantlypowerfulto during stablestellarevolution,itdoesnotappear eject themwouldprobablymodifythecomposition. processes leavetheproductnucleistilltightlybound the timerequiredforsignificantweakinteraction. 9 oxygen burning.Whilehisworksurpassesinmany time scalethatis,inallbutafewcases,shorterthan notably (y,n),woulddestroytheseedabundanceina Finally, onemustconfronttheproblemthatsuch interactions occuratreasonablerates(cf.Reeves temperatures requiredtomakephoton-inducedweak and Stewart1965),photodisintegrationreactions, In §IIIanalternativemechanismispresentedfor For thesereasonsmodelsbaseduponexplosive Vol. 36 197 8ApJS. . .36. .2 85W 2 62 9 1/2 18-1 5-3 9 9 -3 -32 4-3 p-nucleosynthesis insupernovae.Inparticular,what ^-nuclei atanearlyuniquevalueoftemperature.The tures matter. to firstconsiderthestatusofothercurrentmodelsfor and densityofthezonestreated.Onlyabundances of seednucleiandthedistributionphotontempera- that existintheliteratureallsharefollowingset are theweaknessesincalculationsofBFH,AT, and othersthatleadustosearchforalternativesites and resultsofthesecalculations,however,itisuseful No. 2,1978 We findseriousflawsineachoftheseassumptions. neutron reactionsoccurringonheavyseednucleiand temperature abalanceisattainedwherebyphoto- of ‘canonical”assumptions(cf.BFH,AT): proton captureonlighterseednucleiproceedat attain temperaturesinexcessof2x10K.Atthis to thelocalhydrodynamictimescale,r=446/(p) comparable rates,makingpossiblethesynthesisofall and methodsforproducingthesenuclei? nova expansionvelocitiesimplyanenergyinputof generate onlyabout10ergsg.Observedsuper- contained intheradiationfieldpergramofbaryon zones ofanycommonastrophysicalevent?Itdoesnot abundance distributionofheavyelements. synthesis. time scalefortheexpansionisassumedtobeequal of asupernovathatduringtheirexplosiveejection have beenenhancedbyafactor of100!Ifnoenhance- is theamountofmaterial persupernovathatAT tion fieldofthesametemperature. Thevalue0.01M© the energyrequirementsforheatingroughly0.01M© Another wayofseeingthissameresultistoconsider the baryonmassdensitymustbep^10gcm . zones responsibleforthe/7-process,alowerlimitto hydrogen burningitself,nuclearreactionscan mass wouldbe for timesaslong10secondsinthehydrogen-rich ment hasoccurred,acorrespondingly largermass the presentabundanceseven iftheseedabundances predict mustexperience/7-processing toaccountfor appear likely.Undersuchconditionstheenergy of baryonsto2x10Kinequilibriumwitharadia- supernova cansomehowbeconcentratedinthose similar magnitude.Unlesstheenergyoutputofa 2 x10KhasbeeninsertedforT.Exclusiveof where pisthematterdensityingcmandavalueof s forpingcm.Valuesoftherange10to 10 gcmareusuallyemployed. HD0 b b b 9 Before discussingingreaterdetailthemethodology Models oftheexplosive^-processinhydrogenzones 2. Weakinteractionsarenegligibleduringthe 3. Thedistributionofseednucleiislikethesolar 1. Therequiredsynthesisoccursinhydrogenzones Can temperaturesashigh2x10Kbeachieved © American Astronomical Society •Provided by theNASA Astrophysics DataSystem 231 E =aT*lp1.21x10/ergsg",(1) ybPö n. PROBLEMSWITHCURRENTEXPLOSIVE a) ThermodynamicConditions MODELS /^-PROCESS INSUPERNOVAE 2 3 43 23 -3 3 52 2 9 2+ 3- must bespecified.Thismassandanaveragedensity energy is imply avolumeofradiationenergythatmustbe weak interactionswerenegligible. required. Atypicalsupernovaexplosiongenerates deposited withinthat0.01M©ofbaryons.That computed byBFHassuming aproton-linkequilib- earlier work.Thelimitingprotonseparationenergy This waslongcomparedtoassumption(i),andhence minimum expectedpositrondecaytimeofabout10s. gen envelopesofordinarystars.Typicaldensitiesatthe 0.01 M,thedensityrequiredisactuallymuchlarger. those zones.Sincerealisticallyonlyasmallfraction put ofasupernovacansomehowbeconcentratedin namely T=2.0andp = 10gcm”,inequation rium calculatedatT= 2.5 andp=10gcm". where (p,y)additionwill stop,forexample,was actions, eventhoughthecircumstancesnowadays quent workshavealsochosentoignoreweakinter- result ofassumptions(ii)and(iii)wastoyielda elements characteristicofforbiddendecays.The energy ofanyproductnucleusbecomeslessthan4.3 (i) thetimescalefor/7-processis10to100seconds, neglect wasbaseduponacertainsetofassumptions: r- and¿-seedinto/?-nucleitheirprogenitors.This for suchanextremetemperatureisshort(^0.1s), base oftheheliumburningshellshighlyevolved cm isrequiredinthosezonesspecifiedbyATasthe (Schramm andArnett1975).Weconcludep^10g neutrino emissionandkineticenergyofexpansion approximately 10ergs,mostofwhichgoesinto If noseedenrichmenthasoccurredalargervalueis (26) ofBFHnowyieldsS =2.6MeVinsteadofthe Use ofthemoremodernconditions employedbyAT, dictated forthesynthesisdifferinkeywaysfrom MeV, and(iii)allweakinteractionshavematrix (ii) protoncaptureceaseswhentheseparation Truran, andSparks1975).However,thetimescale extreme cases,beheatedto2x10K(Starrfield, be foundonthesurfaceofanaccretingwhitedwarf, therefore seemsunlikely.Largeprotondensitiescan burning shellswouldbeagreatdealsmaller.The density exist?Certainlytheydonotexistinthehydro- site of/7-processsynthesisevenifseedenrichmenthas and (e~,v)thatwouldoccurduringtheconversionof BFH chosetoignoretheweakinteractions(ev) and theamountofmaterialprocessedissmall. of thetotalenergyasupernovacanbedepositedin occurred andalargefractionofthetotalenergyout- and duringanovaoutburstthishydrogenmay,insome occurrence oftherequisiteconditioninsupernovae Howard 1976).Densitiesintheoverlyinghydrogen stars areontheorderof10gcm(Lamb,Iben,and q 9b 9 b b p Where intheGalaxydohydrogenzonesofsuch Following thesepreliminarycalculations,allsubse- In theirearlycalculationsof/7-processsynthesis Ey b) RoleofWeakInteractions 54 2.4 x10M ergs 0.01M• Pb0 287 (2) 197 8ApJS. . .36. .2 85W rocess 56 2 /7-nuclei innonenrichedzonesplacessevereenergy photon bathsufficiently intense toinducenuclear vented, butthenatureofseeddistributionand it explodes.Thereisnoapriorireasontobelievethe parameters remainsevereproblems. itself probablychangesresultsofthe/7-processvery i.e., notther-processseed(Arnould1976).Thisin which areduetothe¿-processshouldbesoenhanced, ¿-processing inornearthezonesconsidered.One to energeticsandweakinteractionscanbecircum- properly calledthe“y“P-”Wewillfindthat composition, andevolutionarystateofthestarwhen requirements ontheexplosion.Therefore,more processing hasoccurredduringthepreexplosive for reasonsthatwillshortlybecomeobviousismore dances. distribution shouldresemblesolar¿-processabun- abundances isacomplicatedfunctionofthemass, mate, isthedistributionofelementsininterior little sincether-processnucleiarenotespecially hancements ofheavyelements,presumablybyprior realistic approachtypifiedbyATdemandslargeen- tion ofabundantseedmaterialupwardfromFe sensitivity oftheresults tounknownexplosion objections raisedintheprevioussectionwithregard of starsthathavedone¿-processing.Thisset stantially, however,andwhatisverydifficulttoesti- important seeds.Whatcanalterthesituationsub- obvious implicationisthatonlythoseseednuclei evolution, itmaybeanexcellentapproximation,but, heavy elementsasseedsforthe/7-process?Ifnos- into thelighter/?-nucleiisadistinctpossibility. considered atleastforthelighternuclei.Thepropaga- proton driplinewillbeformed. as mentionedbefore(§II, relatively slowlyvaryingfunctionoftemperatureand is thea-particleseparationenergy,andDagaina where Aisthereducedmass,roughlyequalto4, photodisintegration accompaniedbycharged-particle Rough estimatesfortheconstantsCandDcanbe and itbecomesenergeticallymorefeasibleforthe nuclear properties.Asimilarexpressioncouldbe emission isincreasing.Forexample,therateof proton ora-particleisdecreasingandtheratefor Kp +Ka>Kn(seeTable7).Theresultsofsucha (y, d)reactiononanucleuswithZprotonsisroughly larger, andtherateofphoto-neutronreaction each neutronejectedSbecomes,ontheaverage, slower. Atthesametimeseparationenergyfora (Fowler, Caughlan,andZimmerman1967).With tion energyofthespeciesunderconsideration where Cisaslowlyvaryingfunctionoftemperature and nuclearpropertiesSistheneutronsepara- that thedominantphoton-inducedreactionwillbe 9 (y, ri).Therateofneutronejectionisgivenby the r-and¿-processesnuclearsystematicsaresuch reactions. Forstableelementsthatareproducedby n 9 ypya yp na na9q ypyayn n n 5/61/31 = DTexp[-r/r-11.6055(MeY)/r]s", 9a A moreaccuratecalculationofthebranchingpoint 3/21 A =CTexp[-11.605S(MeV)/:r]s",(3) yn9n 21/32/3 r =4.2487(4ZZ)^10.7(Z-2),(4) a Vol. 36 (5) 197 8ApJS. . .36. .2 85W No. 2,1978 branching. Nucleiwithoddneutronnumbersthathave y-process solongasoneconsiders(i)temperaturesin in theirdestruction. reactions onsuchnucleiisalwayslargeanddominates masses greaterthanthenumbersgiveninTable2are numbers ofneutronsmayalsobesitessignificant interactions willbecompletelynegligibleforthe not branchingpointsbecausetherateof(y,n) tory half-livesofspeciesinTable2. the rangeof2-3billiondegreesorlessand(ii)time element reachesthecriticalpointgiveninequation particle. Ifitejectsneutronsanotherwaitingpointis feasible toejectneutronsorittoomayacharged in thecaseofalphaemission.Theproductnucleus in thenuclearchargeofelement,adecreaseby2 scale valuecomesfromanexaminationofthelabora- eventually reachedwherecharged-particleemission thus formedmayonceagainfinditenergetically (5), furtherphotoninteractionwillleadtoachange scales lessthanabout100seconds.Thelimitingtime- interest, however,isthenucleosynthesisthatoccurs equilibrium isattained. protons, andalphas.Astateofnuclearstatistical mixture ofiron-groupnucleiandfreeneutrons, flow ofmaterialdownfrom leadtowardironformsa iron. Insteadofasinglenucleus onemayenvisiona process occurs(see§IV).Whatisofconsiderable particle-producing reactionsinthesitewhere form anegligibleperturbationonthemoredominant ejected bythisy-process.Theywillpresumedlyjust occurs andtheprocesscontinues.Ultimately not sointenseastototallyreduce allheavyelementsto for valuesoftemperatureandtimescalethatare original heavynucleusisphotodissociatedintoa sufficient toinducesome nuclear transformationyet of interestherenorarethefreeparticlesthat distribution ofseednuclei extendinguptolead,all subject tothesameintense radiationbath.Thenthe One immediateconsequenceofTable2isthatweak Once thephotodisintegrationflowforagiven The extremecaseoftotalphotodissociationisnot © American Astronomical Society •Provided by theNASA Astrophysics DataSystem Branching PointsforHeavyElementsUndergoingPhotodisintegrationatT=2.5 9 /^PROCESS INSUPERNOVAE TABLE 2 196190 ^-nuclei butanuclearchargelargerby2.Forexample, various pointswheretheflowisimpededbecausesome to someparticularseednucleus.Hereandthereare will accumulateatornearthesewaitingpoints, near thebranchpointsgiveninTable2.Material element ofnuclearchargeZthelongestphoto- nucleus hasanunusuallylonglifetime.Foreach stream withmanytributaries,eachstretchingback temperatures, namely2^r3,waitingpoints heaviest nucleiconsidered.Theveryinterestingaspect 2.5) thedominantphotodisintegrationflowsfor especially fornucleiwithaclosedneutronorproton nuclei arepartiallybutnottotallyphotodisintegrated. that woulddecaytop-nucleibypositronemission which showsforarepresentativetemperature(T= disintegration lifetimesontheflowpathtendtooccur progenitors havingthesameatomicweightas after ejection.Thisrangeoftemperaturesisalso odd-particle nuclei. shell. Verylittlematerialwillaccumulateatoddand that thiscorrelationhadonly todowiththelifetime That suchacorrelationdoesindeedexistwaspointed correlation betweentheobservedsolarabundances not haveoriginatedinaproton-richenvironmentat down totheelementerbium.Suchacorrespondence For higherZthecorrespondenceistoproton-rich of specialinterestbecauseatsuchtemperaturesheavy of suchascenarioisthatforreasonablerange all butinsteadinaphoton-dominatedprocess. suggests thatthenucleiattributedtop-processmay For Z<66thep-nucleithemselvesarewaitingpoints. seem tocorrespondeitherthep-nucleiornuclei several p-nucleimightreflect thenuclearpropertiesof also neglectedthepossibility thattheabundancesof energy) andignoredtherole of(y,p)anda).He against (y,n)reactions(and henceneutronseparation out byMacklin(1970).However, Macklinsuggested of thep-nucleiandtheirphotodisintegrationrates. Hg isproducedasPb,Pt,andsoon 9 Q This behaviorisqualitativelyillustratedinFigure1, If thisconjectureiscorrect,onemightexpecta 289 197 8ApJS. . .36. .2 85W + 6 290 theless, Macklin’splotsofabundanceandneutron nuclei and,whereappropriate,theirproton-rich progenitors ratherthanthoseofthemselves.Never- alpha flows,respectively.Inthismassregionandattemperaturethep-nucleiareprimarilyproducedasproton-richprogenitors disintegration rateA=+forthep- separation energyshowstrikingcorrelation. solar abundancepatterntoaplotoftotalphoto- which decaybypositronemission(arrowslabeledß)aftertheexplosion. symbols representallthestableisotopesofgivenelement.Arrowslabeledwith“/i”or“a”photo-neutronand photo- disintegration. with closedneutronorproton shells. Theabundanceofthep-nucleiappearstobestrongly anticorrelated withtheirrateofphoto- mass number.Alsoshownisa plotoftheirsolarabundancebynumberrelativeto10silicon atoms.Thearrowsindicate/^-nuclei ynypa A moreproperapproachwouldbetocomparethe Fig. 1.—Photodisintegrationflowsinthevicinityofheavy/?-nuclei{doublesquares).Thecircleslabeledwithelemental Fig. 2.—Totalphotodisintegration ratesAforthep-nucleiandtheirproton-richprogenitors atT=3.0asafunctionoftheir 9 © American Astronomical Society •Provided by theNASA Astrophysics DataSystem "Fe" il 4 3 np io 1^1 densities ofroughlypx10-10gcmforsuch (Arnett 1969;WAC).Argumentsbaseduponnucleo- still largervaluesoftemperature.Suchtemperatures working hypothesisregardlessoftheexactvalue synthesis andpresupernovastructureyieldarangeof peak photontemperatureassumed.Thecurrent knowledge ofsupernovastructureandevolutionis ya feel thatexplosivecarbon andoxygenburningform from anexactspecification ofitssite.Thus,whilewe present time.Thissimple approximationhasthe accurate asanyotherwe might caretomakeatthe sufficiently uncertainthatparametrizationisas the mostreasonablecontext forourcalculations,the advantage ofdecouplingthe treatmentofthey-process m 9m 9 T r m 12 We nowmovefromthequalitativeconsiderations In allthatfollowswewilladoptr=1sasa r TT =3thdV(247rGp)l33S-s.(7) mP tí) ResultsofNumericalCalculations TU/) =Texp(-i/r).(6) dnr 291 197 8ApJS. . .36. .2 85W radiation bathhavingatemperaturehistorygivenby photodisintegration liesnearthevalleyofbeta are giveninTable4.Foreachpeakexplosiontem- equations (6)and(7)forarangeofpeaktemperatures sidered in§Hid).Thiscompositionwasexposedtoa calculations, asolar-systemdistribution(Cameron interactions wereignoredbecauseoftheshorttime of 2.1isotopes maybeimportantforunderstandingthe pointed outthatthep-processcontributiontothese the speciesXeandXe.Clayton(1976)has approximate representation ofthesolarabundances. and Sabu1972;Lewis,Srinivasan,Anders1975). 4400. a distributionofexposures inordertoobtainevenan assumed, aresultthatisexpectedfromthequalitative origin ofso-calledcarbonaceouschondritefission 1800. 310. 490. 340. 270. 380. 760. 380. 160. 190. 120. 2.6 72. 29. 26. 13. 86. It isreadilyapparentfrominspectionofTable4 10. 4.0 0.1 0.5 2.8 3.2 2.9 9.8 7.0 1.0 6.0 3.2 1.8 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Temperature 3.0{~2) 1100. 160. 290. 100. 560. 220. 170. 590. 4L 2.7 81. 40. 96. 27. 20. 76. 16. 18. 15. 14. ’ 0.2 0.1 6.2 1.0 1.6 1.0 1.1 1.9 1.0 1.1 1.0 1.6 2.3( —2)2.8(-4) 1200. 680. 100. 270. 200.’ 410. 530. 120. 2.8 23. 82. 45. 23. 70. 83. 15. ’2.4 3.9 9.9 8.1 1.0 3.5 1.1 1.1 1.9 1.0 155. 690! 140. 2.9 92. 30. 23. 42. 86. 63. 36. 66. 38. 15. '4.8 0.2 5.7 2.0 0.5 2.6 5.4 1.3 1.4 1.0 290. 320. 360. 120. 160. 3.0 38. 37. 59. 18. 15. 15. 2.0 4.9 0.1 8.6 7.6 0.2 4.4 8.2 3.1 8.5 5.1 5.2 1.2 61 16 17 32 65 14 3.1 8 7 Ó 4 6 3 7 7 293 34 85 3.2 11 17 2 197 8ApJS. . .36. .2 85W 9 8 in theGalaxy’shistory.Furthermore,itisimportant vicinity of2-3x10Kshouldreachsomeunique if atimescale100timeslongerisemployedandthe we havefoundthatverysimilarresultsareobtained used togenerateTable4isnotunique.Forexample, to notethatthetemperature-timestepcombination by considerationofthevarietysupernovamasses value. Instead,anyrealsupernovawillexhibitarange values ofA)relativetosolarabundancesthat condition 2tQ=1andA^Z,A)denotesthenucleo- peak temperaturesinsiliconburning.Theproblem, peak temperaturescaleisshifteddownwardby 294 have prepared“caseA”inTable5whichshowsthe explosion characteristicswhichwecannothopeto preexplosive evolutionofthetypicalsupernovaand where C*issomeweightingfunctionsubjecttothe the totalsynthesisfromy-processbegivenby the siteofy-processsynthesismustbespecified.Let ith valueofTsm-TheCiarefunctionsboththe summation abundance vectorsinTable4,thecharacteristicsof 2 x10K.Similarargumentshavebeenproposedby of conditions,arangethatwillbefurtherbroadened specify atthepresenttime.Forillustrativepurposeswe synthesis vectorresultingfromexpansionthe strengths hasactuallyoccurred. of course,istoknowwhatdistributionexposure Michaud andFowler(1972)toaccountforarangeof In ordertocomputethepropersummationof © American Astronomical Society •Provided by theNASA Astrophysics DataSystem c) ResultsAveragedoverPeakTemperatures 164 168 156 158 174 190 138 144 i84 196 130 132 136 128 14614 i8 130 138 162 Er Yb Dy Dy.! 162£ Hf Pt Ce Sm os* Hg Ba Ba Ce [202/l96]. [Xe]t [Sm/Sm]t. [°Tait! [Xe]t [La]t [Gd]f r PbHg1 t Bracketedspeciesnotincluded incalculationofmean. * RelativetoCameron1973. NUZ,A) =^CN(Z,A),(8) i Species Overproduction Factors*for/?-NucleiAveragedoverTemperature 2.4 (-2) Case A 220. 270. 320. 660. 320. 500. 140. 190. 110. 160. 42. 20. 38. 82. 86. 12. 11. 0.5 4.2 3.4 1.2 WOOSLEY ANDHOWARD 2.3 (-2) 1000. Case B 1100. 260. 460. 540. 660. 300. 160. 340. 690. 310. 140. 170. 160. 93. 18. 15. 14. 2.1 6.8 1.1 TABLE 5 92 78 84 94 96 74 98 108 i2 80 102 106 114 126 112 124 76 9292 116 113 Mo Kr Sr Mo Ru Se Ru Cd °Te [KrJt Pd Cd Sn Xe Sn Xe [Se]t [Nb/Mo]t. [sn]t..’!!!! [In]t 113115138152180 113115 152138180 p-nuclei areconsistentlyproducedrelativetoone to exploding,thestellarzonesunderconsideration A ofTable5,itiscertainlyanerroneousone!Prior is initiallysolar.Althoughthisassumptionmaynot be thesolecauseunderlyingalldeficienciesincase in assumingaseeddistributionforthey-processthat tion of^4<110p-nucleiisthatwehaveerredgreatly least anorderofmagnitudelessthanthatvaluewhich five nucleithatareunderproducedlikelytobe is impressive.Allp-nucleiheavierthan=110except perature contributesequally,i.e.,C=1/12forall result inthesimplestpossiblecasewhereeachtem- typifies theproductionofp-nucleiheavierthanA= however, thesituationisnotsoencouraging.Many model representedbycaseA,thisisaresounding production factor).Mostarewithinafactorof3. for In,Sn,La,Gd,andTaarecon- another, buttheaverageoverproductionfactorisat Isotopic ratiosareespeciallywellreproduced.Those attributed tothep-process.Eventhissimplestcase success forthetheory!Belowmassnumber110, sidering themanyuncertaintiesinherentinsimple synthesized byeitherthe¿-process(In,Sn,and solar abundance(i.e.,relativetothemeanover- sistently coproducedwithinafactorof5their Figure 3aforthosestableelementswhicharegenerally Gd) orbyspallation(LaandTa).Con- 110. Howisthistobeexplained? t Meant One possibleexplanationforthedeficientproduc- d) NonsolarSeedandNonlinearTemperature Species These resultsarealsodisplayedgraphicallyin Distributions 4.8 (-3) Case A 110. 100. 120. 41. 35. 71. 34. 36. 22. 11. 2.5 2.8 9.3 2.1 0.2 2.6 7.1 3.5 3.0 1.8 2.1 (-3) Case B 260. 290. 260. 180. 100. 110. 100. 99. 99. 77. 32. 22. 66. 75. 99. 4.4 0.4 5.9 5.7 5.0 197 8ApJS. . .36. .2 85W temperatures. 5-process enhanceddistribution ofheavyelementswithalltemperaturesweightedevenly, (c), Resultsforan5-processenhanced distribution ofheavyelements, butwiththecontributionfromhighertemperaturesweighted 3timesmorethanthatfromlower element, (a).Resultsforaninitial solardistributionofheavyelementsandalltemperatures weightedevenly.(b)Resultsforan 9 Fig. 3.—Relativeoverproduction factorsforthe^-nucleiasafunctionofatomicweightA. Linesconnectisotopesofthesame © American Astronomical Society •Provided by theNASA Astrophysics DataSystem 197 8ApJS. . .36. .2 85W 180 132 138 174 i84 96 130 130 136 138 166 164 168 l80 196 98 128 152 144 158 74 76 80 102 106 108 113 112 114 115 120 124 126 84 92 94 92 2 14614 perhaps carbonburningaswell.Theyaretherefore elements upto^4ä;90.Thesewereaccompaniedby productions ofroughlyafactor50occurredfor hancements ofheavierones.IntheworkbyCouch, nonsolar patternof¿-nucleicharacterizedbylarge kamp, andArnett(1974)Lambetal.(1977)have have verynonsolarabundances.Couch,Schmiede- have experiencedhydrostaticheliumburningand essentially noproductionofheaviernuclei.Lamb as initialseedonlyironandlighterelements,over- burning inmassivestars.Bothstudiesyieldedavery overproductions oflightelementsandsmalleren- studied the¿-processthatoccursduringcorehelium almost certaintobeenrichedin^-processseedsthat w Schmiedekamp, andArnett(1974),whichemployed 296 Ba Ce Hf os\‘!’. ! Ru Xet Ba Ce La Dy 162£j. Er Yb Ta..!.!!!!! 190pf Hg Ru Xet Gd Sm Dy... !....! Se Set ^Kr Krt Pd Cd Cd In Sn Sn Sn Te Xe Xe ment fromheliumburning(Lamb etal.1977). Sr Mo Mo [Nb/Mo]... [02/196]f . [Sm/m]., PbHg f Bracketedratiosgiveproduction oflong-livedunstableisotopetostable77-nucleus. Î ^-processnucleuswithinteresting y-processmodification.Theproductionratiogivenhere includesthepreexplosiveenhance- * Relativetosolar(Cameron1973) abundances.Entriesthatareitalicizeddominantlythe radioactiveprogenitor(Z+2,Z). © American Astronomical Society •Provided by theNASA Astrophysics DataSystem Species Overproduction Factors*for^-NucleiatVariousExplosionTemperatures(Enhancedseed) 7.5(-5) 610. 170. 74. 43. 12. 10. 73. 11. 2.1 2.7 4.7 4.5 1.0 2.9 7.1 5.0 1.8 1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 7.8 (—4) 2500. 210. 870. 640. 180. 2.2 44. 38. 75. 14. 11. 0.9 2.8 4.5 6.9 7.5 5.1 3.3 1.0 1.0 6.7 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.1 1.0 1.0 1.2 1.0 1.0 1.0 1.0 1.4 6.4(-3) 4100. 1700. 1700. 980.' 550. 750. 620. 100. 40. 2.3 25. 63. 81. 11. 0.7 2.1 2.3 3.6 7.6 7.1 5.0 2.0 1.0 3.2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.2 1.1 WOOSLEY ANDHOWARD 9.9(- 3.4( —2) 2000. 1800. 1300. 1100. 1500. 330. 750. 760. 370. 130. 2.4 28. 92. 30. 13. 17. 4.2 4.1 0.2 7.0 8.1 1.0 7.0 1.0 1.0 1.2 1.4 1.0 1.1 1.0 1.0 1.1 1.0 1.3 1.0 1.0 1.0 1.0 1.6 1.9 1) 2.4( —2)8.3(—6) 7.0(—2) l.K-2) 1100. 4700. 4300. 940. 2400. 1000. TABLE 6 600. 220. 390. 100. 190. 120. 2.5 88. 94. 20. 37. 13. 0.1 4.4 2.6 3.2 2.4 3.8 6.8 1.0 9.8 1.0 6.0 3.2 1.0 1.0 8.8 1.0 1.4 1.9 1.0 1.0 1.0 1.0 ^-nuclei exclusivelyfromthoseisotopeswhichare A >90.Theabundancesoftheseheavynucleiwere yielded significantenhancementsofisotopeswith to thoseincaseAofTable5. production ofstilllighter^-nuclei.Thususethe ment oflighterseednucleiwillselectivelyincreasethe heavier thanthe/^-nucleusitself,asystematicenhance- was roughly3.Sincethey-processalwayssynthesizes increased byhighlyvariantfactorsthemeanofwhich they foundarearrangementofheavynucleithat all nucleiuptoandincludinglead,alsofounda burning shouldyieldimprovedresultsascompared actual seeddistributionfollowingstellarhelium et al.(1977),usingasseedaPopulationImixtureof similar enhancementof^90nuclei.Inaddition 2.2 (—2) 3.2( —2) 5100. 8900. 1300. 1400. 840. 280. 460. 660. 500. 560. 190. 680. 170. 140. Temperature 2.6 43. 23. 94. 39. 13. 15. 12. 12. 16. 0.1 0.5 0.7 1.0 1.0 3.3 8.4 7.6 1.1 1.1 1.0 1.1 1.1 1.0 3.0{-2) 5.6 (—4) 2200. 2100. 1100. 220. 360. 280. 170. 930. 790. 370. 510! 120. 90. 2.7 94. 47. 23. 86. 35. 67. 31. 54. 0.2 0.2 0.4 1.1 3.0 3.6 1.8 1.6 1.4 1.3 1.0 2.2 (-2)2.5( 2400. 1400 480. 480. 400. 270. 300. 610. 940. 310. 660. 2.8 88. 23. 73. 96. 92. 59. 17. 12. *8.9 3.3 4.8 0.2 6.0 6.7 1.0 1700 250 330 230 140 350 320 190 130 110 110 2.9 63 28 24 Ï6 62 36 21 14 17 0 Ó 1 1 -4) 430 290 750 770 830 112 150 146 170 120 3.0 69 33 27 29 74 24 17 14 15 *0 15 *4 0 8 490 210 110 515 620 150 140 3.1 35 18 18 15 9 Ó 7 Vol. 36 2700. 3.2 240. 260. 550. 58. 197 8ApJS. . .36. .2 85W 747884 92949698 9294968 p-nuclei, thesituationisstillfarfromcompletely the increasedamountofheavyseedavailable.For heavy nuclei,A^110,isverysimilartothatobtained format similartoTable4.Thenucleosynthesis calculations discussedin§III6usingthemodifiedseed yield anoverallimprovementintheproductionof larger increaseduetothenatureofseed lightest ^-nuclei,Se,Kr,andthereisamuch with solarseed(caseAandFig.3a)exceptforan averaged overpeakexposuretemperatureisalsogiven The resultsaredisplayedinTable6,whichhasa overall increaseofroughlyafactor2reflecting as caseBinTable5andFigure3b.Thesynthesisof distribution ofLambetal(1977)fora25Mstar. too abundantandthereisinsufficientseedofatomic prepared Figure3ctoillustratethiseffect.Thisfigure higher explosiontemperaturesthanthosewhichmake maximum productionofthelightnucleioccursfor What istheexplanation?Apossibilitytobebriefly distribution. large enhancementsnotonly of^4^90butalso likely thattheresultantseed distributionwouldhave tional ¿-processingwilloccur (ArnettandTruran ment! See§IVformoredetaileddiscussion.)Helium parative simplicitywefavortheformerofthesetwo reactions duringtheexplosion.Becauseofitscom- preexplosive ^-processing,or(2)particle-induced weight ^4>96toeverleadlargeoverproduction production dominates.TheMoandRu/7-nucleiare correct fortheoverall“skewed”productionof but itdoesillustratetwoimportantpoints:(1)a peak temperaturedistributioniscompletelyadhoc employed =1/24for2.1110/7-nuclei,asevidencedin nonlinear peaktemperatureexposuredistributioncan selectively enhancethelighter/^-nuclei.Wehave Mo, Ru,andu.Wefeelthatallfour small synthesesofspeciesintermediatemasslike additional seedmaterialupfrombelow^4=92 Figure 3b,but(2)itcannotsubstantiallyincreasethe of thesespeciesmustbeproducedbyay-or/?-process. sensitively onunknownstellar parameters,butitis ’Mo and>Rumustinvolvethepropagationof simply isnotemperatureinTable6whereMoandRu overall productionofRuandMoisotopes.There 3/24 for2.7photons absorbedbythey-processaresofewcom- burning processesthatoccurinthoseexplodingstellar attractive features. scenario wouldrequirethatthesiteofy-process produces a-particles~10 times faster,therateof from asimilarratiointhereaction ratesforC+ 2% Ne.Theother,typicalofacarbon-exhausted effect uponthebackgroundabundancesofthese approach isclearlyvalid.Theparticlesreleasedand carbon (Arnett1969)oroxygen(TruranandArnett under identicalconditions. This largedifferenceresults magnitude smallerthanresults fromcarbonburning factor indescribingthecharacterofy-process.As zone, was54%0,28%Mg,2%and14% burning processthattheycertainlyhavenegligible and 0+.Sincecarbon burningatT=2.5 exhausted zone,wasbymass50%C,48%0and employed. Onecomposition,typicalofahelium- cases, buttwodifferentinitialcompositionswere e-fold decreaseintemperaturewas1secondall peratures T=2.5and3.0.Thetimescaleforan reaction networkssimilartothoseofArnett(1969) 4a and4b.Thesecurveswereobtainedbyusing the explosionisadiabaticsothatpocT.Theresults in equations(6)and(7).Inadditiononeassumesthat characterization ofexplosionthermodynamicsgiven representative valuesbyemployingthesamesimple restrict flowstowardproton-richnucleiand protons. Thepresenceofthesenucleonsactsto must beconsidered. burning mayalterthecharacterofy-process,and oxygen burningatT=2.5 isroughlysevenordersof Figure 4ashows,theneutronfluxthatresultsfrom Si. expanding fromp=5xl0gcmandpeaktem- and WACtotrackthenuclearevolutionofzones and explosionparameters,itispossibletoobtain exposures duringthey-processinvolveneutronsand a-particles thatarepresentduringcarbonoroxygen abundances themselves,theneutrons,protons,and species. However,theeffectsoffree-particle of foursuchmockexplosionsareshowninFigures of theseparticlesissensitivetounknowncomposition of lowerZ,respectively.Whiletheactualfluxhistory 1970; WAC).Inonesensesucha“perturbation” 9 9m bQ 9 Thus farithasbeenimplicitlyassumedthatthe The choiceofcompositionturnsouttobeakey Besides photonsthemselves,themostimportant IV. EFFECTOFBACKGROUNDPARTICLEFLUXES 297 197 8ApJS. . .36. .2 85W 5-3 2225 72629 298 WOOSLEYANDHOWARDVol.36 pendix AandAiisatypical timescalefortheduration being importantis the branchpoint(Z,^nch)characteristicallyoccurs reaction duringoxygenburning[thecrosssection at (Z,^branch+2),aroughcriterionfortheneutrons listed inTable2.Sincetheslowest(y,ri)rateshortof reactions forsomenucleusshortofthebranchpoints neutron sourcesduringcarbonandoxygenburning, factors forthe(a,ri)reactionsthemselvesdonotdiffer for thepeaktemperatures=2.5and3.0. neutron fluxmustbesufficienttoimpede(y,ri) and thedifferenceisreflectedinfreeneutron markedly atthistemperature].Thesearethedominant function oftimeduringexplosiveoxygenandcarbonburning of neutronmassfraction X.Adoptingtherepre- abundances. sentative valuesp=5xl0 gcm andAä3x pJ^n^nyC^branch “b1)^Max[1/Aí,Ay(^42+2)], Ne (a,ri)Mgreactionduringcarbonburningis where thequantitiesAand AaredefinedinAp- bra ~ 10timesmorerapidthantheMg(a,ri)Si n ny 7lbrailC1 ny yn In ordertosignificantlymodifythey-process,this Fig. 4.—Neutron{a)andproton(b)massfractionsasa © American Astronomical Society •Provided by theNASA Astrophysics DataSystem logt(sec) 10 (9) 4 22 3 22 731 volving theverylightestelementsinnetwork zones incloseproximity,some ofwhichexperiencea ground neutronfluxthatoccursinstellarzonescon- y-process shouldproceedunaffectedbytheback- temperature distributions,mayrequireadditional temperature, r=3.2forexample,somehindrance fied foranyelementduringexplosiveoxygenburning present calculationsmaynot bevalid. Thus forexplosivecarbon burningatT^2.3our produces neutron-richisotopes (Howardetal.1972). photon fluxmaynotbesufficienttodrivethey-process, temperature hasfallensignificantly.Theremaining peak temperatures2.1^Tg3.2. currently experiencingexplosiveoxygenburningwith modification. Forallheavierspecies,however,the uncertain duetotheeffectsofenhancedseedand calculations ofthey-processforA^90,alreadyvery (e.g., Se,Kr,Sr).Becauseofthishindranceour condition becomes remains roughlyconstantbutthepeakvalueoccurs experience carbonburning.Thetotalneutronflux temperatures. can stillproceedaspreviouslydescribedwithonly the neutronfluxhasdecreasedfourordersofmag- increasing neutronnumbertodecreasing 4a showsthatduringthefirst2x10"sofexplosive zones undergoingexplosivecarbonburning.Figure at r<2.5.Forhighervaluesofpeakexplosion and adifferentsortofnucleosynthesis resultsthat neutron flux.Asimilarbehaviorisexpectedathigher nitude fromitspeakvalue.Asaresult,they-process that timethetemperaturehasdroppedonly1%,but carbon burningatT=2.5afluxofroughly3x10 of flowmayoccur,butonlyfor(y,ri)reactionsin- Examination oftheratesinTable7andvalues of flowsdescribedabovedoesnotoccuruntilthe T§m ^2.3thefluxlastssolongthat“turnaround” over alongerexposuretime.Fortemperatures a somewhatalteredbehaviormayoccurinzonesthat number occursatanelapsedtimeofabout0.01s.At carbon burningatT=2.5,thisreversalofflowfrom to theproton-ûchsideofvalleybeta-stabilityby falls offrapidlyandtheheavynucleiaredrivenback tion ofneutrons(dueinthiscasetotheexhaustion by eitherstrongreverse(y,ri)reactionsorthedeple- the floweventuallyreachesastagnationpointcaused result, seednucleimayinitiallycaptureneutrons,but exposure timeisfartooshortfortherequisitebeta- is typicalofr-processnucleosynthesis,butsuchan neutrons cm"ismaintained.Afluxofthismagnitude slight hindrancefromastillrapidlydecreasing (y, ri)reactions.Figure4ashowsthatforexplosive decays thattypifytheusualvarietyofr-process.Asa X inFigure4ashowsthatthiscriterionisnotsatis- Ne). Fortimet^0.001sthefreeneutronabundance 10 cmmole"s"(toanorderofmagnitude),this 9m 9m 9m Q Q n An intriguingpossibilityis theexistenceofstellar At explosiontemperatureslowerthanTæ2.5, This isobviouslynotsoifthey-processoccursin Qm 13 (Z/10") ^Max[1/Ai,A(^+2)].(10) nynbrancll 197 8ApJS. . .36. .2 85W 10 56 53 93 16 12 53 7 //-nuclei. Amixtureofsuchcontiguouszoneswouldbe example. Thisisinterestingbecauseisotopicanomalies type ofr-processandproduceneutron-richisotopes, enhanced inbothther-andp-isotopesofxenon,for zones intotheearlysolarnebulaeitherinformof Anders 1975;Manuel,Hennecke,andSabu1972). previously. Again,foroxygenburning,nomodifica- pertain totheprotonfluxduringexplosivecarbonand Incorporation ofrelativelyunmixedmaterialfromsuch and otherswhichundergothey-processproduce example, theprotonabundanceisatmaximum10" results fromthesameexplosiveexpansionsdiscussed of thisnaturehavebeendiscoveredinmeteorites(cf. Thus suchreactionsshouldbenegligiblewithinthe this impliesalifetimeforFeagainstprotoncapture by massfraction.Atadensityof5x10gcm" tion ofthey-processisindicated.At=3.0,for dust (Clayton1975)orgas(CameronandTruran Reynolds andTurner1964;Lewis,Srinivasan, will havestilllongerlifetimesagainstprotoncapture. oxygen burning.Figure4bshowstheprotonfluxthat time scaleremainsroughlyconstant(~10"gscm") perature ofeitherTqttx—2.5or3.0andapeakdensity much larger,adifferencewhichoncemoreisdirectly context ofa1secondexpansiontimescale. reaction asopposedto0+.Forapeaktem- these conditionsprotoncapturemightbeexpectedto attributable tothegreaterefficiencyofC+ of about10s(Woosleyetal.1975).Heavierspecies the giventimescale,butitmustalsocompetewith Furthermore, theproductofprotonabundancesand of 5x10gcm"theprotonabundanceisabout 1977) mightbeapossibleexplanation. No. 2,1978 as thefreeze-outproceedsattimet>0.01s.Under criterion formodifiedbehavioristhen (usually muchstronger)photodisintegrationflow.The all nucleiofchargeZ<40willbeaffected,fornot occur onnucleiasheavyZæ40.Inactualitynot only musttheproton-inducedreactionoccurwithin where A(A,Z)isthetotalphotodisintegrationrate The synthesisoftheselight//-nucleiduringexplosive network whichsynthesize//-nucleihavingA^100. 10" bymassfractionatanelapsedtimeof0.01s. presently warranted. present uncertainknowledgeoftheinitialseedabun- cated fashionthanwehavedescribed,butgivenour of thenucleus(Z,A).Thisconditionturnsouttobe dances andthermodynamicsofthey-process,wedo carbon burningmayproceedinamuchmorecompli- satisfied onlyfortheverylightestseednucleiin for nucleihavingA^90), andifsuchzonesarethe by thepresenceoffreeparticle fluxescharacteristic not feelthatamorecomplicatedcalculationis of explosiveoxygenburning atT^2.0-3.0(atleast approach isjustified.The y-processislikelytobe site ofthey-process present“perturbation” Q The protonfluxfromexplosivecarbonburningis Similar argumentstothosegivenforneutrons To summarize,they-process isnotgreatlyaffected © American Astronomical Society •Provided by theNASA Astrophysics DataSystem XA(A,Z)Z A(T,Z),(11) Pppy ^-PROCESS INSUPERNOVAE 9 30 9 hydrostatic carbonburning.Suchapicturewouldbe that, priortoexplosioninasupernova,completed the processwehavedescribedisthosestellarzones though notnecessarilyunique,astrophysicalsitefor manner. Thissuggeststhatthemostpromising,al- may stillfunction,althoughinamorecomplex modified. burning attemperaturesTq^çz2.0-3.0.Infactthe No suchoverproductionsoccurforexplosiveoxygen busts attemperaturesinexcessofabout2.2x10K. (1974), whofindthatanundesirablenucleosynthesis consistent withtheresultsofPardo,Couch,andArnett explosive carbonburningatthesetemperatures,but modified bythefreeparticlefluxespresentduring light-element compositionisejectedvirtuallyun- complicated ofallnucleosyntheticprocesses.A of lighterelements,e.g.,Si,resultsifcarboncom- involve (i)thedetailedtrackingofcomposition considered merelytheforerunner,mustnecessarily proper calculation,ofwhichthispapermustbe ^4 ä110thatincludesthepossibilityof(/?,y),(//,n) evolution oftheabundanceselementsatleastupto nuclei (ofwhichperhaps100arequiteimportant); lead); (ii)accuratenuclearreactionratesfor~1100 sented, thep-(ory-)processisoneofmost years suchapropercalculationmayactuallybecome abundances ofallstableelementsfromcarbonto tion chaindownwardfromlead.Withinthenextfew and protonbathslibratedduringexplosivecarbon (tz, y),(«,//),etc.reactionsinducedbythefreeneutron (iii) acorrectdetailedhydrodynamicaltreatmentofthe of thepreexplosivestar(explicitlyincluding feasible. Fornow,though,wearecontenttopointout and/or oxygenburningaswellthephotodisintegra- supernova explosionitself;and(iv)anetwork photodisintegration ofheavierseednucleiinwhich some lessonstobelearnedfromthepresent(relatively zones ofsupernovaethatexperiencecarbonand 2-3 x10Kisrequiredfortimescalesofroughly roles. Acontinuumoftemperaturesintherange (y> «)>P)>and(y,a)reactionsallplayimportant simple) investigation. calculation of//-nucleosynthesis. likely sitefortheproductionofthesespeciesarethose suggest anoriginforthesespeciesbaseduponthe slightly lowertemperaturesandlongertimescales).A played byweakinteractions. in hydrogen-richzonesshould notignoretherole bulk of//-nucleosynthesis.Calculations ofthe//-process novae appearunlikelycandidates forthesitesof oxygen burning. of seednucleiisanessentialconsiderationforany 1 second(althoughsimilarresultsareobtainedwith Clearly, fromtheargumentsanddiscussionpre- 2. Thepreexplosiveevolutionofthecomposition 3. Thehydrogen-richzones ofnovaeandsuper- 1. Thesolarabundancesoftheproton-richnuclei V. CONCLUSIONSANDCOMMENTSON COSMOCHRONOLOGY 299 197 8ApJS. . .36. .2 85W 146 92 14214 146 146 14214 146 7 14614 144 146144 142 146 142 144 .formed, butwedifferintheinterpretationofthese ^-nuclei, reasonedthataproductionratioofSm/ /7-process. Thisresultwasessentiallyconfirmedbythe y-process impliesthatthisspecieswillnotmakea from materialneartheboundaryofexplosivecarbon might originatefromthemixingofzonesinsuper- from previousinvestigationsofthe^-process.Audouze critically uponanuncertainhalf-life. made insupernovaebutitspresentabundancedepends useful cosmochronometer.ThespeciesNbmaybe novae thathaveundergoneexplosivecarbonburning meteorites thatcorrelatedwiththeelementalratioof ported thediscoveryofNd/danomaliesin with apparentsuccesswhenNotsuetal.(1973)re- more accuratenetworkcalculationsofATwho based upontheabundancesandnuclearpropertiesof and oxygenburning. at slightlydifferingvaluesofpeaktemperatureor the meteoritewithinseveralhalf-livesofitsformation. late spikeofnucleosynthesissinceSm(t= and Schramm(1972),usinganinterpolativescheme i.e., thatonlyanunmeasurablysmallamountofSm inferred thattherewasnolatespikeofnucleosynthesis. found novariationofNd/d,fromwhichthey 300 the meteoritebecausethereneverwasadetectable results. InourpictureSmwasnotincorporatedin was presentwhenthemeteoriteunderexamination We feelthatthislattersetofmeasurementsiscorrect, 7 x1oyr)wouldofnecessitybeincorporatedinto obtained Sm/m>1,andthepredictionmet Sm intherange0.35to0.60shouldresultfrom More recently,however,Lugmair,Scheinin,and observations Notsuetal.inferredtheexistenceofa Sm; Ndisunaffectedbythedecay).Fromthese Sm/Nd inthesamples(Ndisdecayproduceof we findthattheaverageproductionratioforSm/ existence ofalatespikenucleosynthesis.InTable5 amount tobeginwith!ThustheabsenceofNd Marti (1975)havereexaminedthesesamesamplesand for they-processfollowsinanobviousmannerfrom anomalies saysnothingabouttheexistenceornon- reactions asformulatedbyMichaudandFowler(1970). Theirprescriptionforphotontransmissionfunctionswas from adeterminationbyTruran(1972) the equivalentsquarewellsinparticlechannels.In particular,wehaveemployedtheeffectiveradiusparameters Sm isabout2°/.Thatthisratioasmallnumber adopted withoutchange.However,slightmodifications weremadeintheradiiMichaudandFowleradoptedfor where istheatomicmass ofthenucleusI.Itwasfeltthatthisparametrization wasmoreappropriateforthe correctly suitedtothelighter intermediate-massnuclei(204£;110andtheveryuncertainvaluefor complex situationforthesynthesisof/7-nucleilighter nova andsolarsystemformation,they-processcould (uncertain toafactorof2),thisimpliesNb/b# a currentvaluefortheratioNb/b=1.5x10. as comparedtoSm(whichhasamagicnumberof contract W-7405-ENG-48. through thegenerousallocationsofcomputertime fornia InstituteofTechnology,TheUniversity Illinois, LawrenceLivermoreLaboratory,TheCali- this investigation,includingRiceUniversity,Los this species. mature tobaseanycosmochronologicalargumentson be theoriginofNb.However,givencurrent average productionratioNb/Nbisabout10"so experimental error!AsisshowninTable5,the Energy ResearchandDevelopmentAdministrationunder National ScienceFoundation,grantnumberAST76- by theLosAlamosandLawrenceLivermoreLabora- Physics. Thesecalculationsweremadepossible Earth’s crustatall!),wefeelthatitwouldbepre- Nb half-life(andeventheexistenceofNbin California atSantaCruz,andTheAspenCenterfor of manyhostinstitutionsduringthe5yearcourse 10" atthetimeEarthformed(uncertaintoa 10933. 1 Another /7-nucleuswhichmightbeapossible The authorsarepleasedtoacknowledgethesupport WorkwasperformedundertheauspicesofU.S. 197 8ApJS. . .36. .2 85W 194 200 201 202 182 192 191 193 196 19S 197 192 194 196 198 199 108 166 188 172 180 170 172 174 176 178 174 17e 178 180 182 184 186 188 184 186 188 190 160 162 158 158 leo 162 164 160 162 164 16e 164 170 190 148 148 182 154 1S4 158 156 140 142 144 146 148 146 160 T1 3.0(4) Pb 2.4(2) Pb 3.8(4) Pb 1.2(3) Pt 3.7(0) Hg 4.0(1) T1 1.8(2) T1 2.8(1) T1 7.9(0) T1 2.1(4) T1 2.3(2) Pb 3.6(0) Pb 1.0(1) Pb 3.0(1) Pb 3.5(1) Pb 1.4(4) Yb 2.1(2) Hf 3.3(-1) Hf 2.3(0) Hf 5.7(1) Ta 9.5(5) W 8.0(-1) W 4.0(0) W 1.0(1) W 6.0(1) W 7.8(2) Os 7.8(-1) Os 1.0(0) Os 2.6(1) Os 3.9(1) Os 1.0(3) Pt 6.6(1) Pt 3.4(2) Pt 1.4(2) Hg 2.0(0) Hg 9.6(-1) Hg 2.6(1) Hg 4.5(1) Dy 1.2(1) Dy 1.0(1) Dy 2.1(1) Er 2.0(0) Er 8.8(0) Er 6.5(1) Er 4.6(2) Yb 3.0(-1) Yb 7.0(-1) Yb3.0(0) Yb 3.0(1) Hf 4.1(-1) Hf 3.4(1) Pb 1-0(-1) Gd 1.2(-2) Gd 5.4(1) Gd 7.7(2) Gd 5.0(2) Dy 6.0(1) Dy 1.1(2) Er 8.0(0) Sm 2.0(-3) Sm 2.7(-3) Sm 1.9(-2) Sm 4.5(2) Sm 2.1(3) Eu 1.8(-2) Gd 2.4(2) © American Astronomical Society •Provided by theNASA Astrophysics DataSystem Species _l Calculated PhotonuclearReactionRatesinsforSelectedSpeciesatT=2.5and3.0 a 2.9 (1) 8.1 (0) 2- 7(-1) 4.5 (-2) 2.7 (-4) 6.2 (-1) 6.4(1) 8.3 (0) 3.1 (-3) 9.6 (2) 7.9 (0) 9.1 (-2) 9.1 (-1) 5.6 (2) 2.7 (0) 2.0 (-1) 6.8 (3) 7.6 (2) 5.7 (2) 2.7 (1) 2.0 (0) 9.6 (-1) 2.0(1) 2.7 (-3) 7.6 (0) 3.2 (-2) 2.7 (-3) 5.0 (0) 1.4(3) 8.5 (-1) 5.2 (-2) 5.8 (-1) 1.3 (-2) 6.7 (-3) 2.3 (2) 2.1 (-1) 2.0 (-1) 4.0 (-5) 1.2(0) 5.0 (-4) 1.3 (-1) 1.9 (-2) 1.5 (2) 1.0(1) 2.4 (-3) 2.0 (-4) 5.5 (-5) T =2.5 2.3 (-5) 4.0 (2) 9.1 (-1) 4.7 (-4) 6.1 (-1) 5.0 (-2) 3.5 (-3) 8.7 (-4) 5.6 (-1) 3.9 (-1) 1.3 (-2) 1.8 (-2) 1.6 (-5) 1.6 (-4) 1- 0(-3) 1.2(1) 1.0 (-1) 1.5 (-2) 1.2 (-4) 9 TABLE 7 2.1 (1) 9.6 (3) 4.8 (-1) 2.9 (2) 2.9 (2) 2.1 (1) 8.8 (3) 2.1 (1) 2.8 (2) 8.6(1) 5.1 (2) 3.5 (0) 4.7 (4) 2.6 (2) 4.2 (-2) 4.8 (0) 2.2 (-1) 3.0 (0) 6.9 (-2) 5.5 (2) 8.9 (1) 8.9 (1) 1.2(3) 3.6 (—1) 9.6 (0) 4.1 (3) 4.8 (2) 8.7 (3) 2.0 (-2) 6.3 (3) 9.6 (1) 2.0 (-1) 5.5 (1) 9.0 (-1) 5.4 (1) 1.1 (3) 1.6(0) 1.8(3) 5.3 (2) 1.3 (3) 1-3 (1) 1.6(1) 1.0 (-2) 1.4 (-2) 1.8(3) 5-3 (-1) 2.5 (-2) 4.5 (-1) 2.0 (-3) 4.5 (1) 3.0 (-2) 3.3 (1) 9.0 (-2) 1.7(0) 1.6(3) 1.8 (1) 1.6(2) 3.5 (-2) 3.4 (-3) 1.8 (-3) 3.6 (-3) 1.5(5) 1.2(0) 1.1(1) 1.7 (-2) 5.9 (2) 4.7(4) 4.3 (3) 5.9(5) 2.2(5) 8.1 (3) 3.5 (3) 6.9 (4) 2.4 (4) 2.5 (4) 3.0 (3) 2.0 (3) 2.5 (8) 3.6 (3) 2.5 (4) 3.5 (3) 3.6(3) 8.8 (4) 6.1 (4) 1.9(7) 3.5(5) 8.3 (4) 7.6 (4) 2.7 (4) 7.1 (3) 6.9 (5) 7.3 (4) 3.7 (5) 9.0 (3) 8.3 (4) 6.5 (4) 7.7 (4) 1.1(4) 1.6(5) 1.1 (5) 1.6(4) 1.1 (7) 1.4(4) 3.5 (4) 6.6 (6) 4.0(5) 9.6 (1) 9.7 (5) 6.5 (5) 3.5 (4) 5.0(4) 2.0(5) 1.3 (3) 1.6(3) 1.1(5) 1.4(4) 1.1 (5) 11 (6) 1.5(6) 2.3 (1) 8.7 (1) 3.4(5) 1.3 (5) 1.3 (5) 1.0(4) 1.5(6) 5.0(5) 1.0(5) 1.5(7) 1.1 (1) 1.1 (2) 1.8(6) 4.2 (3) 2.4 (2) 2.2 (1) 2.9 (0) 3.0 (5) 6.3 (4) 5.6 (3) 2.1 (2) 8.6 (5) 9.4(2) 6.4(2) 6.2 (4) 8.3 (3) 4.0 (0) 2.0 (-1) 4.9 (2) 4.7 (1) 3.8 (1) 3.0 (4) 5.4(3) 8.1 (0) 6.8 (2) 1-8(5) 1.8 (3) 1.5(5) 8.7 (3) 2.1 (0) T =3.0 2.5 (-1) 2.7 (0) 6.1 (2) 8.2 (1) 7.9 (0) 5.4(3) 6.0 (0) 3.9 (3) 6.7 (2) 8.6 (2) 8.4 (1) 5.0(3) 5.8 (2) 1.2(1) 1.4(5) 1.3 (3) 1.8 (2) 1.8 (1) 5.0 (-1) 8.3 (1) 8.9 (0) 7.0 (-1) 1.2 (3) 1.7(4) 1.8(2) 1.2(2) 3.0 (1) 8.5 (4) 1.0(3) 5.0 (1) 1-2 (-1) 5.8 (2) 1.2(0) 1.5 (0) 6.4 (-1) 1.7(0) 1.0(4) 1.6(2) 1.8 (-1) a 3.1 (5) 2.2 (3) 2.0 (3) 2.5 (4) 4.9 (2) 4.7 (6) 9.4 (4) 2.0 (2) 2.1 (4) 2.4 (3) 4.9 (2) 2.0(1) 3.3 (4) 2.1 (3) 2.8 (2) 8.2 (4) 3.0 (4) 7.1 (3) 5.8 (4) 6.4 (3) 3.0 (5) 5.3 (4) 2.9 (0) 4.7 (0) 4.7 (3) 4.4(5) 2.4(4) 2.8 (2) 6.0(1) 5.8 (3) 7.8 (2) 6.0 (1) 5.3 (3) 5.7 (4) 7.6 (3) 1.7(4) 8.0 (1) 1.8(4) 7.0 (1) 7.5 (4) 9.2 (3) 8.8 (2) 7.9 (1) 7.1 (0) 7.1 (-1) 2.4(0) 2.5 (5) 4.3 (4) 3.3 (1) 9.3 (0) 3.1 (5) 3.6(2) 1.2(3) 1.7(3) 1.4(6) 6.2 (0) 8.6 (0) 6.0 (3) 1.0(4) 1.6 (1) 1.4(3) 1.0(0) 5.3 (4) 1.4 (1) 1.4(2) 1.4(0) 197 8ApJS. . .36. .2 85W 138 140 142 144 134 138 138 136 130 132 128 130 132 138 124 128 124 128 120 122 118 108 ll2 114 ll8 118 120 12a 102 108 108 110 loa 104 104 100 100 Nd 1.5(—1)2.6(—1)1.6(—1) Nd 2.4(—1)4.2(3)8.0(-3) Nd 7.3(-1)9.0(-5)3.7(-4) Nd 4.3(3)5.6(-6)1.2(2) Ce 1-1(-1)3.5(-2)1.0 Ce 2.8(0)2.2(-3)8.2 Ce 3.8(0)9.3(-5)5.8(-4) Nd 5.6(-3)3.6(0)(-1) Ce 9.8(-3)2.5(0)2.3(0) Ce 5.8(-2)1-2(-1)5.0 Ba 2.1(-1)2.7(-2)7.5 Ba 9.3(-1)1.0(-3)1.7(-2) Ba 1.2(0)1.1(-4)2.2(—3) La 6.5(3)2.5(-3)3.0(-6) Xe 5.2(-1)1.4(-2)9.6 Xe 3.4(-1)(-4)2.3(-3) Ba 8.8(-5)1.9(1)1.6(1) Ba 4.8(-2)7.7(-1)7.0 96 98 Xe 7.4(-3)2.3(1)1.4(2) Xe 7.4(-2)3.2(-1)1.7(0) 92 94 98 94 Te 2.7(-2)2.6(-1)3.2(1) 78 78 80 82 84 82 84 86 88 88 92 94 92 93 90 Sn 9.8(-5)6.1(0)1.5(0) Sn 9.6(-3)2.22.6 Sn 1.8(-2)2.3(-5)5.7 Sn 4.7(2)4.8(-7)9.8 Te 3.1(-3)3.1(0)1.0(2) Te 9.9(-2)3.6(-3)8.8(-1) Te 7.2(-1)5.7(-5)2.6(-2) 74 78 77 80 98 Cd *1.5(1)3.6(0) Cd 9.9(-3)2.02.6(-2) Cd 1.0(-1)1.9(-5)1.4(-3) Sn 2.0(-3)1.8(-1)6.4(-2) Pd 3.1(-2)2.9(-4)1.1 Pd 2.9(-1)12(-6)1.1(-3) Cd 3.6(-4)3.7(-1)1-4 Ru 8.5(-1)1.8(-6)1.5(-3) Pd 4.0(—3)2.8(—2)1.5(—1) Ru 8.8(—3)3.1(-2)3.4(—1) Ru 7.3(-2)1.7(-4)2.9 Mo 1.4(-6)2.8(-2)1.0(-8) Mo 3.2(-1)4.9(-5)2.8 Mo 2.7(0)9.8(-7)8.9(-3) Ru *4.7(0)8.6(-8) Se 4.2(-3) 2.5 (-8)4.7(-7) Kr 3.8(-5)3.1(-3)6.0 (-4) Kr 8.4(-5)3.92.4 (-5) Kr 2.1(-3)1.7(-7) (-7) Kr 1.4(-2)6.4(-9)4.9 (-10) Sr 4.1(-5)4.4(-2)1-1 (-3) Sr 1.2(-5)7.13.1 (-6) Sr 3.0(-4)•1.4(-6)8.6 (-9) Sr 3.4(-4)3.0(-9)1.3 (-12) Zr 7.6(-6)1.2(-3) (-7) Zr 9.7(0)5.7(-8)1.0 (-2) Zr 4.9(1)2.1(-9)3.4 (-5) Nb 1.4(2)1.2(0)2.2 (-7) Nb 5.9(0)4.0(-1)2.3 (-1) Mo 8.0(-8)1.8(0)5.9(-7) Se 2.8(-5) 1.0 (-3)1.1(-2) Se 7.7(-4) 2.5 (-6)9.6(-5) Se 4.6(2) 1.1 (-6)1.8(-5) Se 1.3(-1) 3.1 (-10)2.7(-9) "Zr 1.8(—5)1.94)1.6(-10) Pd *5.2(0)6.0(-1) * Reactionlinknotinnetwork. © American Astronomical Society •Provided by theNASA Astrophysics DataSystem Species T =2.5 a TABLE 7—Continued 2.2 (3) 4.0(2) 9.3 (3) 3.1 (6) 4.6 (1) 9.5 (3) 3.0(1) 8.0 (2) 2.1 (3) 2.8(6) 5.1 (2) 4.2(2) 5.2 (1) 6.6 (-1) 3.1 (2) 3.7 (3) 3.6 (3) 1.0(3) 2.1 (3) 4.2 (2) 4.5 (0) 2.5 (5) 2.4(1) 1.4(2) 1.2(3) 1.1 (3) 4.4(2) 6.0(1) 7.7 (1) 4.7(3) 6.7 (1) 5.0(1) 2.9 (2) 2.2(3) 9.9 (2) 1.7 (1) 4.1 (4) 8.3 (2) 3.0(1) 1.6(2) 1.4(0) 9.4 (4) 7.9 (3) 3.3 (-3) 3.7 (-2) 4.5 (-1) 6.2 (0) 9.2 (-1) 6.8 (1) 3.1 (0) 2.7 (0) 2.8 (-1) 2.1 (5) 6.5 (-1) 1.1(4) 2.1 (1) 3.9 (2) 5.7 (-1) 1.9 (—1) 1.4 (-1) 1.5(1) * * * 2.9 (-1) 2.1 (3) 3.7 (3) 5.7 (-2) To =3.0 4.2 (2) 7.3 (1) 6.6 (0) 5.2 (-1) 3.7 (2) 3.2 (1) 8.3 (2) 3.1 (0) 5.8 (-1) 5.1 (0) 1.7(2) 1.0(1) 3.6 (-1) 4.9 (2) 5-0(1) 6.3 (-3) 3.4(3) 1.7(4) 1.5 (0) 1-2(4) 6.2 (2) 9.3 (-2) 7.4(0) 1.1 (1) 5.8 (0) 5.7 (3) 3.2 (2) 8.0 (1) 8.9 (-1) 2.4 (-2) 1.9 (-1) 6.7 (2) 3.5 (2) 3.0 (-1) 5.1 (3) 5.7 (3) 5.8 (1) 1.0(0) 1.2 (-2) 1.3(4) 2.7 (-1) 4.1 (0) 9.2 (-4) 6.8 (-5) 7.0(1) 1.4 (-2) 4.5 (0) 2.4 (-3) 8.2 (-5) 8.8 (-1) 1.9 (3) 9.7 (1) 5.3 (-1) 1.4 (-2) 1.8 (-2) 6.0 (-4) 1.6 (-5) 1.8 (1) 1.9 (-4) 1.4 (-2) 4.8 (1) 6.6(1) 3.3 (-1) 2.2 (4) 2.5 (2) 2.0 (0) 5.8 (0) 5.6 (-1) 5.1 (0) 1.4(4) 2.8 (0) 4.1 (-3) 7.2 (3) 2.3 (0) 3.9 (1) 8.4 (-3) 6.3 (2) 1.8 (2) 2.1 (1) 4.1 (1) 3.6 (2) 5.8 (2) 5.1 (1) 3.4(3) 1.8 (2) 2.1 (2) 8.6(1) 1.9(4) l.KD 2.5 (1) 3.0 (2) 1.7(0) 5.4 (2) 1.0 (-1) 1.8 (1) 4.2 (-2) 2.6 (-3) 9.8 (-5) 7.0 (0) 5.7 (-4) l.KD 1.4(0) 1.2 (3) 1.6(0) 1.0(2) 2.8 (-1) 4.1 (-5) 9.6 (-6) 9.0 (-5) 5.9 (-8) 6.5 (-4) 2.4 (-6) 6.4(0) 1.4 (-3) 1.3 (2) 1.7(2) 2.4 (-3) 8.8 (-2) 1.3 (-3) 1.9(0) 1.5 (-2) 1.7 (1) 1.1 (-1) 1.4(0) 197 8ApJS. . .36. .2 85W 21/3 point becausetheparticleseparationenergiesplaysuchakeyroleiny-process.Forthosefewnucleion parity informationandexcitationenergiesofthefirstexcitedstate(usedincomputingphotonwidths)weretaken, minations werenotavailable,themassrelationsofGarveyetal.(1969)employed.Ground-statespinand proton-rich sideofthevalleybeta-stabilitythatwechosetoincludebutforwhichexperimentalmassdeter- for thesixreactions(n,y),(/?,(p,n),(a,p),andn)werecomputed.Inaboveformulais level diagram(SeegerandHoward1975)wasemployed.Usingthisinformationthethermallyaveragedratefactor, when available,fromLederer,Hollander,andPerlman(1967).FornucleiwithunknownspinparityaNilsson particular thephotodisintegrationrates,whichareonlypertinentonesforpresenttreatment,givenby average crosssectioninbarnsforthereactionatcenterofmassenergyEiMeVandÂisreduced the sixvarietiesofreactionsusingprinciplereciprocity(cf.Fowler,Caughlan,andZimmerman1967).In mass ofthereactantsinentrancechannel.Inaddition,ratefactorswerecomputedforinverseseach of thebindingenergiesemployedhaveexperimentaldeterminations(WapstraandGove1971).Weemphasizethis given byequation(A2),andS¿istheseparationenergyofparticleiinMeV. rates andarethereforeuninterestingasbranchingpointsorwaitingpoints.Typicallythephotoneutronrate foran they wereofcourseincludedinallcalculations.Thedestructionsuchnucleiisalwaysdominatedbylarge (y,n) given inTable7.Forthemostpartentrieshavenotbeenforoddnucleiandodd-massnuclei,even though computer timethatwouldberequiredfortheirpropertreatment.Exceptthephotonchannel,itwasassumed where gjisthegroundstatepartitionfunctionfornucleus/inreactionAjitsatomicmass, is particular, a(p,y)cross-sectioncalculationthatneglectsthepresenceofhighdensityoutgoingstates inthe Truran (1972),recentstudiesofWoosleyetal.(1975)haveshownthatsuchneglectcanleadtosizableerrors. In assumption hasbeencustomaryinpastastrophysicalcalculationslikethoseofMichaudandFowler(1970) and that agivencompoundnuclearstatecoulddecayonlytothegroundofparticlechannel.Though this boring evennuclei. peak energy,E=0.122(ZZ2xir)MeV,exceedsthethresholdfor(/?,n)reaction.Similarconsiderations odd nucleusatthetemperaturesweareconsidering(21%-Timestepswerechosensothatnospeciesofinterestchangesitsabundancebymorethan15% maxmax Cameron, A.G.W.1957,ChalkRiverRept.CRL-41;seealso max Clayton, D.1975,Ap.J.,199,765. Cameron, A.G.W.,andTruran,J.W.1977,Icarus,30,447. Frank-Kamenetskii, D.A.1961,SovietAstr.,5,66. Fowler, W.A.,Caughlan,G.,andZimmerman,B.A.1967, Couch, R.G.,Schmiedekamp,A.B.,andArnett,W.D.1974, Joukoff, A.1969,Astr.Ap.,3,186. Hainebach, K.L.,Schramm,D.N.,andBlake,J.B.1976, Ito, K.1961,Progr.Theoret.Phys.,26,990. Howard, W.M.,Arnett,D.,Clayton,D.andWoosley, Garvey, G.T.,Gerace,W.J.,Jaffe,R.L.,Talmi,I.,and Lamb, S.A.,Howard,W.M.,Truran,J.W.,andIben,I.,Jr. W. M.Howard:T-Division, L-71,UniversityofCalifornia,LawrenceLivermore Laboratory,Livermore,CA Lamb, S.A.,Iben,I.,Jr.,andHoward,W.M.1976,Ap.J., 90 Santa Cruz,CA95064 S. E.Woosley:LickObservatory, BoardofStudiesinAstronomyandAstrophysics, UniversityofCalifornia, 94550 2 M.N.R.A.S., 146,58. F. 1957,Rev.Mod.Phys.,29,547(BFH). Ann. Rev.Astr.Ap.,5,525. 1974, Geochim.Cosmochim.Acta,38,4185. Ap. J.,190,95. 1957, Pub.A.S.P.,69,201. 207, 209. Ap. J.,205,920. Kelson, I.1969,Rev.Mod.Phys.,41,51. S. E.1972,Ap.J.,172,201. 1977, Ap.J.,217,213. © American Astronomical Society •Provided by theNASA Astrophysics DataSystem y +1)j1 iV ={[Y+nAyn°^{k77)Y^X^^\kp)\ko)]At kyvk+ U)1 + Y}(lA^^^AO".(B3) k (i+1)+1 Y =T^/a+,Atí°'>-t^(B2) 1 WOOSLEY ANDHOWARD REFERENCES .1972,Ap.J.,173,157. Lederer, C.M.,Hollander,J.andPerlman,I.1967, .1973,inExplosiveNucleosynthesis,ed.D.N.Schramm, Pardo, R.C.,Couch,G.,andArnett,W.D.1974,Ap.J., Notsu, K.,Nabuchi,H.,Yoshioka,O.,Matsuda,K.and Lugmair, G.W.,Scheinin,N.B.,andMarti,K.1975,Earth Lewis, R.S.,Srinivasan,B.,andAnders,E.1975,Science, Takahashi, K.,Yamada,M.,andKondoh,T.1973,Atomic Schramm, D.N.,andArnett,W.1975,Ap.J.,198,629. Reynolds, J.H.,andTurner,G.1964,Geophys.Res.,69, Reeves, H.,andStewart,P.1965,Ap.J.,141,1432. Truran, J.W.1972,Ap.SpaceSei.,18,308. Stanfield, S.,Truran,J.W.,andSparks,W.M.1975,Ap. Seeger, P.A.,andHoward,W.M.1975,Nucl.Phys.,A238, Truran, J.W.,andCameron,A.G.W.1972,Ap.J.,171,89. Truran, J.W.,andArnett,W.D.1970,Ap.J.,160,181. Michaud, G.,andFowler,W.A.1970,Phys.Rev.C,2,2041. Manuel, O.K.,Hennecke,E.W.,andSabu,D.1972, Malkiel, G.S.1963,SovietAstr.,7,207. Macklin, R.L.1970,Ap.J.,162,353. Wapstra, A.H.,andGove,N.D.1971,Nucl.DataTables,9, Woosley, S.E.,Fowler,W.A.,Holmes,J.andZimmer- Woosley, S.E.,Arnett,W.D.,andClayton,D.1973, Planet. Sei.Letters,27,79. 491. Nature, 240,99. 190, 1251. Table ofIsotopes(6thed.;NewYork:Wiley). {Letters), 198,LI13. 3263. Ozima, M.1973,EarthPlanet.Sei.Letters,19,29. and W.D.Arnett(Austin:UniversityofTexasPress). 191, 711. Ap. J.Suppl,26,231(WAC). 265. man, B.A.1975,CaltechOrangeAidPreprintOAP-422. Data andNuclearTables,12,101.