Silicon burning at temperatures in the neighborhood of 4 × 109 °K has been studied with the aid of a quasiequilibrium model which describes the abundance of the nuclei in the interval 28\u3c~A\u3c~62. It is found that, for a broad range of temperatures and densities, silicon burning leads to nuclear abundance distributions which match important features of the natural solar-system abundance distributions and that a large nuclear energy release accompanies silicon burning

Bodansky, David

Clayton, Donald D

Fowler, William A

English

Clemson University: TigerPrints

Clemson UniversityTigerPrintsPublications Physics and Astronomy1-22-1968Nucleosynthesis During Silicon BurningDonald D. ClaytonClemson University, claydonald@gmail.comDavid BodanskyUniversity of WashingtonWilliam A. FowlerCalifornia Insititute of TechnologyFollow this and additional works at: https://tigerprints.clemson.edu/physastro_pubsThis Article is brought to you for free and open access by the Physics and Astronomy at TigerPrints. It has been accepted for inclusion in Publicationsby an authorized administrator of TigerPrints. For more information, please contact kokeefe@clemson.edu.Recommended CitationPlease use publisher's recommended citation.VOLUME 20, NUMBER 4 PHYSICAL REVIEW LETTERSNUC LEOSYNTHESIS DURING SILICON BURNING*22 JANUARY 1968David BodanskyUniversity of Washington, Seattle, Washington, and California Institute of Technology, Pasadena, , CaliforniaDonald D. Clayton'tRice University, Houston, Texas, and Institute of Theoretical Astronomy, Cambridge, EnglandWilliam A. FowlerCalifornia Institute of Technology, Pasadena, California,and Institute of Theoretical Astronomy, Cambridge, England(Received 3 January 1967)Silicon burning at temperatures in the neighborhood of 4 x10~'K has been studied withthe aid of a quasiequilibrium model which describes the abundance of the nuclei in the in-terval 28-4- 62. It is found that, for a broad range of temperatures and densities, sil-icon burning leads to nuclear abundance distributions which match important features ofthe natural solar-system abundance distributions and that a large nuclear energy re-lease accompanies silicon burning.It is generally believed that in the evolutionof the thermonuclear gas which constitutes thematter of stellar interiors, an epoch is reachedin which the matter is primarily in the formof Si and, to a lesser extent, of 3 S. Thisphase can be reached after the fusion of '60at temperatures in the neighborhood of 2&& 10 'K.It follows from general considerations'~' basedon the unusually large nuclear binding energyof ' Si that little subsequent nuclear activityoccurs until the temperature becomes sufficient-ly high to cause (y, p) and (y, a) reactions on"Si. This breakdown of "Si by photodisintegra-tion is accepted'~2 as being the precursor toa reassembly of the nucleon gas into the nucleiwhich constitute the iron-group natural abun-dance peak (predominantly isotopes of Fe andNi). By a sequence of (y, n) reactions, andto a lesser degree (y, p) and (y, n) reactions,"Si nuclei are decomposed into n particles,protons, and neutrons, which are then capturedby other 2 Si nuclei leading to S and then heav-ier nuclei. The present paper describes theresults of an analysis which clarifies the de-tailed nature of this process, termed siliconburning, which determines the time scalesand energy generation during silicon burning,and which shows how silicon burning accountsfor many crucial features of the observed na-tural solar-system abundances of the nucleibetween A = 28 and A = 57. A more completediscussion of these results and their astrophys-ical applications is being prepared for publi-cation elsewhere.For simplicity in this analysis, it was assumedthat the starting point is a gas of pure "Si andthat the gas remains at constant temperatureand density as the conversion of ' Si to othernuclei proceeds. The rate of buildup of thenuclei heavier than "Si is governed by the rateat which n particles are made available throughthe photodisintegration of ' Si.'~2 The crucialqualitative feature of this rate is that it is slowcompared to the nuclear reaction rates aboveSi. The rate is determined by a photodisin-tegration chain in the nuclei lighter than Si.In the first instance, 24Mg is formed and itsdensity rises to a value limited by equilibriumjn the reactions Mg+ o. Sj+y. By virtue ofthe high n-particle binding energy in 'Si, the24Mg number density is small compared to theSi density. The further dj.sjntegration of Sithen occurs by way of the photodisintegration ofthe much less abundant, and also tightly bound,"Mg.' It is the slow "Mg photodisintegrationrate which sets a limit on the effective photo-disintegration rate of Si and allows the reac-tions in the heavier nuclei to come into the qua-siequilibrium condition discussed below.As the e particles are liberated by the pho-todisintegration of ' Si they are initially con-sumed by the reaction 28Si(n, y)s2S, resultingin a buildup of "S. However, because the "Sundergoes (y, o.) reactions with a shorter life-time than ' Si, the capture of n particles andthe buildup of S is halted by the equilibrationof the inverse reactions Si+ He —'S+y.[If substantial amounts of S2S are admitted to161VOLUME 20, NUMBER 4 PHYSICAL REVIEW LETTERS 22 JANUARY 196Sbe initially present, the same equilibrium isestablished by (y, n) reactions on "S.] In asimilar manner, the reactions involving heav-ier nuclei subsequently achieve equilibrium,and the heavier nuclei build up to concentrationssuch that they liberate n particles at virtual-ly the same rate at which they consume e par-ticles; therefore, the e-particle density assumesa quasistatic value. Qn a much longer timescale the ' Si slowly "melts, " thereby inject-ing more e particles into the bath. The newn particles are consumed in the formation ofmore heavy nuclei, establishing just the abun-dance required to maintain a new equilibriumbetween (n, y) and (y, a) reactions. In an anal-ogous manner, quasistatic concentrations offree protons and neutrons are maintained byequilibration of reactions involving nucleons,photons, and e particles. We call this situa-tion nuclear quasiequilibrium, in that the nu-clei heavier than ' Si are in equilibrium underthe exchange of protons, neutrons, and n par-ticles. It is not a true nuclear equilibrium be-cause the Si itself, which is disintegratedcomparatively slowly, does not have sufficienttime to come into equilibrium with the freeconcentrations of light particles and becausethe quasiequilibrium densities change slowlywith time.In the quasiequilibrium, the number densi-ties n(~Z) of nuclei heavier than '8 Si are de-termined relative to the concentration of "Siitself by the number densities of free n parti-cles, protons, and neutrons and by the temper-ature. Accordingly, one has the set of equa-tionsn( Z) = C( Z)n( Si)n ~g Pn ~,A A 28 . 5~p nwhere each nucleus ( Z) is thought of as beingcomposed of "Siplus 5~ n particles plus 5pprotons plus 5„neutrons. The quantities C( Z)depend only upon nuclear binding energies, nu-clear partition functions, and the temperature.The e particles and nucleons are themselvesin mutual equilibrium via rapid chains of nu-clear reactions in heavier nuclei. Thus onlytwo of the densities n~, np, and n„are inde-pendent. At a given temperature, there is aunique solution to Zq. (1) for each value of theamount of residual Si if the density and nucle-ar charge-to-mass ratio are specified.We have studied the silicon-burning problemby finding n(~Z), for nuclei in the interval 28&A &62, for a succession of quasiequilibriumconfigurations, each with a progressively low-er amount of "Si remaining. The temperatureand density were taken to be constant. Thetime to progress from one configuration to thenext is controlled by the effective 'Si photodis-integration rate. These time intervals deter-mine both the rate of nuclear energy genera-tion and the decrease, due to P-decay process-es, of the nuclear charge-to-mass ratio, whichstarts at 2 for the initial "Si. Electron captureis the principle p-decay process. It was foundthat, in the most likely silicon-burning circum-stances, the conversion is fast enough that P-decay processes can only slightly alter the ra-tio. In consequence, the equilibrium solutionsof the present analysis are characterized bymuch higher densities of free protons than offree neutrons, and thus by high densities ofnuclei on the proton-rich side of the valley ofnuclear stability.Calculations of the evolution of abundancesin silicon burning were carried out for temper-atures extending from (3.4 to 5.0)x10''K andfor densities extending from 10' to 10' g/cm'.The quasiequilibrium abundance distributionsfound through this analysis have considerablydifferent properties than the equilibrium solu-tions which have been studied by other workers'»'as the source of the iron-group abundance peaks(commonly called the e process after Ref. 4).The crucial differences stem from the highratio of the free-proton to free-neutron num-ber densities and the retention of a substantialfraction of the material in the form of ' Si.The most striking characteristic of the pres-ent solutions is the production of ' Ni as themost abundant iron-group nucleus for a widerange of temperatures and densities. Howev-er, in the lower range of temperatures (near3x 10''K) the conversion is slow enough thatp-decay processes reduce the ratio np/n„caus-ing ' Fe to replace MNi as the most abundantiron-group nucleus. Some aspects of these re-sults have been reported in a study of siliconburning in which the individual reaction rateswere integrated numerically. ~~6In Fig. 1 we show as an example the quasi-equilibrium abundance distribution that obtainswhen initially pure 'Si has been disintegratedto 35 /o of its initial value at a temperature of4.4x 10~'K and a density of 10' g/cms. (Thispoint is reached after 0.3 sec of "Si burning. )A recent compilation of the natural solar-sys-VOLUME 20, NUMBER 4 PHVSrCAI REVIEW I, FTTzRS 22 JANUARY 19687lOIIiII~ NATURAL (CAMERON l967; Fe x I/5)~ E,QUILIBRIUM Tg = 4.4p = lO g/cc5~ lOZO 4z lO—Q33~ lO)lOCLIlO—pIItlO0I30I40MA55I I50NUMBER (A)I60tern abundances in this mass range is shownfor comparison. There is a strong similarityin these abundance patterns for the most abun-dant nuclei below A = 58, namely the A = 4n nu-clei and the iron group for 50~3 &57. In thiscomparison, account is taken of the P-decayprocesses which occur after silicon burningis completed so that, for example, the naturalabundance of MFe is attributed to the decay ofMNi.The results shown in Fig. 1 are typical ofthe main features of the abundances achievedin partially burned ' Si over a band of temper-atures and densities extending from about 3.8&& 10' K and 10' g/cm' to 5.0 x 10' 'K and some-what over 109 g/cms. (Note that at high tem-peratures, high densities are required to main-tain the abundance of MNi against dissociationinto ~Fe+2p). Because of this broad regionof agreement with observed abundances andbecause silicon burning now appears to be anatural epoch in the history of a thermonucle-ar gas, we surmise that the natural abundanceFIG. 1. Comparison between quasiequilibrium abun-dance reached under typical conditions in Si burningand the natural solar-system abundances. (Cameron'svalue for the Fe abundance has been reduced by a fac-tor of 5, corresponding to a choice of the solar abun-dance for Fe rather than the meteoritic abundance. )The vertical lines with arrows represent cases wherethe quasiequilibrium abundances fall off scale.pattern between A = 28 and A = 57 reflects pri-marily a superposition of silicon quasiequilib-rium burning sequences, followed by ejectionof the material from the site of the burning,probably supernovae. If this surmise provesto be correct, the less common nuclei (primar-ily the neutron-rich isotopes of these elements)must be attributed to a secondary process,most likely the freezing reactions that occurduring the expulsion and cooling of this gas,or, alternatively, a subsequent s process. 4~'The silicon burning process is strongly ex-oergic under those conditions of temperatureand density which lead to agreement with theobserved natural abundances, largely becausethe dominant product, MNi, is tightly bound.Typical energy releases, calculated from thechange in total rest mass, are in the neighbor-hood of 100 keg per nucleon of disintegrated"Si, which is equivalent to 10" erg/g. Thetime rate of energy release is governed by theeffective rate of the silicon photodisintegrationand increases rapidly with increasing temper-atures. Over the temperature interval from(3.6 to 5.0) && 10' 'K, the rate of energy releasewhen the "Si has been half consumed rangesroughly from 10" to 10"erg/g sec. This pow-er can provide for a short epoch of thermonu-clear stability in the core of a presupernovastar. The detailed implementation of theseresults should aid in the understanding of theenergy balance in supernova events.In summary, the distinctive conclusions ofthe present analysis are the following: (1) Thesynthesis of the n-particle nuclei above A = 28and of the iron-group nuclei occur simultaneous-ly during silicon burning (specifically, the nprocess and the e process of Ref. 4 occur si-multaneously). (2) The chief quasiequilibriumproduct in the iron group is generally ~Ni, andits decay after the expulsion of the matter fromthe star probably accounts for the high naturalabundance of MFe. (3) Under the most likelyconditions, the production of the iron-groupnuclei in silicon burning is accompanied bya large release of nuclear energy. (4) The nat-ural abundance of Ni cannot be understood un-til the secondary processes responsible forthe heavy isotopes of Si, S, A, and Ca are un-derstood in detail, but equilibrium explanationsfor the abundances of "Ni and Ni now appearto be unpromising.*Supported in part by the National Science Founda-Vor.UMs 20, NUMsxR 4 22 JwNUxRv 1968tion, Grant No. GP-7976, formerly GP-5391; the U. S.Office of Naval Research, Grant No. Nonr-220(47); theAir Force Office of Scientific Research, Grant'No.AFOSR-855-65; and the Atomic Energy Commission,Grant No. A T(45-1)-1388.)Alfred P. Sloan Research Fellow.~W. A. Fowler and F. Hoyle, Astrophys. J. Suppl. 91,201 (j.964).~J. W. Truran, A. G. W. Cameron, and A. Gilbert,Can. J. Phys. 44, 563 (1966).3A. Finzi and R. A. Wolf, private communication.4E. M. Burbidge, G. R. Burbidge, W. A. Fowler, andF. Hoyle, Rev. Mod. Phys. 29, 547 (1957).5F. E. Clifford and R. J. Tayler, Mem. Roy. Astron.Soc. 69, 21 (1966).6J. W. Truran, W. D. Arnett, and A. G. W. Cameron,Can. J. Phys. 45, 2315 (1967).7A. G. W. Cameron, in Proceedings of the Symposi-um on the Origin and Distribution of the Elements,Paris, 1967 (to be published).D. D. Clayton, T. E. Hull, W. A. Fowler, and B. A.Zimmerman, Ann. Phys. (N.Y.) 12, 331 (1961).EVIDENCE FOR THE I= z N~(1400) RESONANCE PRODUCTION IN w P INTERACTIONS AT 6 GeV/c*Robert B. Bell, David J. Crennell, Paul V. C. Hough, Uri Karshon, f Kwan Wu Lai, J. Michael Scarr,Thomas G. Schumann, j Ian O. Skillicorn, and Richard C. StrandDepartment of Physics, Brookhaven National Laboratory, Upton, New YorkAlvin H. Bachman, Philip Baumel, Robert M. Lea, and Alexander Montwil15The City College of the City University of New York, Neer York, New York(Received 1 December 1967)Results from a number of high-energy miss-ing-mass spectrometer experiments have in-dicated the presence of a peak in the strange-ness-zero and baryon-number-one systemat a mass of about 1.4 GeV. ' Because its pro-duction is peripheral and the width is large(approximately 200 MeV), kinematic interpre-tations of this peak are possible. a However,an extensive pion-nucleon phase-shift analy-sis suggests that an amplitude, with the samequantum numbers as the nucleon (1=-, and Jp=-,'+), exhibits resonant properties near thismass region with a large width and inelastic-ity (vinel/crtot I=-,'). In order to associatethis Nz*( 1400) deduced from the pion-nucle-on phase-shift analysis with the peak observedfrom production experiments, it is essentialto determine its quantum numbers from itsdecay products. To date, the only relevantbubble-chamber data with adequate statisticshave come from a study of the reaction pp—PP~+m at 6.6 GeV/c, ~ where a kinematic in-terpretation of this enhancement is favored.In this Letter, we report our observation ofwell-defined m+n and w p enhancements cen-tered at 1.42 GeV with a width of the order of100 MeV, from the reactions ~+p-w+n+n andm p-w'v p at 6 GeV/c. The resonance inter-pretation of this enhancement is clearly favoredin our data. We have determined its isospinto be —,', and we associate it with the N„s~(1400)suggested by the phase-shift analysis.ReactionNumberof eventsEvents/Crosssection equivalent(events jpb)(1) ~ P- ~ x n.(2) x+p- x'w+p(2)w p wm n(4) ~-p- ~'~-p1195265533433761.50.34.84.8In these four reactions, there are two ma-jor sources contributing to the background ob-served in the low (mN)lz ~1 mass region.ZThey are (a) the reflection of strong mw res-onances, ' which contribute to reactions (2),(3), and (4) but not to (1), and (b) proton dis-sociation into (mN)l -+,' at the nucleon ver-tex without N, ~* formation, which contributesto all (vN)lz +~ combinations but not to (m p)in reaction (4). It should be emphasized thatthe (w+n) and (m p) mass spectra from reac-tions (1) and (4), respectively, are the onlyThe samples of events for this study comefrom a 6-GeV/c m+p experiment in the Brooknaven National Laboratory (BNL) 80-in. liquid-hydrogen bubble chamber. About 30000 two-prong events in the v+p exposure and 60000two-prong events in the ~ p exposure wereanalyzed. About one-half of the events weremeasured by conventional measuring machinesand the other half by the BNL flying-spot dig-itizer. The size of the event samples and cross-section equivalents of the four reactions stud-ied' are shown below:

Nucleosynthesis During Silicon Burning

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Nucleosynthesis During Silicon Burning

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