7'reh. Soc. Cat. Biol.. Vol. 39 (1986) 49-71

NUCLEOSYNTHESIS OF THE CHEMICAL ELEMENTS

VICTOR E. VIOLA, JR.

Department of Chemistry and Cyclotron Laboratory.University olMaryland. College Park, MD 20742. USA.

SUMMARY

From our previous discussions we have seen that cosmological nucleosynthesis is primarily re-sponsible for the formation of hydrogen and 'He, with a small amount of deuterium, 3He and 7Lialso being contributed to the earth's elements. Subsequently, stellar evolution synthesizes all thenuclei between carbon and uranium (or heavier), and the abundances calculated on the basis ofthese two models agree rather well with experimental data. Furthermore, formation of the elementslithium, beryllium, and boron can also be understood when one adds interactions of galactic cos-mic rays with the interstellar medium. Undoubtedly, cosmic ray interactions also contribute verysmall amounts to the abundances of other elements, but these probably represent only a minor per-turbation of the major elemental abundances. Thus, with the above processes we can synthesize theatomic nuclei that make up our universe and provide an energy source for subsequent evolutionof our solar system and surrounding galactic phenomena. At this stage, then, the basic materialsare present to permit the subsequent evolution of planetary bodies, atoms, molecules, and even-tually, life.

INTRODUCTION

During the 15 billion years or so thathave elapsed since the Big Bang - from

which we trace the origin of our universe -a complex array of evolutionary processeshas occurred. These phenomena, includingthe emergence of galaxies, stars, planetarybodies, and their constitutent chemical ele-ments, have been vital precursors to the

formation of intelligent life on our planet

(or elsewhere). The synthesis of atomic nu-

clei via nuclear reactions in cosmological

processes (nucleosynthesis) is an especially

important precursor for the development

of life.It is currently believed that the primor-

dial universe was composed largely of thesimplest constituents of matter, the ele-mentary particles. Until such a time in our

50 1 h FOR I 1101, I JR

history when the element carbon hadevolved, there was no possibility for eventhe simplest organic molecules to form.Similarly, the existence of increasinglycomplex molecules of biological signifi-cance depended upon the existence ofother complex atoms, such as nitrogen,oxygen, phosphorus, iron, etc. Of furthersignificance, in order for living systems tosustain themselves, a constant source ofenergy was essential. As we shall discussbelow, this energy was provided by nuclearreactions which synthesize the elements instars.

Despite what might at first appear to bean exceedingly complex problem, duringrecent years great progress has been madein understanding the origin of the ele-ments. Important early contributions reston the theories of nucleosynthesis pro-posed by Gamow (1); Burbidge, Burbidge,Fowler and Hoyle (2), and Cameron (3).For a detailed review of both the historicaland current status of this subject the inter-ested reader is referred to the excellent re-view article by Trimble (4).The present model for the origin of the

elements draws upon many diverse fieldsof science. In Fig. I we schematically showthe idealized picture that is followed in thepresent development of the subject. Themodel contains three basic components,all of which must be self consistent:

1. The basic principles - First of all acosmological setting must be proposed thatis consistent with the observed behavior ofmatter in the universe. Into this environ-ment we then introduce the presentlyknown fundamental particles and the basicforces of nature. Thus, we must first re-view the salient properties and basic lawswhich describe the particles and forces.

2. Interaction processes - Given the sys-tem defined by the above principles, wemust then ask what reactions will occur.Since in this discussion we are primarilyconcerned with the formation of atomic

nuclei, our main concern here will be nu-clear reactions. In order to understandthese we must draw on extensive experi-mental and theoretical results derived fromthe study of nuclear science.

3. Products - Finally, the products thatare predicted from the interactions that oc-cur in the model system must correspondto observed experimental data. Specifical-ly, in the context of this paper, this meansthat the abundances of the chemical ele-ments and their isotopic ratios in naturemust be adequately predicted.

THE MODEL

In practice, there has been considerableinterplay between the various parts of themodel outlined in Figure 1, as indicated bythe arrows between the components. Forexample, our knowledge of the abundancesof the elements has frequently served as aguide to the types of nuclear interactionsthat have been responsible for their pro-duction. Now let us review these modelcomponents in more detail.

A. Principles

In general all cosmological phenomenamust be considered as possible sites of nu-cleosynthesis. However, we know that inorder for most nuclear reactions to occur,the colliding nuclei must posses energieson the order of a million electron volts(MeV) or more. This energy corresponds toa temperature of about 1010 °K (that is,10 thousand million degrees Kelvin) andhence, this criterion restricts our possiblesites to very hot energetic phases of theuniverse.The fundamental particles which are the

starting ingredients for forming atomic nu-clei in these environments are summarizedin Table I. These particles include the pro-

tiCC7.FOS}:4'THE.S. 01:lHEC/tEl1!('.ILELF..bfEVii' 51

ORIGIN OF THE ELEMENTS

articles

Cold Hot

forces

Principles Processes - Products

universe

solar system

Atomic Nuclei

Interactions

Conservation laws

Atoms & Molecules

Fig. I. Recipe for discussing the origin of the ele-ments. Add the fundamental particles to the universeand allow the basic forces to act (principles). The in-teractions that result, governed by nature's conserva-tion laws (processes) will produce the existing uni-verse (products).

Geological Formations

Biological Systems

TABLE I

Particles and forces of concern in nucleosynthesis

FUNDAMENTAL PARTICLES mass charge

Baryons protons iH 1.0078 amu + I

neutrons 'on 1.0087 amu 0

Leptons electron ° e 0.00054 amu - 1

neutrino 00 -0 0

Photons light, x-ray, y- ray, etc. 0 0

BASIC FORCES

Gravity-massElectromagnetism -chargeNuclear-baryons

52 17(7OR k 1701.1 .lR

ton; neutron, electron, neutrino, and pho-ton (or electromagnetic radiation). Alth-ough many additional particles are known,they have very short lifetimes. Thus, onlythe small group of particles listed in Tab-le I live sufficiently long to play a signifi-cant role in the structure of our universe. Itshould be noted here that the neutron infree space is radioactive and decays into aproton with an average lifetime of about16 minutes. However, inside atomic nucleithe neutron is stable, i.e. it retains its iden-tity for the lifetime of the nucleus in whichit resides.

Each of the fundamental particles can becharacterized by two primary properties,mass and charge. Other properties alsoserve to distinguish the particles morecompletely, but these will not be necessaryfor the present discussion. There also ex-ists a class of particles called antiparticles.These are essentially the same as the parti-cles in Table I, except that all their proper-ties are reversed. For example, the anti-electron (or positron) is an electron with apositive charge (+I) and negative mass of- 0.0054 amu.The two particles in which most of the

present mass of the universe resides are theproton and the neutron, which belong to aclass of particles called baryons. Thesehave nearly identical masses and differonly in that the proton has a charge of + Iand the neutron has a neutral charge (0).The electron and neutrino belong to an-other class of particles, called leptons. Theelectron has a very small mass relative tothe baryons and has a negative charge. Weshall say very little about the electron inthis discussion since under the conditionsof nucleosynthesis, the temperatures are sohigh that all atoms are completely ionized.The primary importance of the electron inthis description becomes clear when wediscuss nuclear P decay, a radioactive de-cay process whereby a neutron changesinto a proton, an electron and an antineu-

trino. The neutrino is an elusive particlewith an unmeasureably small mass and nocharge. Both the electron and neutrinohave very important roles to play in theevolution of stars (5), but these will not bediscussed here. The final particle is thephoton, or electromagnetic radiation. Thephoton has no mass or charge, and isknown by several names depending uponits wavelength and source. For example,light, ultraviolet, infrared, microwave andy-radiation are all different forms of thephoton (e.g. y rays are very short wave-length radiation which originate in nuclei).The basic forces listed in Table I deter-

mine how the fundamental particles willinteract with one another - i.e. they repre-sent the glue whereby the fundamentalparticles are held together. These are:

1. The gravitational force. This is an at-tractive force that depends upon the massof the constituent particles in a system.Hence, it will primarily affect protons andneutrons, and to a much lesser extentelectrons. This force is normally very weakwith respect to the other forces listed be-low. But, for massive astronomical bodiessuch as the sun, MO=2 x 1033 grams(Mo) = mass of the sun), it can become veryimportant.

2. The electromagnetic force. This forcerepresents a repulsion between chargedparticles of the same charge and an attrac-tion between opposite charges. Thus, theproton attracts the electron to form thehydrogen atom ('H). Two protons will re-pel one another and hence, must be acce-lerated toward one another in order toovercome this repulsion and bring themtogether. The electromagnetic force bet-ween two fundamental particles is about1031 times stronger than the gravitationalforce.

3. The nuclear force . The nuclear forceis attractive and acts primarly between ba-ryons. It is the strongest of the forces,about 137 times stronger than the electro-

NL'('LFOSY.N7'HESIS OF' 7'HE ('IIE.tIICAL ELEMENTS' 53

magnetic force . It is effective only when

the particles are very close together

(.- 10-12 cm ), whereas gravity and electro-

magnetism exert their force over much

longer distances . Hence, in order to gener-

ate nuclear reactions , it is necessary to

bring baryons (or nuclei ) very close to-

gether.Two additional fundamental relation-

ships will also be necessary to understand

nucleosynthesis . The first of these is the

well known Einstein equation:

E=Mc2 (1)

where T is temperature and p stands for

the density of a body. Under the force of

gravity, massive astronomical bodies con-

tract, thereby increasing their density. The

resultant gravitational pressure causes

massive amounts of cosmological matter to

heat up, leading to the formation of stars.

In this way very high temperatures can be

obtained that provide a means of increas-

ing the energies of nuclear particles to the

point where they can react with one an-

other, converting mass into energy and

providing a long-term energy source for

our universe. At the same time new ele-

ments are created.

4. The weak force. In contrast to the nu-

clear force, the weak force (also referred to

as the weak nuclear force) does not lead to

the release of large amounts of energy in

nuclear reactions. As its name implies, this

is a very weak force with a strength that

falls between that of the electromagnetic

force and the gravitational force. Its range

is even shorter than the range of the nu-

clear force.

That is, energy (E) and mass (M) are inter-

convertible. In many nuclear reactions that

occur in stars, substantial mass is convert-

ed into energy. This relationship deter-

mines the amount of energy our sun (or

any star) emits. The second fact to keep in

mind is that:

Tocpv'

ZO

uaz

0

I

120

110

100

90

:-) 70

s0

z 50W

40

60

30

20

10

StABLE NUCLEI / -

NUMBER OF PROTONS - Z

Fig. 2. Plot ofthe proton number (Z) versus neutron number (N) for the stable nuclei observed in nature (dots).

The long-dashed line encompasses most of the nuclei that have been observed in the laboratory and the short-

dashed line represents nuclei with equal neutron and proton numbers. Representative stable nuclei are indicat-

ed by heavy dots.

54 I R IOR /__ I/OL.1 IR

B. Nuclear Interactions

Extensive studies of nuclear reactionprocesses and the systemic behavior of nu-clear matter have made it possible to refineour theories on the origin of the elements.In order to combine the basic ingredientsin such a way that the observed solar sys-tem abundances of the elements result, it isvaluable to ask the question: Assuming allpossible combinations of neutrons andprotons may exist, what atomic nuclei areactually observed? Measured trends in nu-clear stability serve as an important guidein this respect.

In Figure 2 a plot of neutron number (N)versus proton number (Z) is shown for thestable nuclei found in nature. It is appar-ent that light nuclei prefer to have appro-ximately equal numbers of protons and

_•-

BINDING ENERGY

• r•

• /.

I.

6

7H

Q_ - a. - _.56

,(,Fe

I I I I

20 40 60 80

• *L.

neutrons, whereas increasingly heavy ele-ments tend to have an excess of neutronsover protons. It should be noted that theneutron-proton ratio is a rather continuousfunction that forms a very narrow band ofstable nuclear species.

In Fig. 3 the energetic behavior of nucleiis summarized in terms of a plot of theaverage binding energy of a nucleus (theaverage energy with which the observednuclei are held together). In such a plotnuclei that have the highest binding ener-gies are held together most strongly andhence are the most stable. Note that "Fe isat the peak of this curve, making it themost stable nucleus in nature. This facthas important consequences for the synth-esis of heavy elements. Figure 3 can heused to estimate the energetic trends in nu-clear reactions. For example, reactions bet-

- -

52 U

^ I I I I I I I

100 120 140 160 180 200 220 240

MASS NUMBER

Fig. 3. Plot of the binding energy per nucleon versus mass number for the stable nuclei. The binding energy re-presents the strength with whic-, the neutrons and protons in a nucleus are held together.

S( Y,LF.o. y:vTIIh.'SI.SOFTHh.CHF..41I(.l1.ETF'MENTS 55

ween light nuclei (fusion) will generally

lead to more stable nuclei and thus will re-

lease energy. In contrast, reactions bet-

ween heavy nuclei will have the opposite

energetic trends and therefore must absorb

energy. Similarly, by splitting a heavy nu-

cleus into two pieces (fission) to form more

stable lighter nuclei, energy will be re-

leased. When considering whether or not a

nuclear process will release or absorb en-

ergy, Fig. 3 provides an important predic-

tive tool.

The information in Figures 2 and 3 is

combined in Fig. 4 to present an allegori-

cal summary of nuclear stability trends,

known as the osea of nuclear instabi-

lityo (6). Here the neutron and proton

numbers for the various known nuclear

combinations are shown in the horizontal

plane and the vertical dimension repre-

sents the degree of nuclear stability (or

binding energy). Sea level on this plot

corresponds to nuclei which are sufficient-

ly stable to retain their identity for about

one second or more. It is observed that the

nuclei stable enough for us to study in a la-

boratory (- 1800 of them) form a rather

narrow peninsula extending into the sea of

instability. All other species are submerged

below sea level; i.e., they are very unstable

and thus disintegrate before they can be

observed. Further topographical structure

arises when the quantum mechanical ef-

fects on nuclear stability imposed by

closed shells (or magic numbers) are in-

cluded. These are indicated by the solid

lines for certain proton and neutron numb-

e rs.Uranium, element 92, is the heaviest

element observed in nature, whereas ele-

ments as high as atomic number 106 have

been observed in the laboratory (7).

Beyond the known limit of existing nuclei

there is a small island of nuclei near

<SEA OF INSTABILITY>>

Closed Shells

NNeutrons

Fig. 4. The «Sea of Instability» represents a summary of the stability of nuclei which survive for about one se-

cond or longer. Neutron and proton numbers are plotted in the horizontal plane, whereas stability is indicated

by the vertical dimension. Solid lines correspond to closed nuclear shells. The <island of stability> near 114 pro-

tons and 184 neutrons represents «superheavy nuclei», which have not yet been observed.

56 1 R IOR L: 1/0/ .ix

Z = 114 and N = 184. These are the hy-pothesized superheavy elements which, ifthey exist, are a consequence of the stabi-lity associated with nuclear shells withthese proton and neutron numbers. Thusfar, searches for the existence of these spe-cies in both nature and in the laboratoryhave been unsuccessful. (For a thoroughreview of the more or less current status ofthis subject the reader is referred to refer-ence 7.)Once it is known whether or not a nu-

cleus is stable, the probability of it formingin nuclear reactions must be considered.Extensive measurements of the probabili-ties of nuclear reactions, or the reactionrates, have been made in many laborator-ies throughout the world, in particular atthe California Institute of Technology (5).Based upon these measurements one canevaluate the course of any chain of nuclearevents that might lead from the fundamen-tal particles to more complex systems. Inorder to discuss these nuclear reactions weshould take a moment and define the no-menclature that will be used throughoutthis article. The standard nuclear notationfor describing atomic nuclei is given as fol-lows:

A

XZ

Here the X stands for the chemical symbolof an element; that is, H stands for hydro-gen, He for helium, etc. The Z representsthe atomic number of a nucleus, or morespecifically, the number of protons it con-tains. This subscript is frequently omittedsince it is redundant with the element sym-bol. The A represents the mass number ofa nucleus, which is the total number ofprotons and neutrons contained in the sys-tem. Isotopes are nuclear species X whichhave the same Z, but different A.

In writing nuclear equations the sum ofthe mass numbers for the reactants must

equal that of the products. This is also truefor the sum of the atomic numbers for thereactants and the products. As an example,we can consider the equation

'He+'He-;Li+;H

This equation represents the reaction oftwo 'He nuclei (total A=8, total Z = 4)with one another to form the isotope of 'Liand deuterium, 'H (total A = 8, total Z =4). This will be our standard way of de-scribing nuclear reactions.By combining the known behavior of

nuclear energetics and the measured pro-babilities for the reactions of interest innucleosynthesis, one can then hope to pre-dict what elements might be formed in cos-mological processes and also estimate therelative abundances of these products. Incases where experimental data are lacking,one must then rely upon calculated nu-clear properties and reaction rates in orderto make these estimates.

C. Solar System Abundances

The critical test of any theory of nucleo-synthesis is its ability to reproduce solarsystem abundances of the elements andtheir isotopic ratios. Determination ofsuch abundance ratios is a complex taskdependent upon a knowledge of the com-position of all components of the solar sys-tem. Such information is derived from thestudy of spectral lines from the sun as wellas analysis of earth, lunar and meteoriticmaterial. Because of the varied chemicalhistory of solar system material, elementalabundance ratios vary from place to placeand thus very careful consideration of suchfactors is required. Isotopic ratios for a gi-ven element, on the other hand, tend to bevery uniform throughout the solar system,thus providing a rigorous test of nucleo-synthesis theories. Because the sun consti-

VCCLEOSt.v7JIESY.S 0E 71IE ( 7IE11IC . 1L IELESIIL.A I.S 57

H

10`

104

IU--1 _l^_J_._1 J I I I 1 1

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

ATOMIC NUMBER

Fig. 5. Solar system abundances of the elements , relative to silicon , as a function of atomic number.

Lutes the major fraction of the solar system'smass, some simplifications result. Also, bystudying the spectra of other stars, onenotes considerable (although certainly notcomplete) uniformity for much of theuniverse. For this reason the solar systemabundances are sometimes referred to in amore adventuresome spirit as cosmologicalabundances.

In Table II the* abundances of the ele-ments are listed as a function of massnumber. Similarly, Figure 5 gives a plot of

TABLE 11Abundance of the elements in the Solar System

(by Mass)

Hydrogen : ' H (214) 71%Helium : 4 He ('He) 27 %A = 5,8 0,Li, 413e, SB 10_5 %i2C _ 20Ne 1.8Sodium - Titanium (Z = 1 1-22) 0.2 %Iron Group 0.02 %63 z A z 100 10s (YoA > 100 10-5 %

the relative abundances of the elements as

a function of atomic number. It is impor-

tant to note in Table II and Fig. 5 that

most of the universe is composed of hydro-

gen, 'H. In addition, there is a small

amount (1 part in l05) of hydrogen of mass

2, or deuterium. Helium is the next most

abundant element and is composed pri-

marily of 'He. These two elements consti-

tute most of the mass of the universe.

However, a universe composed only of this

material would be very uninteresting be-

cause in order for life to evolve, the pre-

sence of carbon and more complex ele-

ments is essential.

Another important feature of the solar

system abundances is that nuclei with

mass numbers A = 5 and 8 do not exist in

nature. Both are very unstable nuclei

which do not hold together for any appre-

ciable length of time. This fact severely

limits the pathways for synthesizing hea-

vier elements from 'H and 4He, and has

very important consequences for our

58 1 /( YOR / 110L.l JR

theory of nucleosynthesis. It is also inter-esting to note that the elements lithium,beryllium, and boron (Li, Be, B) have verysmall abundances. This is due to the factthat these nuclei are extremely fragile andare easily broken up. As the elements be-come gradually heavier, one finds that theelements carbon through neon representabout 1.8 percent of the nuclei in nature,and for increasingly heavier elements theabundances become still smaller. In Fig. 5,it is worth noting that there is a peak in theabundance curve corresponding to iron.This peak is a consequence of the unusualnuclear stability of 56Fe. It is also apparentthat for heavy elements beyond iron, thereis some structure in the abundance curves.This is associated with features of nuclearstructure that are involved in the synthesisof heavy elements.

In addition to the abundance ratios ofthe elements, there is also a large amountof data on the isotopic ratios of a given ele-ment. For example, the ratio of 5Li to 6Liin nature is known to be 12.5. Isotopic ra-tios have been measured with high accur-acy for all of the elements and are found tobe remarkably uniform throughout the so-lar system. Observation of anomalies inthe isotopic ratios frequently indicates un-usual evolutionary features of the elementin question (8).

Thus, our model of nucleosynthesisbegins with the basic principles, appliesexisting knowledge of nuclear interactions,and the final result should then describethe abundances and isotopic ratios of theelements. Research over the past 25 yearshas indicated that there are three majorsources responsible for the synthesis of theelements. These include, (1) cosmologicalnucleosynthesis in the Big Bang, (2) nu-cleosynthesis during stellar evolution, and(3) nucleosynthesis in the interstellar me-dium via galactic cosmic ray interactions.We shall now turn to a discussion of eachof these processes in more detail.

MAJOR SOURCESOF THE ELEMENTS

A. Cosmological Nucleosynthesis

The earliest era to which we can tracethe origin of our universe is that of the BigBang explosion, which is believed to haveoccurred about 15 billion years ago (9).Under the initial conditions of the BigBang, all matter and energy existed in theform of a hot, dense fireball which con-tained only the elementary particles. Theexpansion of this material into space, andsubsequent cooling, eventually led to theformation of the more complex systems wenow observe - nuclei, molecules, galaxiesand life itself.

Experimental evidence for the Big Bangrests primarily on two important observa-tions:

(1) Red-shift measurements - The spec-tra of stars in all galaxies of the visibleuniverse are known to be Doppler-shiftedtoward the red, indicating that the lightsources are receding from the earth. Theimplication of this fact is that we live in auniverse that is currently expanding.

(2) The universal 2.7 °K background ra-diation - Radioastronomical measure-ments have shown that a uniform back-ground radiation exists in the universewhich corresponds to a black-body sourceat 2.7°K. Penzias and Wilson recently re-ceived the Nobel Prize for this discovery.This background radiation field is pre-sumed to be the remnant of the radiationfield associated with the Big Bang explo-sion. From these two facts, a great deal canbe inferred about the primordial conditionof the universe.

During the first few minutes of the bigbang, the fundamental particles existed inan intense sea of radiation at temperaturesof 1010 to 10'2 °K or greater (9). Neutronsand protons existed in equilibrium with

VC'( LEO.S)',A l7/ES/S of THE C l/L'll(AL ELE,4tEN7S 59

one another according toequations:

the following

'H+e ='n+v

'n+ e' ='H+v

The combination of a neutron and a pro-ton to form deuterium (2H) -the essentialfirst step in the synthesis of more complexnuclei- is not possible at such high tem-peratures because the 2H nuclei instantan-eously disintegrate.

However, as the universe continued toexpand, the temperature eventually de-creased to a point where 2H nuclei couldsurvive for a finite length of time. At thispoint, approximately three minutes afterthe initial explosion (9, 10), the tempera-

ture had dropped below about 1010 °K, andthe following series of reactions - all ratherwell studied in the laboratory - becamepossible

'H+'n- 2H+'y

'H+'n -'H+y;'H+'H -), 'He+y

2H +' H -* 'He + y; 'He +'n -f 4He + y

'He+'He---> 'Be + y

The formation of nuclei heavier than 7Liduring the Big Bang was strongly inhibitedby the instability of nuclei with mass A = 5and 8, shown in Table II.With continued expansion and de-

creased density, the universe eventuallycooled to a point where nuclear reactionscould no longer be sustained. The remain-ing neutrons then decayed to protons asfollows:

in -*'H+e +v

(average life times= 16 minutes)

Thus, the unreacted protons and neutronsfrom the Big Bang resulted in a large resi-

dual hydrogen abundance in the universe.The primary nuclear reaction product ofthe Big Bang was 'He.One strong argument in favor of this hy-

pothesis is that the abundance of 4He ap-pears to be rather uniform (- 24-28 %)

everywhere we look in the universe, thus

giving rise to the conclusion that most of

the helium must have been made at ap-

proximately the same time. Otherwise,there would be much greater differentia-tion in helium compositions among thestars of different galaxies. Thus, we believethat cosmological nucleosynthesis in the

Big Bang produced primarily 4He, plus theresidue of protons that led to the very large

abundance of hydrogen atoms in the uni-verse. In addition, trace amounts of deute-rium, 'He, and Ti were also formed andthis process is thought to be primarily re-sponsible for these isotopes.

B. Stellar Evolution

In the aftermath of the Big Bang, cosmo-logical dust consisting largely of hydrogenand helium atoms filled the expandinguniverse. The decreasing density which ac-companied this expansion cooled the BigBang remnants to temperatures well belowthose at which nuclear reactions could oc-cur. If it were not for the force of gravity,element synthesis would have ceased atthis stage. From our personal point of viewthe result would be a very dull universe,for it would not allow for the existence ofcarbon and heavier elements, the essentialatoms for biological systems.

However, eventually the attractive forceof gravity began to produce massive lumpsof matter in space. This process represen-ted the beginning of galaxy and star forma-tion, and at the same time provided uswith a new environment for synthesizingelements.As these embryonic stars condensed,

their density increased and they began to

TEMPERATURE

CENTRALTEMPERATURE

14 MILLION ^^^ DEGREES

i=^^ R ^ b/ y`^

^^ ^ ^^` ^b^1

a:^'^^^ ~^

:1 N _^ -

6 ^^O/ ^. O

^^^

'i3;, x.r.14'r X^\

Mass = 2 x I O;;g

Radius = 10 ^ ^ cm

il/_ ^

i

MASS

Fig. 6. Schematic drawing of the structure of the sun, showing the temperature and fraction of mass as afunction of solar radius.

heat up once again. At sufficiently hightempe-ratures, about 10,000 °K, hydrogenatoms become ionized into protons andelectrons. Under increasing gravitationalpressure, the density of the nuclei in thecore of a developing star eventuallyreaches very high values, corresponding toabout 100 g/cm`, or a temperature of about15 million °K. Such conditions are certain-ly extreme when compared with thoseexisting for hydrogen on earth, which isabout 300° K and 0.001 g/cm;. On theother hand, this is much less dense thannuclear matter, which has a density ofabout 1014 g/cm'. [t is important to realizethat only the core of the star reaches themaximum temperatures and densities; forexample, the temperature at the surface ofour sun is only about 5,700° K, while itscore is thought to have a temperature ofabout 14,000,000 °K. The density andtemperature profiles characteristic of starslike our sun are illustrated in Fig. 6.

Hydrogen Burning: Main Sequence Stars

When the core of a star reaches a tem-perature of approximately ]0 to 20 million°K and densities approaching 100 g/cm',the protons in the core acquire sufficientenergy that nuclear reactions again becomepossible. The process of hydrogen burning(or proton burning) characterizes what arecalled main sequence stars, of which oursun is an example (1 1). About 90 percentof the stars in the universe are main se-quence stars. Such stars burn protons intohelium by means of the following series ofnuclear reactions, also illustrated in Fi-gure 7.

'H+'H^'-H+p++v

'-H + ^ H ^ 'He + y

'He+;He^4He+2'H

NET:4'H^4He +2^3++2v+26.7 MeV

AcrLEOSYNTHESlSOh IRE C/IEI(.-1LELEMEA7S 61

HYDROGEN BURNING:THE FUSION OF ORDINARY HYDROGEN

IN MAIN SEQUENCE STARS

Density = 100 grams/cm3

Temperature ^ 10-20 x 106 °K

'H+ 1H _ 2H+13++v

2H+ 1H - 3He+y

23He * 4He+2 'H

NET: 41H 4He+213++2v+26.7 MeV

Fig. 7. Schematic diagram and equations describing the hydrogenburning process in which hydrogen is

fused into 4He nuclei in main sequence stars.

In this way the element helium is syn-

thesized during hydrogen burning. The

above reactions have been studied in the

laboratory and several variations of this

reaction sequence are known to be possi-

ble, depending on the temperature at the

core of the star. The net effect in each case

is to convert 'H into 4He. These are exam-

ples of fusion reactions which serve to fuse

two nuclei together and form a heavier nu-

cleus. The amount of energy released in

this reaction makes it one of the most effi-

cient energy sources known. For example,

there are about 1.5 x 10" calories liberated

per gram of hydrogen burned in the above

reaction, more than 20 million times the

amount of energy liberated in the chemical

burning of a gram of carbon. The energy

released in hydrogen burning serves to sta-

bilize a condensing star, counteracting the

force of gravity. When these two effects

counterbalance one another, the star ap-

pears to be a stable body. As long as the

nuclear fuel lasts, the star continues to

provide a constant source of energy in

space.The mass of a star determines the rate at

which it burns nuclear fuel and thus howlong it will live. The heavier the star, thefaster it burns. In main sequence stars theslowest step is the fusion of two protons tomake deuterium. Note that positrons (an-

62 ! Y ( YOR L 1 1K.ia_

tielectrons) are produced in this reaction(the first of the above equations). This isunusual in nuclear reactions and usuallycauses the nuclear process to proceed veryslowly, accounting for the relatively longlifetime of main sequence stars. From anexperimental knowledge of how fast thisreaction occurs and how much hydrogenexists in the sun, it is possible to calculatethat our sun will continue to shine for an-other 5 billion years or so.

In summary, hydrogen-burning reac-tions stabilize a condensing star and gener-ate energy by producing helium fromhydrogen. However, the net product of thisprocess is only a small amount of helium,which was already present in the initiallyformed star. In order to synthesize morecomplex elements, we must examine moreadvanced stages of stellar evolution.

Helium Burning: Red GiantStars

As a main sequence star becomes older,it begins to develop into two phases:

(1) A core composed largely of the he-lium produced during hydrogen burning,and (2) an outer envelope consisting large-ly of unburned hydrogen. Hydrogen burn-ing continues at the interface between thecore and the envelope. However, at tem-peratures of 15 million `K, reactions bet-ween helium nuclei are inhibited becauseof the electromagnetic repulsion betweenthe two nuclei. Furthermore, studies of thenuclear stability of the elements lithium,beryllium, and boron (Z = 3, 4 and 5) showthat these are extremely fragile nuclei andthat at temperatures above about I million`K they disintegrate. For this reason Li, Beand B cannot be formed in any appreciableamount in stars (see Table II). Hence,further element synthesis subsides in thecore.

If the mass of the star is sufficientlylarge, the force of gravity begins to con-tract the core once again, leading to stillhigher temperatures and densities. Thiscauses the envelope of the star to expandgreatly and gives rise to a new stage in theevolution of the star, called the red giantstage. Stars which are not heavy enough tosustain more advanced stages of nuclearburning simply exhaust their hydrogenfuel and undergo no further evolution.These are known as white dwarf stars,which represent the stellar graveyard.

During the red giant stage of a star thegravitational force continues to contractthe core. When the temperature reachesabout 10' 'K, which corresponds to a den-sity of 10' g/cm', a new type of nuclearreaction becomes possible. Of the severalpossible nuclear reactions that might con-ceivably lead to the production of heavierelements from hydrogen and helium atsuch temperatures, laboratory studies haveled us to believe that only one is likely.This reaction, called helium burning, is re-presented by the equation:

'He + 4He ---> ['Be]* + y(lifetime= 10-10 seconds)

[813&]* +4He _'2C +y

To produce a helium-burning reaction,three 'He nuclei must collide almost si-

multaneously, as shown in Figure 8. The

chances of this occurring are low due tothe very short half-life of the 'Be interme-

diate, which is about 10-10 seconds. As a

consequence, the red giant stage of a star

can last for millions of years. Thus, the

element-synthesis chain skips over the ele-

ments lithium, beryllium, and boron to

produce carbon. At this stage in the star's

development the basic element for the for-

mation of biological compounds has now

been synthesized.Once helium burning begins, the core of

the star is again stabilized and a new equi-

t*CLcost.v rJ/taisor tin: (nftnc . a1. ELEarE A rs 63

librium situation results. Under this newcondition, gravitational contraction andexpansive nuclear burning again offset oneanother. At the same time it is possible toproduce oxygen by means of the followingreaction:

4He+ 12C - 160+yy

The evolutionary cycle of our schematicstar thus far is indicated in Figure 9. Thestar has begun by burning hydrogen in themain sequence and converting this into he-lium nuclei. As the helium concentrationincreases, the core of the star heats upfurther to the place where three heliumnuclei fuse to form 12C and, dependingupon the conditions of the star, 160. Atthis stage if the star is of sufficiently lowmass, it will burn out and become a whitedwarf. On the other hand, if the mass issufficiently great, much more complicatedsets of nuclear reactions can occur. Theseare described below.

Carbon and Silicon Burning: Massive Stars

As a star passes through the red giantstage, new core conditions eventuallydevelop , as illustrated in Figure 9. For themost part the core contains '2C and 160surrounded by envelopes composed of he-lium and hydrogen. The large charge ofthe 12C nucleus prevents the occurrence ofnuclear reactions at these temperatures.Hence , the core undergoes further gravita-tional contraction and heating if the star issufficiently massive. Its subsequent fateunder these conditions is probably one ofthe more poorly understood phases of nu-cleosynthesis . The core of he star may con-tinue to evolve via processes similar to theequilibrium situations that exist in mainsequence and red giant stars, although thelatter stage would be much shorter lived.On the other hand , the evolution of the

HELIUM BURNING:THE FUSION OF HELIUM IN RED GIANT

STARS

Density ^ 105 grams/cm?

Temperature ^ l08 °K

4He + 4He = [sBe `]; t 1 2 = 10-16 sec

[SBe•]+4He _ 12C+y

12( +4He _ 160 + y

Fig. 8. Schematic diagram and equations describingthe helium-burning process in which 4He is fused into12C in red giant stars.

star may become quite rapid and developexplosive conditions under which nucleo-synthesis occurs very rapidly.

If the core temperature and densityreach about 600 million °K and 5 x105 g/cm ;, new types of nuclear burningbegin . The first type that becomes possibleis called carbon burning . This reaction in-volves the fusion of the 12C and 160 rem-nants from helium burning which formstill heavier nuclei . These reactions arecomplicated but can be represented byequations of the type:

12C + 12C -> 20Ne +4He

160 + 160 --), 28Si

+ 4He

64 ) n FOR t( lo[.( JR

lowMass

highMass

White ExplosiveDwarf Nucleosynthesis

Fig. 9. Schematic diagram of stellar evolution from themain sequence to the red giant phase. Hydrogen-burning core in main sequence phase evolves into 4Hecore. This eventually undergoes helium-burning,leading to a greatly expanded envelope in the redgiant phase. Low mass stars become white dwarfswhereas heavier stars undergo more advanced stagesof nuclear evolution.

Because these reactions can occur rela-

tively rapidly at high temperatures, the

evolution of the star proceeds much faster

at this stage and a much more varied nu-

clear composition develops. As the life cy-

cle of a heavy star continues, a new core

composed largely of nuclei near 2tSi

evolves. At temperatures near I x 10' °K

and densities about I x 106 g/cm3, a process

known as silicon burning begins. Because

of the large electric charge on nuclei such

as silicon, it becomes increasingly difficult

for fusion reactions between two 21ST nu-

clei to proceed. However, because of the

high temperatures and the variety of nu-

clear reactions that can occur in this ad-vanced stage of stellar evolution, reactions

involving ejection of an a-particle (4He) byy-rays [(y, a) reactions] and the inverseprocess of 'He capture [(a, y) reactions] be-gin to occur. This complex reaction chain

is summarized as follows:

28Si + y 24Mg + 4He

4He +28Si -+ 32S + y

32S+4He = 36Ar +y

(a. Yl (a. Y) (a. Y) la. Y)Net: tSi 3 S 36Ar, = 40Ca

etc.

A=56 (56Fe)

These reactions can go in either direction

but the reaction going toward the right al-

ways occurs to some extent. This chain of

reactions primarily produces nuclei with

mass numbers A= 32, 36, 40, 44, 48, 52,

and 56, which turn out to be unusually

abundant in nature. In addition, because of

the much richer composition of nuclear

matter that exists in the stellar core during

silicon burning, a much more diverse

batch of other nuclear reaction products is

possible. Hence, many of the remainingnuclei below 56Fe will also be synthesized,

but in smaller quantities.

Of particular importance in the silicon-

burning process is the fact that it stops

near mass number A = 56. Recall that we

stated earlier (Fig. 3) that 56Fe is nature's

most stable nucleus. Because of this fact,

fusion reactions which produce nuclei hea-

vier than 56Fe in the stellar core absorb

energy rather than releasing it. Thus, when

an iron core develops, the absence of en-ergy-liberating nuclear reactions removes

the major source of stellar support resisting

gravitational contraction.To summarize our account of stellar

evolution to this point, we have described

A (Y LEOS YA 7HhSLS OF HIP (HESL/('AL. ELEMENTS 65

a rather complex star, containing most ofthe elements up to iron in various layers.This is indicated in Figure 10. Most of theelements needed to sustain life have nowbeen constructed. At each stage of stellarevolution, the processes become less effi-cient and more diverse, accounting for thesteadily decreasing abundances of the ele-ments, observed in Figure 3 and Table II.The difficulty in producing nuclei beyondiron creates a sink for Fe-like nuclei, pro-ducing the peak at iron in Figure 3, andalso accounts for the low abundances ofthe heavier elements. Further, the unusualstability of nuclei in the iron region alsomeans that nuclear reactions can no longeract as a source of energy to sustain thestructure of a star against strong attractiveforces of gravity that exist at these veryhigh densities.

Heavy Element Production:

the r - Process

The accumulation of the iron group ele-ments in the core of a star leads to catas-trophic conditions. Because nuclear reac-tions can no longer release energy andprovide their stabilizing influence, gravita-tional force causes the core to collapse;that is, an implosion of core upon itself re-sults, as indicated in Figure 10 in the cen-tral region. The implosion process occurson a time scale as short as seconds, duringwhich the density of nuclear matter mayreach 10" g/cm' with a corresponding tem-perature of 6 x 10° °K in the center of thecore. It is thought that this process of gra-vitational collapse and rapid heating is fol-lowed by a massive shock wave that leadsto explosion of the star. This phenomenonis believed to be associated with supernovaexplosions.

There are two important consequencesof gravitational collapse and the rapidheating which follows. First, the tempera-

ture increase triggers a varied array of nu-clear reactions throughout the outer enve-lopes of the star. This leads to an enrich-ment of nuclear species from the elementspreviously formed. A second important

consequence stems from the conditions inthe very center of the core where the tem-perature and density are highest. Underthese extreme conditions iron nuclei beginto break up by means of photodisintegra-tion reactions, leading to the followingschematic processes:

"Fe +y---> 13 'He + 41n

4He+ y-2'H+2'n

'H+e-i'n+v

The important point is that large num-bers of neutrons are produced in the cen-tral core region. The "laboratory" analo-gue of this process is found in thermonu-clear explosions (hydrogen bombs), whichhave permitted us to gain useful insightsinto this mechanism. The neutrons serveas a source of nuclear particles which caninteract with previously processed nuclearmaterial in the star and further enrich thevariety of nuclei that are produced. Be-cause neutrons have no electric charge,they can be absorbed by the iron group nu-clei without the restrictions of electro-magnetic repulsion experienced bycharged particles.

This stage of nucleosynthesis is calledthe r-process (r for rapid) and is assumedto be responsible for elements beyond ironaccording to the following series of reac-tions:

z6FeIn, I

"FeIn, YI

ssFe I--*) -> __+ 26 Fe

etc.

These reactions produce highly neutron-rich nuclei which are well submerged be-low the sea of instability in Figure 3. As

66 1 W1 OR L I IOLi JR

II

1

SUPERNOVA SCHEMATIC

I'll

1H-+ IHe

4He -* 12C, 160

7

I

C,0-->Si

Si Fe

F

r-process/

N

1

I I I/ / /

/ /

N

(sprocess)

Fig. 10. Schematic diagram of stellar structure at the onset of the supernova stage. Nuclear burning processesare indicated for each layer. The process is associated with the disintegration of iron nuclei in the central regionof the star; a process which liberates neutrons.

this process of neutron addition continues,nuclear beta-decay (conversion of a neut-

ron into a proton) becomes increasingly

probable, thus producing the next higherelement, as shown below:

2,Fe 27Co+e +v

79Co(n. -* 80CO (n, Y1 1

81 Co

81Co-*81Ni+e +

This sequence of neutron-capture and beta

decay produces heavier and heavier ele-

ments.It is the r-process that forms the heaviest

elements in nature and must account for

the possible existence of any "superheavy"elements. There is no other nuclear reac-

tion mechanism known by which we canaccount for the production of the amounts

of uranium and thorium that we find in

nature today. A schematic diagram of the

r-process is shown in Figure 11. The upperlimit to element synthesis in the r-process

is imposed by nuclear fission reactions

which become increasingly probable as the

nuclear charge increases beyond Z = 90.Fission involves division of the nucleusinto two nuclei of roughly the same massnumbers. Thus, the nucleosynthesis pro-

cess is terminated and nuclear materialsimply cycles between the buildup of very

heavy elements and their fission into in-

L CLEOS YN THESIS OF THE CHEMIC II. ELEMENTS 67

100

90

80

70

t6o

50

40

30

t--

Z=28

Cycle time = 5 sec

201 - I-^_^ . i i 1 1 i 1 i i 140 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190

Z--a.

Fig. 11. Diagram of the r-process path on a proton versus neutron number plot. The stable heavy isotopes are

indicated by the open circles. The dashed region shows the the path followed by the r-process, which is termin-

ated by nuclear fission (heavy vertical line). The s-process path is given by the solid line through the stable

heavy isotopes.

termediate - mass elements . It is not clear atwhat point fission becomes dominant in

the r-process chain of mass buildup, but

most probably it occurs around mass

number A = 270, which would mean that

the superheavy elements (A - 300) are

probably not produced in nature. At the

present time attempts to discover these ele-ments experimentally , both in nature and

via nuclear reaction studies in the labora-

tory, have been unsuccessful (7). However,

these attempts continue and it may well be

possible that eventually superheavy ele-

ments will be observed.Although there are other significant pro-

cesses responsible for element production(to be discussed in the next section ), the r-process is thought to conclude the life cy-cle of a first generation star ; that is, a starcomposed of original big bang material.Following gravitational collapse , the su-

pernova core is believed to form a dense

neutron star (density - 1014 g/em3). Neut-

ron stars are believed to be the explanation

for the existence of pulsars, which are

small, massive sources of periodic radio-

wave emission.

The supernova explosion itself ejects

processed nuclear material out into space

where the temperatures and densities are

much lower. This material then attracts

electrons to form neutral atoms and mole-

cules and the entire cycle begins anew.

First, the gravitational force begins to con-

dense matter to form second generation

stars, or, in the case of smaller amounts of

mass, planets, meteorites, and cosmic dust

are formed. In this way succeeding genera-

tions of stars, richer in nuclear reaction

possibilities, evolve. Our sun must be at

least a second generation star because we

see evidence that it contains heavy ele-

68 1A TOR E l7OL 1 JR

ments in addition to its hydrogen and he-lium content.The life cycle of a star is depicted in Fi-

gure 12. If one recalls the abundances ofthe elements shown in Table II and Fig. 5,it is clear that none of the successive stagesof element synthesis need to be very effi-cient to produce nature's elements. Hence,even after the complete evolution of a star,98 % of the material still will be in theform of hydrogen and helium.At this point, our basic picture of stellar

evolution and the production of elementsin nature is roughly complete. Many re-finements are required to give a thoroughdescription of these processes; in fact,many pieces of experimental informationare still lacking or incompletely under-stood. Nonetheless, the model representsour best current understanding of the ori-gin of the elements.

The s - Process

Up to now we have emphasized the pro-duction of new elements in the initial cycleof the star ' s lifetime. In later generationstars the presence of previously processednuclear material makes it possible to formelements in many new ways . Among themost important of such mechanisms iswhat is called the s-process (s for slow).This process , like the r-process , involvesthe capture of neutrons , but it takes placein relatively stable stars where nuclearreactions produce neutrons at a slow,steady rate. For example, in red giant starsneutrons can be produced by means ofreactions of the following type:

13C+'He 160 +' n

"0 +'He 20Ne +' n

When sizeable amounts of iron groupelements are present as seed nuclei, it is

Gravitation

Condensation(T, p)

Mixing, Rotation

LIFE CYCLE OF A STAR

Stellar Gas, Dust, etc.

WhiteDwarfs(low M)

r-Process (Supernova)Heavy Elements

1e-Process: 28Si burning

1 `6Fe

C-and O-Burning

1

28Si 325

Helium Burning(Red Giants) -s- process

3 (i _ 12(', 160 1f Heavy

Elements

Hydrogen Burning(Main Sequence)

4'H --. 4He

PPI, PPI1 , PPIII, CNO

Stellar Bodies(M, R, L, T)

Fig. 12. Life cycle of a star. M, R, L, T refer to themass, radius, luminosity and temperature of a star.

possible to build up heavy elements muchthe same way as in the r-process. However,unlike the r-process - where many neut-rons are captured by a single nucleus in amatter of seconds-in the s-process a sin-gle nucleus captures a neutron every fewthousand years or so (hence, slowly) andtherefore beta-decay can occur before an-other neutron is captured. Since red giantsexist for millions of years, the s-processcan exert a strong influence on the produc-tion of heavy elements in stars. The differ-ence in time scales between the s-processand the r-process results in the formationof different isotopes in the elements. Forexample, compare the following chain ofs-process reactions on "Fe seed nucleiwith that for the r-process on 56Fe in thepreceding section:

NL'CLEOS I'NTHESIS OF' 7'HE C'HEMIC'AL ELEMENTS 69

56Fe(n, r) s'Fe (°.'") 58Fe'°. rl 59Fe X59 Co + e +26

59Co ¶ ' 60Co -* 60Ni + e + v etc.

The r-process tends to form the heavierisotopes of a given element, whereas thes-process forms the lighter isotopes. This isillustrated in Figure 13 where both the s-and the r-process paths are shown for a gi-ven region of atomic nuclei. The s-processcan be studied extensively in nuclear reac-tors and is thought to be understood fairlywell.One other process, the p-process, is re-

sponsible for forming the lightest isotopes

of many heavy elements. In general theabundances of the p-process isotopes areextremely small because they are formedby (p, y) and (y, n) reactions on the s- andr-process residues.

In the various processes ranging from

hydrogen burning through the s- andr-processes one sees that stellar evolutionresults in the formation of all of the ele-ments between carbon and uranium, andperhaps heavier ones, as yet undiscovered.Simultaneously, stellar evolution leads notonly to the formation of the elements, butalso to the richness of cosmological pheno-mena that we observe in our universe,ranging from main sequence stars to super-novae.

C. Nucleosynthesis in the InterstellarMedium

From our previous discussions it is seenthat cosmological nucleosynthesis in theBig Bang and element synthesis duringstellar evolution can account for nearly allthe elements of the periodic table. Ho-wever, three elements have been omittedin our scenario: the elements lithium, ber-yllium, and boron. As we stated earlier,these elements are known to be extremelyfragile and consequently disintegrate

quite readily during stellar evolution andcannot survive. It is thought that some 'Lihas survived since the Big Bang, but the re-maining isotopes of these elements, 6Li,'Be, 10B and "B, must have been producedby some other mechanism. It is currentlybelieved that these elements have their ori-gin in interactions of galactic cosmic rayswith the gas and dust of the interstellarmedium. Such reactions involve primarilyreactions of protons and 'He nuclei withother 'He and carbon, nitrogen and oxygennuclei present in the interstellar medium.These reactions occur at rather high ener-gies, much higher than those characteristicof the Big Bang and stellar evolution, butin an environment which has a very lowdensity. Consequently, the temperature islow and the Li, Be and B products can sur-vive after their formation.

This is one case of a nucleosynthesisprocess where rather extensive knowledgeexists for both the salient nuclear reactionsand the astrophysical processes involved(12). For example, the energy spectrumand the composition of the cosmic rayshave been widely studied. Furthermore,the composition of the interstellar mediumis also thought to be relatively well under-stood. Hence, measurement of nuclearreaction cross sections for these systemsshould allow one to calculate the elemen-tal abundances observed for'lithium, beryl-lium and boron if this proposed mechan-ism is correct. It is found that one is able toreproduce the abundances of 6Li, 'Be, '°B,and "B quite well with this model. Ho-wever, the isotope 'Li is greatly underpro-duced, which further strengthens the beliefthat 'Li was synthesized in the Big Bang.

In fact, if one assumes that the addition-al 'Li necessary to match the abundancesof the lithium isotopes in the solar systemcomes from the Big Bang , it is possible toinfer basic conditions which characterizedthe Big Bang from this information. In Fi-gure 14 we show a plot of the ratio of the

70 t I( /OR I. t 101 1.1R

P

P

(Neutron-rich matter)

NV.

Fig. 13. Plot of N versus I (as in Figs. 3 and I I) showing production of isotopes of the elements by the r-, s- andp-processes. The squares represent the stable isotopes of an element. Wavy lines indicate the beta-decay path ofneutron-excess isotopes produced in the r-process. The solid line through the center of the stable isotopes showsthe s-process path of neutron capture.

abundance of ILi, which we attribute to the

Big Bang, divided by the abundance of

deuterium (which is thought to have been

formed only in the Big Bang) as a function

of the matter density of the universe. The

solid curves are the predicted 'Li/2H ratios

for the Big Bang as a function of the den-

sity of the universe, based upon calcula-

tions involving all possible nuclear reac-

tion cross sections for these species (10). It

is observed that the ratio of 'Li to deuter-

ium corresponds to a present matter den-

sity of the universe of about 6 x 10-3° g/cm3.

This density would have been much

greater at the time of the Big Bang, since

our universe has been expanding for

15 billion years.

An important related question is whetheror not the universe will continue to ex-

pand forever. Do we live in an ever-expan-

ding (open) universe, or will it eventually

stop expanding under the force of gravity

and contract again (a closed universe)? In

the latter case, a primeval fireball corre-

sponding to the Big Bang might once again

result. This is a subject of considerable de-

bate in current astrophysical theory. Since

the 'Li to deuterium ratio is seen to be

such a critical function of the density of

the universe, one can estimate whether or

not the universe is open or closed from

these data. The estimated density required

to close the universe is about

6 x 10-29 g/cm3, as indicated by the arrow

in Figure 14. The present results indicate

that the matter density of the universe is

thus too low by about a factor of ten to

permit a closed universe. Hence, these nu-

NL CLEOSF.ti'THESIS OF THE C'HEM1C'.1L ELEMENTS 71

[7Li] BB

[2H]BB

10°

10-I

10-2

10-3

10-4

10-5

10-

I 0-7

10-8

CriticalDensity

I Pfnt

^10 32^

I _0-1 31 10-30 10 29Ph (g/em3)

Fig. 14. Solid lines show a plot of the ratio of 7Li to 2H formed in the Big Band as a function of the present den-sity of the universe, as calculated by Wagoner (10). The dashed line corresponds to the observed 7Li/2H ratioand the corresponding density. The density required to close the universe, p«;t, is shown by the heavy arrow.Curves marked = 0.5, 1.0 and 2.0 correspond to different assumptions concerning the parameters involved inthe calculation.

cleosynthesis data also impinge on veryfundamental concepts of our universe andindicate that the universe is open and willcontinue expanding forever.

3.

4.5.

6.

ACKNOWLEDGEMENTS

The General Research Board of the University ofMaryland is acknowledged for providing a FacultyResearch Grant for the Spring 1979 semester, duringwhich time this paper was prepared. This researchprogram was supported by grants from the U.S. De-partment of Energy and the National Science Foun-dation.

7.

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Super-Heat'v Elements, Lubbock, TX, March,

1978.

8. SCHRAMM , D.N. and CLAYTON, R.N. Scientific

American , 239. no 4 (1978).

9. WEINBERG, S. The First Three Minutes (Basic

Books, Inc., NY) 1977.

10. SCHRAMM , D.N. and WAGONER, R.V. Ann. Rev.

Nucl. Sci. 27, 37 (1977).

11. BAHCALL, J.N. and DAVIS, R. JR. Science 191,264 (1976).

12. MOYLE, R.A., GLAGOLA , B.G., MATHEWS, G.J.BIBLIOGRAPHY and VIOLA, V.E. JR. Phys. Rev. C19, 750 (1979);

1. GAMOw, G. Rev. Mod . Phys. 21, 367 (1949). GLAGOLA, B.G., MATHEWS, G.J., BREUER, H.F.,2. Bt-RBIDGE , E.M., BURBIDGE , G.R., FOWLER, W.A. VIOLA, V.E., Roos, P.G., NADASEN, A., and AUS-

and HOYLE , F. Rev . Mod. Phys . 29, 547 (1957). TIN, SAM M. Phys. Rev. Lett. 41, 1968 (1978).