•CT* feature
THE ORIGIN OF THE ELEMENTS They [atoms] move in the void and catching each other up jostle together, and some recoil in any direction that may chance, and others become entangled with one another in various degrees according to the symmetry of their shapes and sizes and positions and order, and they remain together and thus the coming into being of composite things is effected. —SMPLICIUS (6th Century Α.Ό.)
Dr. William A. Fowler California Institute of Technology, Pasadena, Calif.
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The question of the origin of the ele ments and their numerous isotopes is the modern expression of one of the most ancient problems in science. The early Greeks thought that all matter consisted of the four simple substances—air, earth, fire, and water— and they, too, sought to know the ulti mate origin of what for them were the elementary forms of matter. They also speculated that matter consists of very small, indivisible, indestructible and uncreatable atoms. They were wrong in detail but their concepts of atoms and elements and their quest for origins persist in our science today. A century ago, chemists concluded that the elements were immutable
under all chemical and physical trans formations known at the time; the al chemist was self-deluded or was an out-and-out charlatan; matter was atomic and God-given immutability characterized each atomic species. The periodic system of these im mutable elements was proclaimed by Mendeleev in 1868. Any theory of the origin of the elements was required to account for the formation of each ele mentary species which remained im mutable and unchanged thereafter. An English physician, Dr. William Prout, noted that most atomic weights seemed to be integral multiples of that of hydrogen and suggested that all of the heavier elements consisted of the
Hydrogen-Burning in Stars Yields Helium and Energy
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He 4 with the emission of 26.7 m.e.v. or 4.3 X 10~r> erg of energy from the small fractional difference (0.7%) between the mass of the helium atom and the mass of four hydrogen atoms. From the standpoint of nucleosynthesis, the /;-/; chain is important because it is a mechanism by which pure hydrogen can be converted into helium. The p-p chain is now thought to be
As Stars Age Their Composition Changes Material is interchanged between the stars and interstellar space EJECTION (Stars and sun)
EXPLOSION (Novae and supernovae)
Nuclear!
ement synthesis eneration
STARS
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S HL,
INTERSTELLAR GAS AND GAS AND DUST CONDENSATION (Young, bright stars associated with interstellar material) MAR.
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the predominant mode of conversion of hydrogen into helium in the sun. In the lifetime of the sun a consider able amount of He 4 has been pro duced. This He 4 reacts with He 3 and enters catalytically into the produc tion of additional He 4 . This is shown by the complete set of major p-p chain reactions written in modern nuclear notation as follows:
Stars Lose Material to Interstellar Space
H 1 ( p ^ + v)D2(p,y)He3(He;\2p)He4 or 4
7
(He ,y)Be (e-,v)Li-(p,a)He4 or (p,y)B«(0 + v)Be«*(a)He-* In the two last alternative chains, the interaction of He 4 with He 3 with the addition of a proton finally results in the production of two He 4 , and the emission of neutrinos of various ener gies from intermediate products, Be 7 and B 8 . Those neutrinos accompany ing the production of D- have an av erage energy equal to 0.25 m.e.v. Those from the decay of Be 7 fall into two approximately monoenergetic groups at 0.88 m.e.v. (90%) and 0.40 m.e.v. ( 1 0 % ) . The neutrinos from B s have an average energy equal to 7.4 m.e.v. The relative production of these various neutrinos depends sensi tively on the central temperature of the sun and their detection cross sec tions increase rapidly with increases in energy. A solar neutrino detection experiment such as that under way by Dr. Ray Davis at Brookhaven using the process CI 137 + ν (neutrinos) —» A 37 + e~~ (electrons) may serve to make an independent determination of the sun's central temperature which can at the present time be inferred only from models of the sun's internal structure. Thus, a solar neutrino de tector might also be called a neutrino thermometer.
Stars Make Helium bij Proton
Giant stars such as Lyra lose mass at a steady rate to space. The smoke ring of this planetary nebula is a spherical shell of material moving away from the star
Fusion
The fusion of protons into helium can occur in stars even tnougn protons are all positively charged and mutually repel each other. However, on the basis of classical Newtonian mechan ics, fusion cannot be justified, because even at stellar temperatures the pro tons do not have sufficient relative velocities to overcome their mutual repulsion. Sir Arthur Eddington, who proposed hydrogen fusion as the source of energy in stars in 1920, 96
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Supernovae such as Crab nebula in the constellation Taurus may lose by explosion all or a substantial part of their mass to interstellar space
gave the following magnificent answer to those who criticized him on classical grounds: "We do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotter place." Sir Arthur's critics were saved from their classical fate by modern quantum mechanics, which accounts for the be havior of atomic particles and explains how fusion may occur even when it is impossible to rationalize in Newtonian mechanics. Stars which live and shine from energy generated through the process 4H 1 —> He 4 fall in a luminosity-color classification called the main sequence. However, as the hydrogen in the cen tral regions of the star is exhausted, the star ceases to be homogeneous in composition throughout its interior and will move or evolve off the main sequence. The conversion of hydro gen fuel into helium ash occurs in the core of the star because the tempera ture and density are highest there. Astrophysical observations show that the reaction product (helium) mixes with the outer envelope (hydro gen) only with extreme difficulty. Thus, a core of helium develops and gradually increases in size as more and more hydrogen is converted. However, because of greater electro static repulsions, the doubly charged He 4 does not burn at 10 billion de grees K. or even at considerably higher temperatures; thus energy generation ceases except in a thin shell surround ing the helium core. This shell now contains the hottest hydrogen in the star. Shell temperatures may reach as high as 30 million degrees K.; and shell density may increase to 10 grams per cc. In the central regions of the shell, the nuclear hydrogen furnace goes out for lack of fuel, and one might expect from ordinary experience with fur naces that the temperature of the star would drop. But this is not at all the case in stars, because of their great potential gravitational energy. The helium in the core begins to contract and its temperature rises as gravita tional energy is converted into kinetic energy. This description of the anomalous behavior of stars is not all pure con jecture; instead, some support for this behavior comes from observations made on red stars. Larger in area and redder in color than main-se quence stars of the same luminosity,
these stars are aptly called the red giants by astronomers. The sudden rise in temperature of the core also heats up the envelope, which then ex pands enormously, increasing the sur face area of the star. The increased area means that energy can be radi ated from the star at a lower surface temperature than before. Radiation at this low surface temperature results in the typically red surface of the red giants. Eventually the helium in the core reaches temperatures (about 100 mil lion degrees K.) and densities (about 100,000 grams per cc. ) at which Coulomb repulsions should no longer critically inhibit nuclear processes be tween two helium nuclei. But just what these processes might be con stituted for a long time the Gordian knot of nuclear astrophysics. Two helium nuclei, upon interact ing, might be expected to form Be 8 . However, as we noted previously, no nucleus of mass 8 exists in nature; and from this observation early investiga tors inferred that nuclei of mass 8 must be unstable. Shortly after World War II, this concept of instability was confirmed in data on the quantitative measurements of Be 8 decay in labora tories at both Los Alamos and Cali fornia Institute of Technology. C 1 2 Is Made in Stars by the of One α-Particle to Bes
Addition
In both laboratories, workers noted that when Be 8 was produced arti ficially in nuclear reactions, it promptly broke up into two alpha particles. However, the energy of breakup was found to be relatively small, slightly less than 100 k.e.v. With this last fact in mind, Dr. Salpeter of Cornell University then pointed out that, although hot inter acting helium in a star will not pro duce a stable Be s nucleus, it will pro duce, at 100 million degrees K. and at a density of 100,000 grams per c e , a small but real concentration of Be s as a result of the equilibrium between the formation and breakup processes. At present, in the laboratory, nuclei are often observed capturing alpha particles and emitting energy in the form of gamma radiation. Dr. Salpeter pointed out that the Be 8 should behave similarly and that if, after its formation from two alpha particles, it collided with a third, the well-known stable carbon nucleus C 1 2 should be formed. Because of the low equilib
rium concentration of Be 8 in this sys tem—about 1 part in 10 billion at 100 million degrees K.—Dr. Hoyle empha sized that the Be s capture process must be a very rapid one—a resonant reac tion in nuclear parlance. Experiments at Stanford, Brookhaven, and Caltech have shown that this is indeed the case: An excited state of the C 1 2 nucleus at 7.656 m.e.v. exists, having almost the exact energy of excitation and other properties which Dr. Hoyle predicted it must have in order to serve as a thermal resonance structure for the formation of C 12 from Be s and He 4 in stars. Thus there now exists a reasonable experimental basis for justification of the concept that a two-stage process exists by which three alpha particles in the hot dense cores of red giant stars can synthesize carbon, bypassing the intervening elements, lithium, beryl lium, and boron. The over-all process can, in fact, be looked upon as an equilibrium between three helium nuclei and excited carbon (C 1 2 *), with occasional irreversible leakage out of the equilibrium to the ground state ( C 1 2 ) . Such a reaction may be formalized as follows: 3He 4 He 4 . In any case, however, astronomical evidence indi cates that the trend toward catas trophic internal temperatures is stopped and the evolutionary track reversed. Stars that become unstable at this point will eject unburned hyMAR. 16, 1964 C&EN
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drogen and helium plus synthesized carbon and oxygen into interstellar space. Stars which remain stable will continue the synthesis process. The C 1 2 and O 1 6 ejected by stars which become unstable will mix with primordial interstellar matter and eventually condense into a second or later generation star. In this new, later generation star hydrogen can be converted into helium through what is called the CNO bicycle since it combines the original carbon-nitrogen cycle of Dr. Hans A. Bethe and Dr. Carl F. von Weizsàcker and a branch involving O 1 6 and O 1 7 . In modern nuclear notation the reactions are as follows: I
(p,y)Oi 5 (/? + v ) N i s ( p , a ) C i 2
J
or 13
>Ν"(ρ,γ)0 (^+,/)Ν Ι 5 (ρ, γ )0 1 6 (p,y)F"(i8+v)0«(p,a)N M .
Π
These reactions have been exten sively investigated experimentally, and cross sections for C 1 2 (p,y) and C 1 3 (ρ,γ) have been measured in several laboratories. Theory has been made to fit the observed data through the adjustment of four phenomenological
parameters—resonance energy, radius of interaction, and probabilities at resonance for both proton absorption and gamma ray emission. Effective thermal energies in hydro gen burning in stars correspond to 10 to 50 k.e.v. and fall below the lowest energies at which the reactions are detectable in the laboratory. Even at 100 k.e.v. the cross sections are only about 10~34 cm. 2 The excellent agree ment with theoretical expectations leads workers to expect some con fidence in the extrapolation of the data to stellar energies. This extrap olation is customarily done by divid ing the cross section by the main en ergy dependence of the Coulomb penetration factor to obtain the socalled cross section factors. The cross section factor can be accurately extrap olated to zero and can then be in tegrated over a weighting function consisting of the penetration factor and the Maxwell-Boltzmann distribution in thermal energies. If resonances occur below the lowest energies measured then the thermal cross sections and reaction rates would be considerably greater than given by the extrapolation of the laboratory data and still not be directly detectable in the laboratory. Fortu nately separate studies involving the
compound nuclei—Νl:i and N 14 in the cases under consideration—can be made to show that no sharp reso nances corresponding to excited states in these nuclei contribute to the cross section in the important but unobservable thermal region. Returning to the subject of helium burning, we can see that nuclear evi dence indicates that this process should only rarely proceed beyond oxygen. Thus C 12 , 0 1 G , or a mixture of both is the product of helium burning. Eventually the helium is exhausted, the core of carbon and oxygen con tracts and heats until the C1L> and O l e begin to burn. The result is the production of a number of inter mediate mass nuclei among which Ne 2 0 , Mg 24 , Si 28 , and S:'2 are the most abundant. This production, expected from the great nuclear stability of these nuclei with mass numbers of an integral multiple of four, is most simply expected on the model in which these nuclei consist of com plexes of the highly stable alpha par ticle. Indeed, these nuclei are the most abundant among the isotopes of the elements neon, magnesium, silicon, and sulfur. In a star which remains stable the evolutionary process continues. The Coulomb repulsions between nuclei
Carbon May Be Formed in Red Giant Stars by the Fusion of Three Helium-4 Nuclei The carDon can capture a Tourtn nenum nucleus to give oxygen-lb directly, bypassing mass 5 and mass 8
ο
ο οο ο 0 ο DENSITY = 100,000 grams per cubic centimeter TEMPERATURE = 130 million degrees K.
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Laboratory Measurements of the Cross-Sections of C13 (pf 7) and C12 (p,7) May Be Used in the Study of Stellar Reactions
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PROTON ENERGY FROM LABORATORY MEASUREMENTS (k.e.v.)
having nuclear charge numbers be tween 10 to 16 are very strong and burning no longer proceeds by the simple fusion of the interacting prod ucts. Instead, as the temperature rises, a number of the intermediate nuclei are photodisintegrated with the emission of alpha particles in the in tense high-energy flux of the end of the Planck distribution. For example, a Si 28 nucleus can be broken down into seven alpha particles at tempera tures near 3 billion degrees K. These alpha particles are captured by other nuclei which escape photodisintegration. Thus it is possible that another Si 28 nucleus could capture seven alpha particles to form Ni r,c . The over-all reaction is 2Si 28 -> Ni 5G . However, the detailed mechanism is not direct fusion, but the alpha-process in which build-up of one nucleus to double its mass and charge occurs upon the breakdown of another into alpha par ticles. Nir,° is radioactive and decays through Co 50 to Fe 5 6 by the successive capture of two electrons from the plasma continuum in a star and with the emission, in each capture, of a neutrino. Many other nuclei near Fe 50 , for example, from Ti 4 6 to Ni 62 , are probably produced in this way.
mum and their binding energies are at a maximum. Both heavier and lighter nuclei have higher internal en ergy content and are less stable in this sense than the iron-group nuclei. Very high temperatures and great densities will be reached in the pro duction of the iron-group elements. Under these conditions, the rates of all possible reactions will be very great, with the situation best described in terms of a nuclear equilibrium. Support for this concept may be found in the shape of the iron-group peak which has been found by Dr. Ε. Μ. Burbidge, Dr. G. R. Burbidge, Dr. Hoyle and me to be in good agree ment with the calculated equilibrium distribution at 3.8 billion degrees K., a density of 3 million grams per c c , and with a free-proton-to-neutron ration of 500 to 1. These temperatures and densities are consistent with con ditions leading to equilibrium; and knowledge of the free proton—free neu tron ratio is essential in determining the proton and neutron numbers in the nuclei produced at equilibrium.
From the standpoint of nuclear physics, it is clear that the sequence of successive burning of heavier and heavier nuclei through charged-particle reactions should terminate at the iron-group nuclei, which are the most stable nuclei in the sense that the absolute magnitude of their internal neutron-proton energies are at a mini
In such a determination it is nec essary to take two things into account: the experimentally known properties of the trround and low-lying excited states of the stable and /^-active nu clei involved in the equilibrium, and the β-decavs that come about during freezing of the mixture. The over all process is called the e-process and
Iron-Group Elements Are Through the e-Process
Synthesized
it is this process by which the irongroup elements are synthesized. Their overabundance relative to their neigh bors can be understood on the basis that enough stars remain stable long enough to develop an iron ball in their centers at the end of a long line of energy-generating, chargedparticle reactions. The α-process and the e-process probably occur at a rapidly evolving or even explosive stage of stellar evo lution. Possibly the collapsing core of a star in its terminal stages as a red giant or in its final catastrophic supernova stage may be a region for such processes. The collapse of the core is brought about because no further generation of nuclear energy occurs after the iron-group nuclei are produced. Gravitational contraction takes place unimpeded. The implo sion is actually speeded up in the inner regions of the core by the re frigerating action of nuclear processes which transfer some of the iron-group nuclei back into lighter nuclei (mostly He 4 and neutrons) and with the ab sorption of energy. The implosion of the core removes the underlying support of the envelope material of the star, which contains unevolved nuclear fuel capable of re leasing large amounts of energy on being raised to high temperatures. The gravitational collapse of the en velope material, however, does just this and energy is released. Energy release by the nuclear reactions in the envelope material further raises the envelope's temperature. The collapse is reversed by expansion of the mate rial, and all or part of the envelope material and probably even a portion of core material are blown out from the star at high velocity. The result is observed astronomically as the oc currence of a supernova in which a star is observed to flare up in a very short time to many times its previous luminosity and to eject a large frac tion of its mass into space. The time scale of the e-process has recently been extensively investigated from the standpoint of the large energy losses predicted from present beta de cay theory which suggests the annihi lation of electron-positron pairs ac cording to the reaction e+ + e~ -> ν + v> At the high temperature of the e-process many electron-positron pairs are produced from the effect of radiation on nuclei. Equilibrium is established when production and an nihilation are equal. The neutrino MAR.
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Iron-Group Elements Form Under Conditions of Very High Temperatures (3.8 billion degrees K.) and Very Great Densities (3 million grams per cc.) Such conditions occur as equilibrium processes in Type II supernovae and as end points in the successive burning of heavy nuclei by charged-particle reactions IRON CHROMIUM
-1
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NEUTRON-CAPTURE
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COPPER
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COPPER OBSERVED (SOLAR) CALCULATED
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emission competes with the reaction e + + e~ —» γ + γ in only about one case in 10 19 ; but gamma rays are trapped in the star, whereas neutrinos and antineutrinos escape directly at the speed of light. They escape with the kinetic energy and rest mass equiv alent energy of the pair and constitute a critical drain on the dwindling en ergy resources of the stellar interior. The evolutionary process is speeded up and the burning processes from O 1 0 to Nir,°, which would otherwise require 1000 years for completion, take place in approximately one day. The time available for the typical decay (Ni™ to Fer,(}) in the e-process is even shorter (in the range of 1000 to 10,000 seconds). From this consideration, the question arises: How does this short time interval affect the resultant equilibrium process abundances? The term equilibrium is applicable only in the sense that ordinary nuclear processes involving nucléons, nuclei, and gamma rays are proceeding very 100
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56 ATOMIC WEIGHT
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rapidly even relative to the short overall time set by the neutrino loss. On the other hand, the slow electron captures proceed in times equivalent to the loss time. Under conditions appropriate for a star having a mass equal to 30 solar masses, for example, the abundance of the isotopes of iron may be calculated as a function of the time available for electron capture. At zero time the α-process has al ready produced nuclei having an equal number of protons (Z) and neutrons (N) so that, on the average, inside these nuclei the ratio of protons to neutrons is one (Z 'N = 1). The ratio of free protons to free neutrons in the gas surrounding these nuclei turns out to be 400 million to one. The most abundant nucleus is Nir>(5, which con stitutes 89.17r of the material by mass. If the α-process material were imme diately ejected from the star at this juncture, the Nir>0 would eventually decay to Fe r, ° which would then have an abundance equal to 8 9 . 1 % of the
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r-process group. This is not observed to be the case. The expectations on the basis of im mediate ejection for Fe r ' 4 , Fe r,T , and Fe r,s also do not agree at all with the observed values for the sun. More over, complete equilibrium values do not agree with observations. These values are calculated for long times compared to characteristically short electron capture times and correspond to the free proton-free neutron ratio expected if all the beta decay proc esses—electron and positron capture and emission—reach equilibrium. Thus the time available for the decays is neither very short nor very long compared to the decay times. The best agreement of calculated values with observed values occurs where time values of approximately 30,000 seconds or about nine hours are used. This applies to a star with a mass equal to 30 solar masses. Exact correspondence of electron capture times and neutrino loss times occurs
for a star having a mass equal to 15 solar masses. Type II supernovae probably evolve at the terminal ex plosive stage of stars in the mass range 10 to 50 solar masses. The average e-process contribution from such stars, properly weighted for the greater num ber of stars in the lower end of the mass range, shows good correspond ence with the observations. Astrophysical Observations Support Theory of e-Process in Stars Thus the relative abundances of the iron isotopes (and of the other e-process isotopes) strongly indicate a presupernova time scale for the e-process of the order of 10,000 to 100,000 sec onds. This is just what is expected if the reaction, e + + e - _ ^ ^ - f - p , occurs at a rate calculated on the as sumption that the process is governed by the universal interaction rate found for such weak interactions as beta de cay and muon decay and capture. Un fortunately, the process has not yet been observed in the laboratory and the calculations are guided entirely by theory. Astrophysical evidence, how ever, strongly implies that the theory is correct or, alternatively, that some unknown process leads to an energy loss that is roughly equivalent (within a factor of 10 either way) to the en ergy loss expected from electron-posi tron pair annihilation accompanied by neutrino-antineutrino emission. The question is often asked: What becomes of the neutrinos and antineutrinos emitted by a star? The scientist may not know, but perhaps the poet does. Witness these lines by T. S. Eliot in "East Coker": "O dark dark dark. They all go into the dark, The vacant interstellar spaces, the vacant into the vacant," Beyond the iron group nuclei, neu tron capture processes have played the primary role in stars in the synthesis of the heavy elements. Because of re pulsive Coulomb forces, charged par ticle reactions have been rather inef fective at the temperatures (100 mil lion to 1 billion degrees K.) at which the main line of heavy element syn thesis has probably occurred. The small relative abundance (0.1 to 1%) of the lightest, charge-rich isotopes of the heavy elements attests to the in frequent operation of charged particle reactions in the synthesis of these ele ments. On the other hand, neutrons
interact rapidly with heavy nuclei at the low energies (where kT ~ 10 to 100 k.e.v.) corresponding to the tem peratures just cited. In fact, neutron reaction cross sections vary roughly in the relationship 1/v ~ 1/£1/2 (where t; is the neutron velocity and Ε the energy). Furthermore, at low energies the only reaction other than elastic scatter ing which can be rationalized on the basis of energetics in most cases is the capture of the neutron. This cap ture leads to an increase in atomic weight by one unit, a slow but sure mechanism for the synthesis of heavier and heavier nuclei. Eventually, of course, neutron-induced fission be comes possible in the very heaviest nuclei at low energies. This process, or alpha particle decay, or even spon taneous fission, depending on circum stances, terminates the synthesis. Dr. Gamow, Dr. Alpher, and Dr. Herman suggested neutron capture as the mechanism of synthesis of all the elements starting with neutron decay in an early, highly condensed, hightemperature stage of the expanding universe. The density was taken to be about 10 ~ 7 gram per cc. and the temperature to be about 10 billion de grees K. (kT ~ 1 m.e.v.). The measurements of the late Dr. Donald Hughes and his collaborators on the capture cross sections of nuclei for fission spectrum neutrons in the m.e.v. energy range indicated an inverse relationship between these cross sec tions (σ) and isotopic abundances ( N) such that Ν is about equal to 1/σ. This relationship is expected, in gen eral, from the point of view of syn thesis in a chain of successive neutron captures. Nuclei with small cross sec tions would likely build up to large abundances in the chain so that the number of captures per unit time would be uniform over contiguous sec tions of the chain. However, in re cent years it has become clear from nuclear and astrophysical evidence that charged particle reactions must have played a considerable role in the synthesis of the light elements. For example, the iron group abundance peak cannot be explained on the basis of neutron capture, since the iron group nuclei do not have anomalously low capture cross sections. Dr. Gamow's basic idea of neutron capture is incorporated in stellar syn thesis concepts, but the difficulties just mentioned are avoided by using the concept that charged particle reactions
during various stages of stellar evolu tion can lead to the synthesis of the elements up to and including the iron group. Neutron production and cap ture, then, serve in the intermediate and terminal stages of stellar evolution as the main line of element synthesis beyond iron. In fact, a small amount (slightly more than 0.1%) of the abundant iron group nuclei are prob ably used as seed nuclei at the start of the chain of captures. Mass spectroscopy data show that the chain is unbroken in atomic mass in this region. The abundance curve shows that two quite different and in dependent neutron capture processes have been necessary to synthesize the abundant isotopes of the heavy ele ments. In one of these processes, called the s-process (s equals slow), the neutron captures occur at a slow rate compared to the intervening beta decays. Thus, the synthesis path lies along the bottom of the valley of mass stability and in general bypasses both the proton-rich, lightest isotopes and the neutron-rich, heaviest isotopes of the elements involved. On the other hand, in the second neutron process, called the r-process ( r equals rapid ), the neutron captures occur at a rapid rate compared to beta decay. The captures lead rapidly from stable seed nuclei, predominantly Fer,fi, to the very neutron-rich side of the mass valley and are stopped only by the weakly bound neutrons photoejected by the ambient gamma-ray flux that is associated with the high temperature necessary for the produc tion of the neutrons. Equilibrium be tween (η,γ) and (γ,η) reactions is thus established and progress along the synthesis path occurs only through electron-antineutrino ejection or beta decay which permits further neutron capture. On termination of the synthesizing neutron flux the neutron-rich isobars at each atomic mass beta decay to the first stable isobar which then shields from r-process production those re maining isobars, if any, having fewer neutrons and more protons. The sprocess and the r-process account in these ways for the synthesis of all the relatively abundant isotopes of the heavy elements. An exposure of a small amount of s- and r-process ma terial to a hot proton flux or to an in tense photon flux results in the pro duction of the relatively rare, protonrich, lighter isotopes of the heavy ele ments. This infrequent mechanism is MAR. 16, 196 4 C&EN
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termed the p-process (p equals pro ton). It follows from the evidence for two different neutron capture processes which occur at quite different rates, that two separate and distinct stages of stellar evolution must occur.
Abundances of Tin Isotopes Make Case for Two-Stage Process in Stellar Evolution The low abundance (less than 1%) of the three lightest tin isotopes supports the contention for the rare occurrence of the p-process in stellar evolution ^^^^^^^^^^^^^^^S
^^^^^^^^^^^^^^^^β
!
' l ^ l ^ U M B E R Ê D ISOTOPE
• The s-process has been assigned to the red giant stage of stars which were formed from galactic material containing light elements, particularly He, C, O, Ne, Mg, and the intermedi ate iron group elements. These ele ments had been previously synthesized in other stars and ejected into the in terstellar medium, mostly primordial hydrogen, of the galaxy. The He, C, O, Ne, and Mg were required for the production of neutrons by a , n-reactions on C 1;i , O 17 , Ne 2 1 , Ne 2 2 , and Mg 2(i during the relatively slow helium burn ing in red giant stars, with lifetimes of 1 million to 100 million years. Pro fessor Greenstein was the first to sug gest a source of neutrons in stars—the exoergic C 1 3 ( α , η ) Ο 1 0 reaction. • The /-process probably takes place in the exploding envelopes or cores of supernova outbursts. In such out bursts energy-producing and neutronproducing processes occur in the short interval of the supernova explosion ( 1 to 100 seconds) and neutron captures accordingly occur at a rapid rate. To illustrate the general importance of these considerations in determining isotope abundances, we can consider the evidence for the operation of the three separate processes, p, s, and r, in the formation of the stable isotopes of the element tin. By following the s-process path we see that the first three isotopes, Sn 112 , Sn 114 , and Sn 115 , cannot be made in the s or the r proc ess. The low abundance of the three isotopes (1% or less) is consistent with their production only in the pprocess. Sn 110 is the first isotope which can be made in the .s-process and the dis continuity in abundance between Sn 115 and Sn 110 is quite marked. Similarly, Sn 120 is the last isotope which can be made in this process, and again, there is a discontinuity in going to Sn 122 and Sn 124 which can only by made in the r-process. The r-process appar ently produces somewhat less abund ances in this region of atomic weights than the .s-process. This difference is a result of the history of synthesis of the elements of the solar system, rather than of any fundamental nuclear properties of these isotopes. 102
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Rad. 114 115
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Rad. 122 Rad.
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MASS NUMBER
The rising abundances from Sn11G to Sn 120 are consistent with σΝ ~ con stant if we note that σ (η,γ), in gen eral, decreases as more neutrons are added; and that σ, for odd-numbered atomic mass isotopes, is higher than σ for even-numbered atomic mass iso topes because of the tendency of neu trons to pair up. These statements are confirmed by recent measurements at Oak Ridge of 30-k.e.v. neutron cap ture cross sections in separated tin iso topes. Observations on measured cross sec tions, compared with relative isotopic abundances for Sn 110 to Sn 124 , show that the product σΝ varies by a factor of 2.6 for the first five isotopes and then drops by more than 10 times for the other isotopes. This drop is ex plicable on the basis that Sn 122 and Sn 124 cannot be produced in the sprocess and that, consequently, their
σΝ should bear no particular relation ship to that of the others. The variation in σΝ for Sn 110 to Sn 120 is puzzling until it is noted that Sn 117 to Sn 1 - 0 can be produced in both the r-process and the «-process, whereas Sn11(J is produced only in the ό-process. Knowledge of the r-production for Sn 122 and Sn 124 makes it pos sible to estimate the r-production for Sn 117 to Sn 120 . Then by subtraction from the observed abundance it is pos sible to calculate the «-production which should be, at most, slowly vary ing over the range of atomic mass be tween 116 and 120; and indeed this is found to be the case. There should be little doubt that the abundances and cross sections of the tin isotopes reveal the nature of the processes by which they are syn thesized. Isotopes of tin from red gi ants and supernovae, once mixed to-
gether in the interstellar medium, have not thereafter been separated and come down to us as clues to stellar events in the distant past of the galaxy. In other stars and other galaxies the relative s-process abundances will probably be much the same as in our solar system; likewise for the relative r-process abundances. But the ratio of (Sn*22 + Sn 124 ) to (Sn1™ + Sn 117 + S n l l s + Sn 110 + Sn 1 - 0 ) may show conspicuous variations relating to the past stellar history of the material involved. The question often arises: Is there evidence that the s-process is occurring in present-day stars or that it has occurred recently? The most convincing answer occurs in the spectroscopic evidence for the existence of technetium in certain stars. Technetium has no stable isotopes and does not occur naturally on earth; but one of its isotopes, Tc 0 0 , is produced in the .s-process chain and has a half-life of 200,000 years. If Tc 0i) had not been produced in the star and mixed to the surface in the last several hundred thousand years it would have decayed to R u " and no technetium line would be observable. Tc 9 7 and TciKS have somewhat longer lifetimes but cannot be produced in the s-process. It is worthy of note that promethium, which has no long-lived isotopes, has not been observed in stars.
It is possible to extend the /-production calculations into the transuranic region and to calculate the abundance of Th2:>>2, U2;{;", and U 2 a s produced in each r-process event. These nuclei are singled out here because they are the parents of a naturally radioactive series having decay lifetimes equivalent to astronomical times. This property of long half-life has been used to determine the age of the meteorites (about 4.6 billion years) and of terrestrial rocks (about 3 billion years). It is also possible to use these chronometers to measure the duration of stellar synthesis in the galaxy once the production abundances of these nuclei are calculated. An important point to remember is that numerous short-lived progenitors of these nuclei are produced in r-process events. Thus, for example, all the material produced at atomic masses of 235, 239, 243, 247, 251, and 255 contributes to the U- îîn abundance, since the nuclei at these atomic masses decay relatively rapidly by alpha particle and beta particle emission to U 2;;r '. At atomic mass of 259 and greater, the ultimate fate of the nuclei is spontaneous fission rather than alpha decay and no contribution is made to the abundance of U2:>,r\ Contributions to U2;>"" thus come from six progenitors. The situation is somewhat more complex for U2:!N and Th2:>·2, but the
The Bulk of the Tin Isotopes Are Made by the s-Process
corresponding numbers are 3.1 progenitors for U2:liS and 5.75 progenitors for Th 2:i2 . Thus, on the basis of number of progenitors alone, the production rate for U-,:J,r' is 1.93 times that for U 2:iS ; and the production rate for Th- 3 2 is 1.85 times that for U 2::8 . Detailed calculations yield 1.65 ± 0.15 to 1 for each of these progenitor ratios, but the exact agreement is accidental. The observed ratios in meteorites are Th 2:{2 /U- Sij = 3.8 and UL'SÔ/U-SS
121
The differential
123
s-PROCESS ONLY
P-PR0CESS
51
0.0072.
both p- and r-process nuclei. The r-process nuclei are the end products of an isobaric β-decay of neutron-rich progenitors made in an intense neutron flux
Neutron number slowly increases by one until negative beta activity occurs and the path moves to a higher proton isobar. The path bypasses
Sb
=
mean lifetimes are 9.63 billion years for the Th 2 3 2 vs. U23« and 1.22 billion years for U 2 3 5 vs. U 23S . The abundance ratios, extended back in time to the origin of the solar system, are simply straight lines on a logarithmic abundance scale. For a single sudden synthesis event at some time in the remote past the extensions to that time are also straight lines back to the relative production ratio 1.65 (±0.15) to 1. However, the dates so determined are discordant by about 2 billion years. Concordant results are obtained from the Th 2 3 , 2 /U 2 3 8 and the U 23r '/ U 23,s ratios on the basis of continuous synthesis in the galaxy beginning some 12 billion years ago. This is a lower limit for the age of the galaxy since it may be necessary to add an interval of 3 billion years for the time for stars to evolve to supernovae in which the r-process occurs.
57
112
114
115
1.02
0.69
0.38
116
117
118
119
120
7.6
24.1
8.5
32.5
43
124
122
Sn 50
113
14.3
6.1
4.8
115
s-PR0CESS PATH
in 49
4.2 7
110
ι
111
112
113
-PROCESS ONLY
-PROCESS
95.8
114
116
Cd' 48
12.4 "*ïV "" 62
12.8 ! """63
24.0 .
12.3
64
65
ISOTOPE
7.6
. 28.8
66
67
68
69
70
71
72
73
74
NEUTRONS
ISOTOPE ABUNDANCE (Percent) MAR.
16, 1 9 6 4 C & E N
103
The r-process may also have oc curred in violent explosions of massive condensations which occurred at the time of the formation of the galaxy. In spite of this and other uncertainties, the abundances of Th 2 3 2 , U 235 , and U 2 3 8 found on the earth point to an age of the galaxy somewhere between 10 to 15 billion years. One should not overlook the com ment of Samuel Pepys when the date of Genesis, calculated from references in scripture, came under question by the geologists of his time. Said Pepys: "To the Rhenish wine house, and there came Jonas Moore, the mathe matician, to us . . . and spoke very many things not so much to prove the Scripture false, as that the time therein is not well computed or un derstood" [Diary of Samuel Pepys, 23 May, 1661.] In conclusion, it is necessary to men tion a new development in astrophys ics which almost certainly has impor tant ramifications in regard to the con cept of nucleosynthesis in the galaxy. Large radio sources associated with certain galaxies are found to radiate at rates approaching 10 44 ergs per sec ond, some 100 billion times the optical luminosity of the Milky Way. If this radiation is caused by the synchrotron mechanism, the energy stored in the
Selected References for Additional Reading 1. Aller, Lawrence, "Nuclear Transfor mations, Stellar Interiors, and Nebulae," New York, N.Y., The Ronald Press Co., 1954. 2. Fowler, William, "Modern Physics for the Engineer," Series I, Chapter 6, "Nuclear Structure and Trans mutation," New York, N.Y., Mc Graw-Hill Book Co., Inc., 1954. 3. Fowler, William, "Modern Physics for the Engineer," Series II, Chap ter 9, "The Origin of Nuclear Species by Means of Nuclear Re actions in Stars," New York, N.Y., McGraw-Hill Book Co., Inc., 1961. 4. Gamow, George, "Matter, Earth and Sky," Englewood Cliffs, N.J., Prentice Hall, Inc., 1958. 5. Greenstein, Jesse, "Modern Physics for the Engineer," Series I, Chap ter 10, "Astrophysics," New York, N.Y., McGraw-Hill Book Co., Inc., 1954. 104
C&EN
MAR. 16, 196 4
magnetic field and the high-energy electrons circulating in the field lie between 10°° to 10 02 ergs, correspond ing to the rest mass energy of 1 million to 100 million solar rest masses. Dr. Hoyle and I have suggested that this energy was made available at the expense of gravitational energy dur ing rapid collapse of objects with masses somewhat greater than the range just indicated. The red shift in the optical emission by radio stars places them at great distances from the galaxy and implies total optical lumi nosities up to 104\
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