ABUNDANCE OF THE ELEMENTS

G. Suess and H. Urey*)

In 1889 F. W. Clarke read before the Washington Philosophical Society a paper in which he outlined a program of research that constitutes the subject matter of the present article. Clarke’s paper,^17 entitled “The Relative Abundance of the Chemical Elements,” was the first among many works by various authors. The paper stated that “in the course of the present investigation an attempt was made to represent the relative abundance of the elements by a curve having, as one coordinate, the atomic weight of the elements. It was expected that some periodicity would be discovered; however, no regularity of this kind appeared.”

During the following fifty years Clarke, with his co-worker Washington, continued along the same line of research. Their classic work is still regarded as one of the most valuable sources of geochemical data. Since then many have tried to find an explanation for the distribution of the abundances of the elements, or at least to find empirical rules determining the basic properties of this distribution. Many suggestions have been made on this subject; most of them were so speculative in character that they could not exert any substantial influence on subsequent development. However, one observation, based on the studies of Clarke and Washington—namely the rule formulated by Harkins, asserting that all elements with even atomic numbers are more abundant in nature than elements with odd numbers—proved to be extremely important in many fields of science.

Clarke and Washington in their investigation at first proceeded from the composition of the earth’s crust. In the course of time it became more and more evident that meteorites are better objects for the study of the mean abundance of the chemical elements in nature than terrestrial minerals. These studies culminated in Goldschmidt’s classic work,^31 which is the basis of all later investigations in this field.

When Clarke in 1889 was looking for periodicity in the relative abundance of the elements, he hoped to find some relation between abundance and the periodic table of the elements. Refinement of the data on the abundance of the elements, the discovery of isotopes, and the determination of the isotopic composition of the elements made it possible, more than 40 years ago, to discover certain types of periodicity; it turned out, however, that these periods obeyed laws different from the laws governing the structure of atoms and had nothing in common with the periodic table. It seemed that the abundance of the elements and their isotopes reflects nuclear properties, and that the matter surrounding us resembles the ash of a cosmic nuclear conflagration in which it was created.

*) Reviews of Modern Physics 28, 53 (1956). Translated by S. A. Kamenetsky.

In 1948 one of the authors of the present article (Suess) attempted to prove this. He showed that between the isotopic composition of an element and its cosmic abundance there exists an empirical and quantitative correlation, which cannot be explained otherwise than by assuming a correlation of some kind between nuclear properties and the distribution of nuclear abundances. Since then considerable progress has been achieved in geochemistry and cosmochemistry, as well as in knowledge of the structure of the nucleus, so that it has become necessary to reconsider and expand the earlier work.

A suitable basis for understanding the empirical and semi-empirical features of the abundance distribution of the various kinds of nuclei in the universe would be a complete theory of the formation of the elements. Such theories have been proposed by various investigators. Attempts have been made to find a suitable cosmogonic model which would lead, in a reasonable way, to an understanding of the formation of nuclei of different kinds in the same ratios in which they occur in nature. These attempts have been crowned with success in the sense that they have made it possible to understand qualitatively the existence of heavy nuclei and their relative quantities. However, none of these theories can explain either the details of the abundance distribution or the quantitative features of the general picture of nuclear abundances.

Independently of any theory of the origin of the universe, one may try to find indications of the nature of the last nuclear reaction that occurred immediately before the final establishment of the abundance distribution observed at the present time. Going back into the past, one may try to determine how the conditions under which these reactions took place developed. As a final step, one may finally construct a cosmogonic model of the course of events. In the present article no such attempt is made. We do, however, call attention to certain data that could serve as a basis for investigations in this direction, and we present certain considerations that may prove useful for further development.

LAWS OF THE RELATIVE ABUNDANCE OF NUCLIDES

All kinds of stable nuclei occur in nature. However, their relative abundance exhibits variations by a factor of the order of \(10^{15}\). Harkins\(^{35}\) was the first to attempt a systematic classification of the stable kinds of nuclei, or nuclides, based on the atomic numbers as corresponding designations of the elements, and on isotopes as limiting constituents of these elements; Harkins’ rules reflect important regularities in the abundance of nuclides. Mattauch introduced additional rules. At the present time these rules can be understood in the light of nuclear binding energies, in particular from the point of view of the shell model of the nucleus, as was established by Mayer\(^{50,51}\) and by Haxel, Jensen, and Suess\(^{36}\).

In Suess’ earlier work\(^{84}\) the following rules for the abundance of stable nuclides were indicated:

1) Nuclides with odd mass numbers: the abundance of nuclei with odd mass numbers \(A > \sim 50\) changes monotonically with mass number. In the presence of isobars, the sum of the abundances of the isobars should be taken instead of the abundance of individual nuclei.

2) Nuclides with even mass number: a) in the region of heavy elements with \(A > 90\), the sums of the abundances of isobars with even mass numbers change monotonically with mass number; b) in the region \(A < 90\), the abundance of nuclei with equal numbers of excess neutrons changes monotonically with mass number.

3) In the region of light elements with \(A < 70\), for a given mass number, isobars with a larger neutron excess are less abundant. In the region

for heavy elements with \(A > 70\), the isobars with the smallest excess of neutrons are the least abundant.

4) Exceptions to these rules occur for those mass numbers for which the numbers of neutrons have definite values—the so-called “magic numbers.”

The empirical side of the question is due above all to the extensive and painstaking work of Goldschmidt and his collaborators. Goldschmidt’s classic work \(^{31}\) still remains the most valuable source of information, and those who studied this subject later rely mainly on his opinion concerning the relative abundances of the elements. The book published posthumously \(^{30}\) made this work more accessible. Ida and Walter Noddack \(^{53,59,60}\) introduced additional data, critically examined by Goldschmidt. When using abundances obtained from meteoritic data, there always arises the problem of a proper average for elements occurring in meteorites of the silicate phase, the troilite phase (\(\mathrm{FeS}\)), and the metallic phase. Goldschmidt adopted the following relative weight of these phases: 10 (silicate) : 1 (sulfide) : 2 (metallic). Noddack \(^{60}\) and Urey \(^{92}\) used chondritic stony meteorites as the corresponding average, since these meteorites quite obviously constitute a heterogeneous mixture of substances from different sources and, consequently, may themselves represent a suitable mixture. Brown \(^{11}\) used a considerably larger proportion of iron, and the abundances obtained by him differ from others, as a rule, by higher values for siderophile elements. Urey and Craig \(^{98}\) found two outstanding groups of chondritic meteorites, which essentially represent the two Prior groups \(^{66,67}\), obtained by means of other criteria. Using the newest methods of analysis, Wiik \(^{101}\) analyzed a certain number of meteorites and confirmed the existence of these two groups. These two groups differ in the relative amounts of the metallic and silicate phases. Although we shall use these observed atomic abundances, we must acknowledge that there are no fully reliable samples of cosmic matter available to us.

The fact that the cosmic abundances of the elements obey noticeable regularities had already been evident for a number of years. The rare earths have very similar chemical properties, so that the separation of the rare-earth elements approaches in difficulty the separation of isotopes. In these elements a noticeable regularity of abundances is found; namely, a regular alternation of the abundances of even and odd elements is observed; the abundance of successive odd and even elements changes gradually and regularly. One of the authors of the present paper (Suess) realized that this means that the abundance of isotopes must similarly reveal a certain regularity and that the abundance of elements must be such that all nuclides must change in some regular way. Accordingly, in the present work it is assumed that the relative abundance of all kinds of isotopes has a definite meaning and is not simply the result of “random” variations. It turned out that this assumption is justified in almost all cases, and we, of course, believe that it is valid in all cases, although we admit quite frankly that we do not always find this to be so. We do not claim a complete explanation of the regularities and deviations from the regularities that we describe. It is quite possible, for example, that the abundance of nuclides with odd mass numbers is expressed approximately by a curve above and below which individual nuclides lie without any definite regularity. We believe that in most cases this is not so, and that the abundance of isotopes of elements

determines the slope of such curves surprisingly well, especially the slope of the curve for odd mass numbers. The logarithms of the abundances of elements with even and odd masses, when properly interpreted, are also expressed by curves shifted relative to one another over most of the mass interval by an almost constant amount.

Below, various elements are considered in connection with the values of their abundances, and adopted abundance values are given that are consistent with the rules set out above. This discussion is essentially based on Goldschmidt’s empirical data, taking into account data that have appeared since then in the literature. As a rule, Urey’s most recent table of abundances is used, in which analyses of chondrites are taken preferentially over other average data.

EMPIRICAL ABUNDANCE DATA

One might have expected that the atmosphere of the Sun contains all elements in the initial relative amounts; it is true that nuclear reactions could have altered this abundance, and, in addition, mixing of the surface and inner layers could have occurred. This actually happened in the case of H and He, owing to the slow conversion of hydrogen into helium, and in the cases of deuterium and lithium, which at the temperature of the Sun’s interior should be converted into helium. De Jager reported the presence of deuterium in the solar atmosphere[^19], but in the present case the identification is doubtful, since it was based only on the Dα line. Greenstein and Richardson[^24] found that the abundance of lithium on the Sun, although very small, is not zero. The presence of deuterium would indicate that there is no convection in the outer layers of the Sun, but observations of lithium lead to the opposite conclusion. It is difficult to obtain exact and reliable values for the abundances of all elements on the Sun, since the intensities of spectral lines are very closely connected with the temperatures in the different layers of the solar atmosphere and, in addition, spectral lines are broadened for a number of reasons—for example, owing to the Doppler effect, collisions, turbulence; finally, natural damping plays a role. The abundances of elements in many stars are very close to their values for the Sun, although substantial differences are also observed. Similarly, the abundances in planetary nebulae are very close to their values for stars. Although for the most part we are in fact discussing values for the Sun, we assume that all the sources are sufficiently reliable that the numerical values can be compared. However, caution must be observed, since substantial differences in composition are observed in stars of different types.

It is obvious that the ratio of elements in the Earth’s crust has undergone various changes. In the course of its formation, the Earth lost a large part of the most volatile elements—hydrogen, noble gases, carbon in the form of CH₄, nitrogen in the form of NH₃ or N₂, oxygen in the form of H₂O; probably some amount of sulfur in the form of H₂S also volatilized, as did halogens in carbon compounds and some amount of other elements, although such losses are not obvious[^96]. There also occurred a marked differentiation of surface regions as a result of partial processes of melting and crystallization and the loss of siderophile and chalcophile elements that went deep inward. Erosion under the action of water led to further differentiation of the surface regions. It is extremely difficult to give any reliable estimate of the average composition of the Earth’s surface; however, there are some data suitable for use in the present work.

It is usually assumed that meteoritic matter, since the time of its formation from solar matter, has undergone less chemical fractionation than any terrestrial matter found on the Earth’s surface—

ness. Fractionation of the kind that can be recognized in meteorites can be divided into three principal phases—metallic, sulfide, and silicate. Accordingly, Goldschmidt divided all chemical elements into three groups—siderophile, chalcophile, and lithophile elements—depending on the meteoritic phase in which the elements occur in the greatest quantity. However, this classification is not always definite, since many elements are distributed between two or three phases in different proportions. In his classification Goldschmidt assumed that all elements were distributed among these three phases in equilibrium relations: if equilibrium had been established, then in all samples of these phases the relative amounts of these elements would have been constant, and this is certainly not true. Craig ^18 offered certain considerations in support of the view that at high temperatures the sulfide phase would have had to dissolve completely in the silicate and iron phases, if they had been completely molten. In that case the elements would have been distributed between these two phases. Owing to the difference in densities, they would have separated even in weak gravitational fields. Subsequent cooling would have led to the separation of the sulfide phase from each of the others, and equilibrium between the sulfide phases in the silicate and metallic fractions could no longer have been established. With falling temperature, inclusions of troilite would have separated from the iron phase, and these inclusions would have collected the elements dissolved in the iron phase in quantities quite different from those that accumulate in the iron sulfide separated from silicate phases. Most investigators studied the iron sulfide from iron meteorites and assumed that the concentrations of elements in the iron sulfide enclosed in silicates were the same. There is no basis for considering such an assumption valid. In fact, it is probably possible to neglect, in determining average values, the amounts of elements in the troilite inclusions of iron meteorites, since they constitute a very small fraction of iron meteorites and, consequently, of the total meteoritic matter.

Table I

Assumptions about the average composition of meteoritic matter made by various authors

Another difficulty arises in calculating the “average” composition of meteorites because of ignorance of the relative amounts of the three principal meteoritic phases. Meteorites that reach the Earth’s surface cannot serve as a basis for estimating these relative amounts, since iron meteorites are better preserved during their fall and on the Earth’s surface than stony meteorites and pallasites. The assumptions made by various investigators are given in Table I.

The values given by G. Brown and Noddack[^58] are obtained from the ratio of the weights of the Earth’s core and mantle under the assumption that the average composition of the Earth reflects the average solar nonvolatile matter. The new value obtained by Rabe[^69] for the mass of Mercury gives a density for Mercury of about 5, and this indicates that Mercury contains a larger relative amount of metallic iron than the Earth. Urey[^91,^94] notes that planets in general have different densities, and gives an estimate of the relative amounts of the metallic phase. He comes to the conclusion that in the process of planet formation there must have been some fractionation, which separated metal from silicate in such a way that silicate was preferentially lost. Consequently, the ratio of the weights of the Earth’s core and mantle cannot serve as a basis for estimating the corresponding cosmic ratios. Urey, proceeding from thermodynamic considerations connected with the chemical processes that led to the formation of the terrestrial planets, came to the conclusion that the Moon and chondrites would give a better representation of the average composition of the nonvolatile part of solar matter. Urey’s value for iron is still smaller than Goldschmidt’s value, and is in better agreement with the solar abundance as determined from the most recent data on oscillator strengths for iron, obtained by Kopfermann and Wessel[^45], who used a new precise method and obtained a new value amounting to \(1/3\) of that previously accepted. Edwards, Johnston, and Ditmars[^23] confirm their lower values for the vapor pressure of iron. Urey derived his values for the ratios of the three phases from the composition of chondrites according to Prior’s data[^68]. The new ratio of silicate to metal in meteorites requires a revision of all abundance values. The empirical data are given in Table II.

Limits of Error

Goldberg and Brown[^28] showed that rhenium is approximately 130 times more abundant, and lead at least 50 times less abundant, than had been supposed earlier. This compelled doubt as to the value of the data published for the cosmic abundance of smaller constituent parts of the less abundant elements. Before Brown’s investigations, the values for rhenium and lead were based entirely on Noddack’s work. Comparison of their work with other data shows that in general the data collected by these authors cannot be accepted uncritically. In many cases there are no other data, and Goldschmidt used Noddack’s values, taking into account, however, possible sources of error in their determinations.

As we shall see below in a detailed consideration of the individual elements, all the available data are not free from serious errors. Data published during the last twenty years and especially after the war are apparently, in general, considerably more reliable than those published earlier. Some data even from such a serious investigator as Goldschmidt have proved to be very erroneous; for example, in the case of tin and lead. As a rule, the quantities reported for rare elements, especially in the range of parts per million, decreased with time. Therefore, in selecting data we have tried to take, preferentially, the lower values. In some cases we selected values that knowingly fall outside the limits of the published analytical values. We assume that some published analytical data suffer from errors exceeding 1000%, for example, the data for tungsten. Only further analytical work can determine whether we are right in our, in some cases rather arbitrary, choice. It is difficult to estimate the accuracy of the astrophysical data. Probably, for the most part, possible errors reach 150%; in particular, in the case of rare elements the data may be still more erroneous.

Table II

Atomic abundances of the elements*)
Silicon = \(1\times 10^6\)

Continuation of Table II

DISTRIBUTION OF THE ELEMENTS

Continuation of Table II

*) The Goldschmidt values given in this table were somewhat modified by Suess and Urey in accordance with data that are now five years old. Urey’s values are empirical data for chondritic meteorites, modified in accordance with the new analytical data considered in this paper. Most of the data have been changed.

The values for the rare earths, for the reasons given in the text, differ from those adopted by us.

DISCUSSION OF THE DISTRIBUTION OF THE ELEMENTS

All atomic abundances are given relative to the abundance of silicon, taken as \(10^6\). Goldschmidt used the value \(\mathrm{Si} = 100\), while Brown took \(\mathrm{Si} = 10\,000\).

We use the value \(\mathrm{Si} = 10^6\) in order to obtain, for the rare elements, values that can be written without using an enormous number of zeros after the decimal point. In the figure (insert) the dependences of the logarithms of the abundances \((H)\) on mass numbers are presented, and in Table III the values selected by us are given.

For many years astronomers have studied the ratio of the cosmic abundance of hydrogen and helium. Unsöld, in his classical work on the atmosphere of \(\tau\) Scorpii, found that this ratio is equal to 7.2; other investigators who performed calculations by Unsöld’s method obtained values close to this [a review of the data is given in Aller’s work\(^3\)]. Unsöld\(^ {99}\) adopted a single value for the electron pressure throughout the whole thickness of the star’s atmosphere. Recently Underhill\(^ {89}\) used a model atmosphere with varying temperature and pressure for a star of type O–9.5 and obtained for the indicated ratio a larger value—20 to 25. Neven and de Jager\(^ {56}\) constructed model atmospheres for four stars of type B: \(\tau\) Scorpii, \(\delta\) Centauri, \(\gamma\) Pegasi, and \(\iota\) Herculis, using the hydrogen spectra of these stars, and obtained for this ratio a mean value of 17.7, with considerable variations of the values for different stars. Aller believes that this ratio depends strongly on the exact model of the stellar

Table III

Continuation of Table III

Continuation of Table III

ABUNDANCE OF THE ELEMENTS

Continuation of Table III

Continuation of Table III

Continuation of Table III

Continuation of Table III

atmosphere. Traving\(^{88}\) carried out a calculation, starting from an atmospheric model for \(\tau\) Scorpii, and found for this ratio the value 5.9. In a private communication, Aller expressed the opinion that the best value would be 10, while Unsöld believes that the correct value of this ratio is 6 or 7 and that unpublished data on solar prominences confirm this value for the Sun. We adopt for the hydrogen-to-helium ratio the value 13, although it is quite possible that the true value deviates greatly from this.

For the ratio of hydrogen to the metals we adopt the geometric mean of the values of Claas\(^{16}\) and Unsöld\(^{90}\), with the correction made by Claas, normalized to the mean of magnesium and silicon. This gives 10.60 for \(\log H_H\). The abundance of deuterium, in comparison with protium in meteorites, turned out, according to Boato\(^{9}\) and Edwards\(^{20,22}\), to be approximately the same as on the Earth. De Jager\(^{19}\) reports that the abundance of deuterium in the atmosphere of the Sun is approximately the same as in terrestrial hydrogen, although this conclusion is based only on the intensity of the \(D_\alpha\) line. We adopt as the ratio \(H/D\) the value 7000, which somewhat exceeds the terrestrial ratio, equal to 6500. The abundance of the isotope \(\mathrm{He}^3\) in the initial solar matter is unknown.

Lithium, beryllium, boron

The abundance of these three elements is apparently \(10^5\) times smaller than that of the next group of elements by mass in the universe—carbon, oxygen, and nitrogen. According to Greenstein and Richardson \(^{34}\), lithium on the Sun is apparently still about 100 times less abundant. The low abundance of these three elements is readily explained by their instability at high stellar temperatures and by the possibility of thermonuclear reactions of these elements with protons. Such reactions could have occurred toward the end of the processes in which these elements were formed.

Goldschmidt \(^{31}\) summarized analyses of erupted rocks and meteorites for these elements. He arrives at the following data for the atomic ratios of Li and Be in the lithosphere and in silicate meteorites to Si, taken as \(10^6\) (see table). We have adopted these data for meteorites. Goldschmidt estimates the atomic abundance of boron as 21. Estimating the abundance of boron on the Earth’s surface is complicated by its considerable content in sediments and ocean waters.

Carbon, nitrogen, oxygen, neon

Our information on the abundance of these elements is based entirely on spectroanalytical astronomical observations of stars (apart from the Sun) and planetary nebulae, since very high temperatures or short-wavelength light are required to excite these elements to high energy levels of neutral atoms or to ionize them. Bowen \(^{10}\) studied one oxygen line on the Sun and obtained an abundance several times higher than the higher estimates for carbon and nitrogen, namely \(7 \times 10^{20}\) atoms cm\(^{-2}\), as compared with \(0.3\) and \(1.0 \times 10^{20}\) atoms cm\(^{-2}\) for carbon and nitrogen, respectively. Minnaert \(^{54}\) summarized the results of Unsöld \(^{90}\), Claas \(^{16}\), and Gnaerter \(^{44}\) for the Sun, while Aller \(^{3}\) summarized these data for the stars. We adopt Aller’s estimates for the data on C, N, and O, normalized to the value for hydrogen \(\log H = 10.60\). The data thus obtained do not differ greatly from the values given by other authors.

Aller \(^{3}\) comes to the conclusion that oxygen and neon are approximately equally abundant in stars and planetary nebulae. Aller \(^{4}\) gives the value 0.28 for the ratio of neon to oxygen in the planetary nebula NC, C 7027. Traving \(^{88}\) estimates the abundance of neon as 0.4 of the abundance of oxygen. If oxygen and neon are almost equally abundant, then the logarithms of the abundances of \(\mathrm{Ne}^{20}\), \(\mathrm{Ne}^{22}\), \(\mathrm{Mg}^{24}\), and \(\mathrm{Mg}^{26}\) lie almost on one and the same straight line. If neon is significantly less abundant than oxygen, this can be attributed to a decrease in abundance at neutron number 8 in oxygen \(\mathrm{O}^{16}\). We adopt the abundance of neon as 0.4 of the abundance of oxygen.

Fluorine

Astronomical values for fluorine have always been highly unreliable, and here one should rely on terrestrial and meteoritic data. The only value for the abundance of fluorine in meteorites, namely \(30 \cdot 10^{-6}\), was given by Noddack \(^{60}\). A recent detailed study of the terrestrial distribution \(^{46}\) yielded \(100 \cdot 10^{-6}\) for pyroxenes and peridotites, with increasing values for more acidic rocks, and an average for the lithosphere of \(700 \cdot 10^{-6}\). These data do not represent an extreme discrepancy in comparison with some

other elements. We take the abundance of fluorine as \(200\cdot 10^{-6}\) relative to silicon, for which the value \(0.185\) by weight in primary solar nonvolatile matter has been adopted; thus, for the atomic abundance of fluorine we take the value 1600.

Elements from sodium to iron

For the elements from sodium to iron there are many, apparently well-founded analyses both for the terrestrial surface and for meteorites. Goldschmidt\(^{31}\), and also Brown and Patterson\(^{12}\), reviewed the earlier analyses; but the most complete and modern review of the earlier analyses belongs to Urey and Craig\(^{98}\). The latter selected 94 of the best analyses of chondrites from the 350 available and gave special justification for such a selection. The abundance obtained in this way differs only slightly from those adopted in Goldschmidt’s table. Urey and Craig showed that there exist two fairly well-defined groups of chondrites with different total amounts of iron, so that the atomic ratios of iron to silicon in these two groups are on average, respectively, 6084 and 8494, if the value 10,000 is adopted for silicon. They found that the amounts of cobalt and nickel in these two groups differ even more than the amounts of iron. They considered the smaller value for the abundance of iron to be more probable, on the grounds that the fractionation\(^{91}\) that occurred in the planets probably, as a rule, took place by loss of the silicate phase, and not of the metallic phase, as Urey had earlier supposed. Wiik\(^{101}\) verified the existence of these two groups and found a somewhat smaller amount of iron in the group with a small amount of iron; he also checked the abundance of nickel. We take the rounded value \(6\times 10^{5}\) for the abundance of iron and the values of Urey and Craig for nickel and cobalt. This small abundance of iron is in very good agreement with the newest astronomical data.

The theoretical values for potassium given in earlier analyses are certainly too large, as was shown in \(^{2}\), where \(0.09\%\) was obtained as the analytical value for potassium in chondritic meteorites. Edwards and Urey\(^{22}\), introducing further improvements into the methods of analysis, showed that the contents of potassium and sodium in chondrites are remarkably constant. We adopt for the abundance of potassium the value \(820\cdot 10^{-6}\) relative to silicon, for which the value \(18.5\%\) by weight in primary nonvolatile solar matter has been adopted, representing the average from analyses of many chondrites carried out by Edwards\(^{21}\). We did not adopt a smaller value for the abundance of this element, as Urey\(^{97}\) had suggested, since the preliminary results of a new calculation of solar abundances, made by Goldberg and Aller, did not confirm Urey’s theoretical value. This gives 3160 for the atomic abundance of potassium\(*\).

* Urey assumes that the concentration of the radioactive elements—potassium, uranium, and thorium—in meteorites increased by a factor of 3–4, while the abundance of other elements, concentrated in appreciable quantities on the terrestrial surface, was the same in meteorites. We discussed many times the advisability of adopting such a point of view. In general, postulates of this kind should be tested by time before further work is based on them. After consulting with Prof. Goldberg and Prof. Aller, we at first concluded that the small value for potassium proposed by Urey would probably be confirmed by their studies of solar abundances. As has now turned out, this is not the case.

We constructed abundance curves for the elements for both assumptions. If the larger meteoritic abundances are adopted, as is proposed in the present work, then smooth curves are obtained when larger values are used for chlorine and sulfur, and, consequently, also for bromine and selenium; the observed values for rubidium and strontium in meteorites lie on this curve. This makes it possible to adopt higher values for krypton and, consequently, for xenon, and this in turn

We adopt the abundances of Na, Mg, Al, and Si from Urey’s most recent work[^101] on meteorites, since in it the analyses for these elements were carried out by the most advanced modern means. The values obtained differ little from those of other investigators, except for Al, for which a somewhat larger value was obtained. Urey found that precipitated iron contains a certain amount of aluminum, and the correction for this error somewhat increased the value for aluminum.

Phosphorus, sulfur, and chlorine

The astronomical data for these elements are always higher than the data obtained from analyses of meteorites. The analytical data for phosphorus give very different values, even in the case of Urey’s latest data[^101]. Therefore we have chosen the approximate astronomical value \(10^4\). Urey’s analytical data give a meteoritic value of approximately 4000. It is possible that phosphorus entered into carbon compounds during the formation of meteorites[^95].

The silicon–sulfur ratio is an important datum, because sulfur exists as a separate phase in the form of iron sulfide, and many elements dissolve in this phase. Goldschmidt’s estimates for sulfur are much lower than the astronomical values; however, the astronomical values are based on data that are very difficult to interpret. Urey gives a smaller value than Goldschmidt. Such values probably contain an error in the direction of being too low, since iron sulfide at moderate temperatures, i.e., at the melting point of iron and below, should have been reduced by hydrogen; therefore sulfur was probably partly lost during the formation of meteorites in the form of hydrogen sulfide. Since sulfur is present in the carbon compounds of carbonaceous chondritic meteorites, as was shown by Mueller[^52], this element may have disappeared in such compounds in the process of formation of the solar system. We adopted a value intermediate between the astronomical and meteoritic ones, namely \(3.75 \times 10^5\). If for sulfur one adopted such a small value as is obtained from analyses of meteorites, it would be very difficult to select for selenium a satisfactory value in comparison with other elements located near it in the periodic system, and at the same time not to deviate pointlessly from the observed sulfur–selenium ratio. Our choice was strongly influenced by the high astronomical values.

The abundance of chlorine has recently been subjected to a detailed investigation by Bence[^8] and Salpeter[^75]. The first of them studied many terrestrial igneous and sedimentary rocks and several meteorites, while the second analyzed a considerable number of meteorites. The two sets of values generally disagree. Bence obtained \(100 \cdot 10^{-6}\) in two chondrites, while the mean of Salpeter’s chondritic values is \(840 \cdot 10^{-6}\). Seligman[^8] gives for one chondrite a value of \(100 \cdot 10^{-6}\). Urey[^92] used Noddack’s value, namely \(470 \cdot 10^{-6}\). Some iron meteorites contain small amounts of chondrites. Mueller[^52] showed that the organic compounds of carbonaceous chondrites contain appreciable amounts of chlorine, and suggested the possibility of loss of this

in turn leads to a larger value for barium. There are also other differences between the two curves, but those noted are the most important.

So long as only nuclear regularities are considered, it is difficult to give preference to one curve or the other. However, if one uses Urey’s smaller values for potassium and other elements that are concentrated during melting processes, one can obtain better agreement between the ratios of scandium to gallium and of copper to gallium for the Sun, although there would still remain large discrepancies. For the time being the very large discrepancies in these ratios cannot be explained; and we definitely refuse to believe that these discrepancies are the result of errors in analyses of meteorites.

of the element through volatile compounds, as was indicated by Urey[^95]. Astronomical data give an abundance almost 100 times greater than meteoritic data. Such a large abundance does not fit our curves without large distortions. We adopted the highest possible value for chlorine and nevertheless retained a sufficient separation of the curves for even and odd masses.

Heavy rare gases

Rare gases, with the exception of helium, are not observed on the Sun because of the low temperature of the Sun and the low abundance of the rare gases. Neon and argon have been observed in type B stars and planetary nebulae. Unsöld[^90] and Aller[^3] give a review of the data. Of course, the limits of probable errors are very large, since the observed lines are ion lines, while it is very difficult to estimate the excitation conditions with sufficient accuracy to obtain the abundance with confidence, within less than a tenfold discrepancy.

The ratios of the amounts of rare gases in the atmosphere are well known. From these ratios one can draw certain important conclusions independently of any theory of atmospheric formation. In particular, one may apparently assume, with sufficient grounds, that at the surface of the Earth the heavy rare gases were enriched in comparison with the light ones. This means that the ratio of krypton to xenon in solar matter should be equal to or greater than the ratio of these gases in the atmosphere. The same will be true for the ratio of argon to krypton or neon to argon, with the exception of the isotope \(A^{40}\). Such an assertion appears quite justified, since no chemical or physical process is known in which a heavy gas would escape more readily than a lighter one. Terrestrial helium and \(A^{40}\) must be radiogenic, and therefore arguments of this kind are not applicable to them.

Astronomical values for the abundance of argon and chlorine in planetary nebulae are considerably higher than those which may be expected as a result of simple interpolation for argon and chlorine from the values for neighboring elements in meteorites. If astronomical values are used for a graphical representation of nuclear abundances, a very remarkable feature is obtained, namely a sharp peak on the abundance curves for even and odd masses at the values 35 and 36, followed by a steep fall toward the small abundances \(Cl^{37}\), \(K^{39}\), \(K^{41}\), \(Ca^{43}\) on one curve and \(A^{38}\), \(Ca^{42}\) on the other. There are no physical grounds to expect such behavior of these curves. We consider such an interpretation incorrect and draw for \(A^{36}\) and \(A^{40}\) a smooth interpolation between sulfur and calcium, and use the value considered above for chlorine. For the krypton—xenon ratio we adopt the atmospheric value 12.5, in accordance with the assumption made above. The value for xenon determines the unknown abundance of tellurium.

From calcium to nickel

The values for calcium in meteorites have been determined with great accuracy. The value of Urey and Craig[^98] is 53,600. The most recent determinations by Wiik[^101] gave 49,000. The concentration of scandium in meteorites was determined by Pinson, Ahrens, and Franck[^65] and proved equal to \(6 \cdot 10^{-6}\), which essentially coincides with Goldschmidt’s value. Wiik obtained \(8 \cdot 10^{-6}\) for chondrites. Russell drew our attention to the fact that the scandium lines in the solar spectrum are considerably more intense than the gallium lines, despite the great intensity characteristic of the gallium lines. Therefore we adopted the largest observed value for scandium in meteorites.

The value for titanium was determined many years ago with exceptional accuracy. The average of Urey and Craig is 0.066%. Careful analyses of a series of chondrites, recently made by Wiik (1955), led him to the conclusion that the amount of titanium is very constant and is about 0.079%, which gives 2440 for the atomic abundance, as compared with the mean value of 2100 of Urey and Craig.

Wiik’s most recent analyses for chromium and manganese agree well with the earlier data summarized by Urey and Craig^98. We use these data for these three elements.

For the abundances of iron, cobalt, and nickel we have adopted values obtained from the data summarized by Urey and Craig^98 for the case of the group of chondrites with a low iron content. These data were confirmed by Wiik, who gives a somewhat smaller value for iron. Greenstein’s astronomical estimate for iron is considerably lower than the abundance adopted by us, and this would not contradict the arguments of Urey and Craig. We use their values in order to provide compatible values for the relative abundances of iron and nickel.

Important abundance ratios of the elements

The ratios titanium—zirconium—hafnium appear to be well established. The available data show that these ratios are almost the same in meteoritic and terrestrial sources. Goldschmidt gives a value close to 20 for the weight ratio Ti/Zr and approximately 50 for the ratio Zr/Hf for both sources. Pinson, Ahrens, and Frank^65 found \(33 \cdot 10^{-6}\) for Zr in chondrites, and Wiik^101 found 0.079% for titanium, i.e., obtained a ratio equal to 24. We adopt this value and regard the atomic abundance of Zr as equal to \(1/45\) of the titanium abundance adopted by us.

The ratio Zr/Hf is based on the extensive investigation by Hevesy and Würstlin^41, ^42 of the abundance of hafnium and zirconium in various sources. Their values for Zr in the Pultusk and Vaca Muerta meteorites differ noticeably from the values of Pinson, Ahrens, and Frank^65. The available data contain some considerable probable error. Thanks to the courtesy of Dr. English (English S. G.), we learned of many recent analyses of zirconium minerals for hafnium, carried out by the U. S. Bureau of Mines. The average of 68 analyses is 2.37% hafnium relative to the sum of zirconium and hafnium. This is a somewhat greater abundance of hafnium than that given by Goldschmidt. It is impossible to establish whether there was a definite concentration of hafnium relative to zirconium in the process of formation of these minerals, but some samples (not included in the mean) have a significantly greater concentration of hafnium. We adopt for this weight ratio the value 55, and for the ratio of atomic abundances—the value 110.

Goldschmidt adopted the terrestrial ratio S/Se as equal to 6000, and the meteoritic weight ratio as equal to 3300. Since then, Behrens^14 has investigated many meteorites, including a series of chondrites. Among the chondrites were Allegan and Tabory, whose fall was observed; the remaining meteorites studied by him were finds. For selenium in these two meteorites values of 13 and \(10 \cdot 10^{-6}\) are given; in the other chondrites smaller values were obtained. Behrens also determined for the weight ratio S/Se in troilite from Canyon Diablo the value 4215, i.e., a value intermediate between Goldschmidt’s values. If Goldschmidt’s meteoritic ratio and our value for sulfur are used, then for the atomic abundance one obtains 47, whereas from Behrens’s data one obtains 24.2. Owing to the difference in stability of \(H_2S\) and \(H_2Se\) and of the carbon compounds of these two elements, it is improbable that

selenium escaped from meteorites just as easily as sulfur. We have adopted 67.6 for the abundance of selenium. For this ratio additional data are needed. The data for tellurium are the least reliable, and we have to interpolate the value for this element.

The ratio of chlorine to bromine is probably more reliable than the values for bromine. This ratio by weight in seawater is 292. Selivanov^30 [see Rankama and Sahama^72] reported values ranging from 100 to approximately 300 for the ratio in terrestrial minerals. Benz^8 gives values for this ratio varying within wide limits in different erupted rocks. We use the oceanic ratio and our value for chlorine, and obtain 13.4 for the abundance of bromine. The oceanic value for iodine has no significance, since iodine is absorbed by living organisms and, consequently, is depleted in the sea relative to sediments.

The ratio of potassium to rubidium has been extensively studied in recent years. Ahrens, Pinson, and Kearns^2 found a weight ratio equal to 100. Edwards and Urey^22 obtained a value of 180 on several meteorite samples. Herzog and Pinson^37 believe that it would be correct to adopt the value 200. This value is quite comparable with the chlorine—bromine ratio. The observed abundance by weight gives \(3.8 \cdot 10^{-6}\), which is equivalent to a rubidium atomic-abundance value of 6.65.

We believe that on the curve in this region there is a minimum for the value of the mass less than 50 neutrons, just as there is a minimum for the mass less than 82 neutrons, and our curve resembles the curve previously given by Suess^85.

Goldberg, Uchiyama, and Brown^29 determined the amounts of Ni, Co, Pd, Au, and Ga in 45 iron meteorites. The gallium content varies noticeably, and here there is a certain slight correlation with the palladium content. The weight ratio of nickel to palladium found by these authors is the most reliable value of this ratio, namely \(2.24 \cdot 10^4\). Adopting our value for nickel, we obtain from this 0.675 for the abundance of palladium. Goldschmidt gives 2.5 for this value. Goldschmidt’s assumption of a larger fraction of the metallic phase increased this value. If 10% of the metallic phase is adopted and the troilite phase is neglected, then this value will be \(0.9 \cdot 10^{-6}\), which is only slightly greater than the value we have chosen. The investigations of Goldberg and others also led to the Ni—Au ratio, and this fixes the position of gold relative to nickel. These two ratios are the most reliable of all those we have for determining our curves in the interval of large mass numbers.

The atomic ratio of krypton to xenon in the atmosphere is 12.5, and in the Sun this ratio must be the same or higher, since krypton could have escaped faster than xenon, as was indicated above. It is curious that in all our attempts to provide abundance values compatible with all the evidence, we never considered it desirable to increase the value of this ratio above 12.5. We adopt for krypton and xenon, respectively, abundances of 51.3 and 4.0, which is compatible with this value of the ratio.

Copper, zinc, gallium, germanium, arsenic, krypton, strontium, ytterbium

Adopting reasonable estimates of error in the published abundances of the elements from iron to zirconium, one can, owing to our choice of the abundance of chlorine and sulfur, obtain in this interval a smooth curve for the elements with odd masses, with a maximum at bromine. The pairs of isotopes of copper, gadolinium, and bromine determine the slope of the curve at three points.

It has been reported that the copper content in meteorites varies within surprisingly wide limits. Goldschmidt, after a careful study of the best data, which differ among themselves by more than a factor of 10, adopted an atomic abundance equal to 460. Unpublished data of Urey and Sandell indicate a greater constancy of the copper data in chondritic meteorites. Our choice of the value 212 for the atomic abundance is in agreement with the data of these two analyses.

Zinc in meteorites is a typical chalcophile and is concentrated in the sulfide phase. For the selection of data made by Goldschmidt it would have been necessary for zinc to be less abundant than copper, which would be surprising. Unsöld’s value, based on three lines in the solar spectrum, exceeds by more than a factor of 10 Goldschmidt’s estimate, equal to 360 for the atomic abundance. We adopt 486 in order to ensure the smoothness of the abundance curves in this interval. This value is certainly within the errors of the analytical values for meteorites.

Gallium in iron meteorites was studied by Goldberg, Uchiyama, and Brown,^29 who found three groups of iron meteorites with different gallium contents, namely 60, 20, and \(2\cdot 10^{-6}\). No satisfactory explanation of these variations has been given. These abundances are puzzling, especially because gallium is to a considerable degree an electropositive element and is concentrated to some extent in surface terrestrial rocks. It appears probable that gallium is also partly present in the silicate phases. Sandell^77 reported his latest data on gallium. These data are very close to those of Goldschmidt and Noddack. We adopt for the atomic abundance 11.4, which is equivalent to Sandell’s value for chondrites, equal to \(5.3\cdot 10^{-6}\). The ratio of scandium to gallium adopted by us, namely 2.5, apparently disagrees with the astronomical values for the Sun, as Prof. Russell pointed out to us. Aller^3 gives for the ratio of scandium to gallium in the Sun the value 15, and more recent data indicate an even larger value. Aller gives for the ratio of copper to gallium the value approximately 400, whereas from meteoritic data about 20 is obtained. There are not sufficient grounds to suppose that this discrepancy is explained by large errors in the meteoritic data. If the solar data are reliable, then between the Sun and meteorites there is a real difference in composition.

Careful investigations by Goldschmidt and Peters^32 of the germanium content in meteorites gave an average of \(79\cdot 10^{-6}\) for the silicate, troilite, and metallic phases. Germanium was found chiefly in the metallic phase. In our average we adopt considerably less iron and less in the metallic phase than Goldschmidt. In order for \(\mathrm{Ge}^{73}\) to fall on our smooth curve for odd masses, we had to adopt for germanium approximately \(24\cdot 10^{-6}\), or an atomic abundance equal to 50.5, instead of Goldschmidt’s value, equal to 188. There are sufficient grounds for considering that the values adopted by Goldschmidt for germanium, as well as for tin and lead, are too high, as will be shown below in the discussion of tin and lead.

Sandell’s latest value^77 for arsenic, equal to \(2.2\cdot 10^{-6}\) in chondritic meteorites, or a value of 4.0 for the atomic abundance, is apparently very reliable. It is the average for 14 chondritic meteorites. Noddack’s values^60 are too exaggerated.

Our values for the abundances of copper, gallium, and arsenic, taken from the latest excellent analytical data, lie on a smooth curve. The astronomical value for copper is higher, and for gallium lower, than is obtained from these data.

As already indicated, during evaporation in the process of meteorite formation there was no fractionation of elements less volatile than mercury. Copper and gallium form very nonvolatile compounds, while all arsenic compounds are volatile to a considerable degree. Nevertheless, all three of these elements fall exactly on the smooth curve. Zinc is also sufficiently volatile. Our value for it is interpolated, but it does not deviate strongly from the approximate analytical data for meteorites.

Pinson, Ahrens, and Frank^65 recently determined strontium in meteorites by an improved method and obtained an average of \(11 \cdot 10^{-6}\). Schumacher^79, applying isotope dilution, obtained \(12 \cdot 10^{-6}\) in the Forest City chondrite. In our view it would be better if the value for strontium were somewhat higher; however, the available data apparently do not permit such an assumption.

The abundance of yttrium and the rare earths is difficult to evaluate. The concentrations of yttrium in acidic and basic rocks are to a considerable extent the same; moreover, they are very close to the published concentrations of them in meteorites. Therefore we adopt Goldschmidt’s value in meteorites, namely \(5 \cdot 10^{-6}\), and an atomic abundance equal to \(8.9\) [see Rankama and Sahama^72 (pp. 510 and 516), where a review of the data is given].

The curves in this interval have a maximum at bromine and a minimum before nuclides with magic number at \(N = 50\). We consider this minimum real and analogous to the minimum preceding the nuclides with magic number at \(N = 82\). We also consider that the minimum at germanium is real and that the curves in this interval, preceding the value \(N = 50\), are similar to the curves in the interval preceding the value \(N = 82\).

From zirconium to tin

The fundamental nickel—palladium ratio considered above fixes the abundance of palladium. The value thus determined agrees well with the determination by Kuroda and Sandell^47 for molybdenum, namely \(1.54 \cdot 10^{-6}\) in chondrites, with the corresponding atomic abundance \(2.42\). This new analytical value is about one-half of the old one^58, ^59. The decrease in the abundance of zirconium isotopes indicates a rapid decrease in abundances after neutron number 50. Nuclides with even masses of elements with even atomic numbers Ru, Pd, Cd, and Sn can be placed on a smooth curve of abundance as a function of mass number, and at the same time it is possible to construct a sufficiently smooth curve for nuclides with odd masses. The ratios of ruthenium, rhodium, and palladium are not well enough known. Goldschmidt estimates these ratios as \(10:5:9\). We adopt atomic abundances respectively equal to \(1.49\), \(0.214\), and \(0.850\), which gives the ratio \(10:1.44:5.7\). This gives a smooth curve, and we believe that our values do not exceed the limits of the errors existing at present, although our ratios differ significantly from Goldschmidt’s ratios. For cadmium we adopt an atomic abundance of \(0.89\), with Noddack’s value for chondritic meteorites equal to \(1.86\). Better analytical data are urgently needed for this element.

Analyses of meteorites carried out by Goldschmidt and Peters^33 and Goldschmidt^31 gave, for tin in the metallic, troilite, and silicate phases, respectively, \(100\), \(15\), and \(5 \cdot 10^{-6}\). Taking the metal:troilite:silicate ratios as \(10:5:85\), we obtain approximately \(15 \cdot 10^{-6}\) and an atomic abundance equal to \(19\). Noddacks^60 gave a value of \(50\) for the atomic abundance of tin. Use of Goldschmidt’s or the Noddacks’ value would lead to distortion of the curve relative to all neighboring elements, if the currently known data are taken as the basis. We come to the conclusion,

that the analytical data for this element are very incorrect. Tin is an element that is widely used in laboratory practice as solder, as material for a distillation apparatus, etc. In the opinion of Dr. M. Fleischer, too high values are often reported for tin in silicate materials owing to the use of soldered sieves for separating ground samples. According to a private communication from Sandell \(^{77}\), he recently found that the average concentration of tin in chondrites is \(1 \cdot 10^{-6}\), which is equivalent to an abundance of 1.33. This value also served for us as the fixed value in constructing the curve in this interval.

For niobium in chondritic materials, Rankama \(^{70,71}\) obtained a value of \(0.5 \cdot 10^{-6}\), which is equivalent to an atomic abundance of 0.81. This value is close to the value 1.00 adopted by us. The adopted value for silver is much lower than the value obtained from the analytical data. Goldschmidt adopted for this abundance the value 3.2 on the basis of his own data and the data of Noddack. We found that we had to adopt for silver a value of 0.26 if we wanted silver to fall on our curve for odd masses. Joensuu pointed out to us that many analytical data for small amounts of silver are incorrect because of the ease of excitation of the resonance lines of silver and because of the presence of silver coins in the hands and pockets of analysts. For this chalcophile element too-high values may also be obtained partly because high concentrations of this element in troilite inclusions from iron meteorites have been reported. According to Noddack, the concentration of silver in sulfide iron from silicate meteorites is \(5 \cdot 10^{-6}\), and in sulfide iron from iron meteorites \(38 \cdot 10^{-6}\). If the troilite phase of iron meteorites is disregarded and the weight of the troilite phase of silicates is estimated at 0.05, Noddack’s data will approach the value we have adopted for silver.

Earlier data for indium give \(0.15—0.20 \cdot 10^{-6}\) in meteorites, but recently Shaw \(^{82}\), using a method whose sensitivity, it is thought, is sufficient to detect \(\sim 0.02 \cdot 10^{-6}\), was unable to detect indium in two chondrites and one achondrite. The interpolated value adopted by us, 0.11, corresponds to \(0.085 \cdot 10^{-6}\) in chondritic meteoritic matter. It is difficult to understand the very small values obtained by Shaw unless it is assumed that the large amounts of iron in meteorites interfered with the spectral analyses he carried out, owing to the large background produced by the great number of iron lines.

On both of our curves the maxima are located at neutron number 58; we were unable to eliminate these maxima by any permissible adjustment of the adopted abundances. At this number of neutrons the shell \(g_{7/2}\) may be filled. Mayer and Jensen \(^{52}\) believe that the shell \(d_{5/2}\) should first be filled at neutron number 56. We find no peculiarity in the abundance at this number of neutrons.

Obviously, it would be highly desirable to obtain new analytical data on the elements from zirconium to tin. Between mass numbers 99 and 123 inclusive there are five pairs of isotopes with odd mass numbers and with a maximum abundance ratio of 1.34, i.e., \(\mathrm{Sb}^{121}:\mathrm{Sb}^{123}\). The values adopted by us were chosen on the basis of the assumption that the abundance ratios of nuclides that are not isotope pairs should be close to this value.

Antimony, selenium, tellurium, iodine, xenon, cesium, and barium

The analytical data on the first five of these elements are of no substantial importance. Undoubtedly, at mass 120 there is a marked depression on the curve of abundances of even masses. Goldschmidt asserts,

that the selenium–tellurium ratio, based on Noddack’s data[^60], “may be,” will give the correct order of magnitude, and for this ratio he gives the value 80. We adopt for the atomic ratio the value 14.5, which also, perhaps, has some basis.

The value for xenon relative to that for krypton is set by virtue of the considerations given above. The krypton–xenon ratio is either equal to 12.5 or greater; we adopt the maximum possible value for xenon. The unusual abundance of its isotopes with odd masses and their ratios to the abundances of isotopes with even masses require maxima on both curves—both on the curve for even masses and on the curve for odd masses—near mass number 130. Recently Pinson, Ahrens, and Frank[^65] gave the value \(8 \cdot 10^{-6}\) for the abundance of barium in chondrites. This gives an atomic abundance of 8.8. Thus the value 3.66 adopted by us is considerably smaller. We would have preferred a larger abundance value, but then, in order to preserve the smoothness of the curve in the region of rare nuclides from tin to cerium (figure), it would have been necessary to adopt larger abundances for xenon and tellurium, which in turn requires a greater abundance for krypton. We were unable to resolve our doubts on these points. It is curious, however, that the uncertainty in these relative abundances leads to values differing only by factors of 1.25 or 1.5. The ratio of strontium to barium adopted by us is 6.6.

The isotopes with odd masses of these elements with even atomic numbers lie off the curve for odd masses. Iodine and cesium, at 0.80 and 0.456, fit the curve well. The data for these two elements are very unsatisfactory. Fellenberg’s data[^26] lead to an average value of \(1.25 \cdot 10^{-6}\) for iodine, while from Noddack’s data[^60] one obtains \(0.035 \cdot 10^{-6}\). The value adopted by us, based entirely on interpolation, is \(0.66 \cdot 10^{-6}\). Our interpolated value for the abundance of cesium is \(0.40 \cdot 10^{-6}\), whereas Noddack[^58,^60] gave two values: 0.01 and \(1.1 \cdot 10^{-6}\).

For sulfur in meteorites Noddack[^59,^60] gives only a few data. We adopted a value that fits the curve for odd masses, namely 0.246, which is equivalent to \(0.2 \cdot 10^{-6}\). This agrees with Noddack’s value if the data for troilite are ignored, assuming that analyses of troilite from metallic meteorites give values for the sulfide phase in average chondritic meteorites that are too high. According to a private communication from Sandell[^77], his approximate analyses fall within the range from 0.5 to \(0.2 \cdot 10^{-6}\).

Obviously, for this interval there are too few observational data, and all of them are of questionable quality. The values chosen by us can to a significant extent be revised as soon as new data are obtained, although we believe that the general form of the curves will apparently be preserved.

Rare-earth elements and hafnium, tantalum, and tungsten

As already indicated, the relative abundance of the rare-earth elements was used as an argument for the stated abundance rules. The rare-earth elements have such similar chemical properties that separation of these elements on any large scale in any cosmochemical process seems improbable. Consequently, analytical data on meteorites should give very reliable values for the relative abundance of these elements with respect to one another. Furthermore, it also seems improbable that even on the Earth’s surface any significant separation of these ...

elements, except for minerals of a definite type, and, moreover, because, according to Goldschmidt and Baur [cited by Goldschmidt^31], europium has a tendency to separate from the other rare-earth elements and in its geochemical behavior resembles strontium and lead. Minami^53 carried out in Goldschmidt’s institute a complete analysis of terrestrial sedimentary rocks for rare-earth elements. He found that in sedimentary rocks europium shows no anomalous abundance; from this he concluded that these sedimentary rocks contain the rare-earth elements in ratios corresponding to the average ratios at the Earth’s surface.

Analyses of meteorites, performed by Ida Noddack^57, led to values differing greatly from Minami’s values for terrestrial sedimentary rocks. The ratio of lanthanum to heavy rare-earth elements, such as erbium, ytterbium, etc., in Minami’s values for sedimentary rocks is approximately 8 times greater than in Noddack’s values for meteorites. It is difficult to believe that, in the process of the Earth’s formation, fractionation of such an order of magnitude could have occurred; it is more probable that one of the series of analytical data contains a considerable error.

We provisionally assume that Minami’s values for the abundances of the rare-earth elements relative to one another in terrestrial sedimentary rocks give a closer approximation to the truth than Noddack’s values. Goldschmidt^31, Brown^91, 93, 94, and Urey^92 used Noddack’s data; therefore, between their tables and the table of the present paper there are significant discrepancies. The abundance of this entire group as a whole relative to silicon was adopted by us arbitrarily—so as to obtain a value which seemed to the authors of the present paper to be a reasonable interpolation between the abundances of elements with larger and smaller masses. Our data certainly do not go beyond the limits of the admissible errors of these data.

Table IV

In comparison with Minami’s values we have made only a slight adjustment, in order to obtain smoother curves. Table IV gives a comparison of the observed and adopted values; both are normalized to lanthanum, taken as unity. The most serious discrepancy occurs in the case of cerium. It is true that the discrepancies are certainly within the limits of observational errors, but it is also true that the true curves may be less regular than we depict them. The abundance of hafnium is taken as \(\sim 1/110\) of the abundance of zirconium, as was already explained above. Rankama^70, 71 gives the value \(0.38 \cdot 10^{-6}\) for the maximum amount of tantalum in meteorites, which is equivalent to an atomic abundance of 0.32. We adopted a smaller value, obtained by interpolation, 0.065. We discussed this question with Dr. Rankama, who agreed that the smaller value is probable.

According to Sandell^76 and Landergren^48, one may consider that the earlier analytical data for tungsten are greatly exaggerated. The results of Noddack^58, 59 and Hevesy and Hobbie^40, obtained on igneous rocks, exceed Sandell’s values by more than a factor of 10. Hence we conclude that

and Noddack’s data on meteorites are also erroneous, and that there are no analytical data on tungsten in meteorites. By interpolation we obtained the value 0.49, corresponding to \(0.59 \cdot 10^{-6}\). This interpolated value is approximately one third of Sandell’s value for igneous rocks.

Rhenium, osmium, iridium, platinum, and gold

Brown and Goldberg \(^{13}\) determined rhenium by the neutron-activation method in five iron meteorites and obtained values varying from \(0.25\) to \(1.45 \cdot 10^{-6}\), with an average of \(0.62 \cdot 10^{-6}\). Assuming that, on average, meteoritic matter contains about 10% metallic phase, we obtain from this approximately \(0.062 \cdot 10^{-6}\) for this element. The thermodynamic properties of rhenium and its compounds are almost unknown, but a discussion of its chemical properties compels one to assume a calchophile nature to some extent, along with its proven siderophile nature. For the atomic abundance we have adopted the value 0.155, exceeding by a factor of 2.5 the value obtained from an estimate of the iron phase alone.

Goldschmidt \(^{31}\) gives the following estimate of the proportions of osmium, iridium, and platinum (in parts per million):

The mean was obtained on the assumption of 10% metallic phase and by neglecting the troilite phase in iron meteorites, as well as on the assumption that these elements are absent from the silicate fraction and its troilite. The atomic abundances adopted by us are 1.00, 0.82, and 1.62, respectively, for Os, Ir, and Pt. Goldschmidt’s estimates are admittedly approximate, and our agreement is satisfactory. Data on these elements with the accuracy achieved by Goldberg, Uchiyama, and Brown \(^{28}\) for Pd and Au would be highly desirable. The curves for even and odd masses should lie close to one another and have maxima at masses 193 and 194, if these curves are smooth and if their slope is determined by the isotope abundance of \(\mathrm{Re}^{185}\) and \(\mathrm{Re}^{187}\), \(\mathrm{Os}^{187}\) and \(\mathrm{Os}^{189}\), and \(\mathrm{Ir}^{191}\) and \(\mathrm{Ir}^{193}\) for the curve of odd masses, and chiefly by \(\mathrm{Os}^{188}\) and \(\mathrm{Os}^{190}\), \(\mathrm{Pt}^{194}\), \(\mathrm{Pt}^{196}\), and \(\mathrm{Pt}^{198}\) for the curve of even masses. The maxima of the curves are similar to the maxima near mass number 130.

In order to fix the atomic abundance of gold, we use the data of Goldberg, Uchiyama, and Brown (1951) for the nickel–gold ratio. These analytical data have a rather wide scatter of values for this ratio, with a mean value of the ratio by weight of \(5.8 \cdot 10^{4}\). The palladium–gold ratios obtained by them are more constant. With our value for the abundance of nickel, this gives 0.140 for the atomic abundance.

Mercury, thallium, lead, bismuth, uranium, and thorium

Mercury is a volatile element that could have partially disappeared from meteorites. Moreover, it is always present to a considerable extent in chemical laboratories, so that all analyses are suspect. Noddack \(^{60}\) reported its presence in the troilite of Canyon Diablo. We obtained for the abund—

of mercury, the value 0.284 by interpolation. It may well be larger or smaller, since our estimates for nuclides with large masses are very unreliable, and also because there is not even an approximate theory for the behavior of the abundance curve.

For the atomic abundance of thallium Noddack (1934) gives the value 0.108, or \(0.15 \cdot 10^{-6}\) in chondrites. Shaw\(^{81}\) could not detect the presence of thallium in two chondrites and one achondrite and gives the value \(< 0.01 \cdot 10^{-6}\). Shaw’s extensive studies established an average abundance in igneous rocks of \(1.3 \cdot 10^{-6}\). We accept Noddack’s data and cannot explain Shaw’s results otherwise than by the influence of interference from the large amount of iron in meteorites, which affected the analysis.

Goldschmidt and Noddack gave rather high values for lead in all phases of meteorites. At present all these data appear doubtful, since Brown and his collaborators established that lead is present in all phases in considerably smaller amounts. Lead is, to a significant degree, a ubiquitous element; it is present in many reagents and in water in small amounts, and also in atmospheric dust—in connection with the use of tetraethyl lead in automobile fuel. Since troilite from metallic meteorites probably does not contribute any significant share to the mean, even the quite reliable determinations of lead by Patterson, Brown, Tilton, and Inghram\(^{63}\) do not increase our knowledge of the natural abundance of lead.

Patterson et al. (1953) determined the amount and isotopic composition of lead from the metallic phase of the Canyon Diablo meteorite and from the troilite phase of the Henbury and Canyon Diablo meteorites. The lead from these meteorites contains the smallest amount of radiogenic lead in comparison with any other known samples of elemental lead. Patterson et al. suggested that this is primordial lead. Patterson et al.\(^{63,64}\), Tilton et al.\(^{87}\), and Patterson\(^{62}\) separated lead from terrestrial basalts, from the Forest City and Modoc chondrites, and from the Nuevo Laredo achondrite. By subtracting the amounts of \(\mathrm{Pb}^{206}\), \(\mathrm{Pb}^{207}\), and \(\mathrm{Pb}^{208}\), relative to \(\mathrm{Pb}^{204}\), taken as unity, in iron meteorites from the amounts of these same isotopes in basalts and in stony meteorites, they obtained the amounts of these isotopes that are, presumably, products of the radioactive decay of \(\mathrm{U}^{238}\), \(\mathrm{U}^{235}\), and \(\mathrm{Th}^{232}\). Without information on the amounts of uranium and thorium, one can calculate an age from the ratio of \(\mathrm{Pb}^{206}\) to \(\mathrm{Pb}^{207}\). The age calculated in this way proved to be \(\sim 4.5 \cdot 10^9\) years. The calculation is based on the assumptions that 1) stony meteorites originally contained lead from the composition of iron meteorites, 2) no chemical processes have occurred since then, and 3) stony meteorites contain such amounts of uranium and thorium as are necessary to obtain the observed amounts of radiogenic lead. This age was confirmed by Wasserburg and Hayden, who applied the \(\mathrm{K}^{40}—\mathrm{A}^{40}\) method to three chondrites. This dating method depends only on the composition of each meteorite and represents the time elapsed since gaseous argon volatilized from the meteorite. Schumacher\(^{79}\) approximately confirmed this age, using the \(\mathrm{Rb}^{87}—\mathrm{Sr}^{87}\) method. All three methods were applied to the Forest City meteorite.

Table V summarizes the data on these abundances of lead and its isotopes and indicates the necessary amounts of \(\mathrm{U}^{238}\) and \(\mathrm{Th}^{232}\) that must be present in meteorites at the present time in order that the required amounts of radiogenic lead could have been obtained.

The amounts of uranium and thorium required for chondrites are close to the values found by Chackett, Golden, Mercer, Paneth, and Reasbeck\(^{15}\) in the Bedgelert chondrite, namely \(0.106 \cdot 10^{-6}\) and \(0.335 \cdot 10^{-6}\), respectively, for uranium and thorium. However, Davis (1950), De Jager\(^{19}\), and Patterson

Table V

with collaborators$^{64}$ published much smaller values, namely from 0.01 to $0.03\cdot 10^{-6}$ for uranium. Urey$^{97}$ pointed out that the larger amounts of uranium and thorium obtained by Chackett et al., on the one hand, and the observed amounts of potassium in meteorites, on the other, lead to great difficulties in explaining the heat balance of the Earth, the Moon, and Mars if the amounts of these elements in the planets and meteorites are assumed to be the same. We have not accepted the abundances proposed by Urey; however, the serious difficulties connected with the indicated problems remain quite real. If the smaller abundances of uranium and thorium are correct, then we must admit the existence of two primordial leads, i.e., leads from iron meteorites and from Nuevo Laredo, since chondritic lead may represent a mixture of both of these leads in the proportion 3:1.

We have not been able to solve this problem. Since throughout the present paper the abundances of elements in chondritic meteorites are used and, in general, they have proved acceptable, we shall use for the abundance of lead the averages of the data for Forest City and Modoc.

For the atomic abundance of bismuth, Noddack gives 0.144; we accept this value.

The data considered above show that the abundance of uranium in meteorites has a value intermediate between 0.01 and $0.1\cdot 10^{-6}$, i.e., the atomic abundance of uranium has a value between 0.0063 and 0.063. The same uncertainty also exists in the case of thorium, but its abundance is 3 or 3.5 times greater than the abundance of uranium.

PROBLEMS CONNECTED WITH THE INTERPRETATION OF THE DISTRIBUTION OF NUCLEAR ABUNDANCE

Theory of the Origin of the Elements

The distribution of nuclear abundances obtained from the foregoing discussion provides a basis for comparing empirical data with various theories of the origin of different kinds of nuclei. We shall not present such a comparison here, but refer the reader to three excellent review articles by Alpher and Herman$^{5,6,7}$ on the theory of orig-

occurrence and relative abundance of the elements. From these articles it is clear that not one of the existing theories can explain, even roughly, all the empirical facts. Consequently, an attempt to explain by means of any one of these theories, in its present form, the finer details described here seems quite hopeless.

However, it is apparently possible that one or another theory in a modified form, in particular with the introduction of certain assumptions concerning secondary and subsequent reactions, may lead to satisfactory agreement. The authors hope that the discussion given below will help in the study of the nature of such reactions.

The values of nuclear abundance obtained by the method described above differ rather strongly in some mass intervals from previous estimates (Suess^85). However, comparison of the figure presented with the corresponding curves published earlier shows that the main features of the abundance distribution have been preserved. These features are essentially independent of the choice of the value for the abundance of an element and represent quite definite problems considered below. This discussion is not complete, and the reader is afforded the opportunity to discover still new features of the figure which may serve as evidence for or against the predominance of a particular mechanism of element formation.

Between the character of the region of lighter ($A < 90$) nuclei and that of heavier ($A > 90$) nuclei there is a substantial difference. In the region of smaller $A$, the curve of the sum of the abundances of isobars for even $A$ has an irregular zigzag form, and the abundance values depend strongly on the number of excess neutrons. At those mass numbers for which there are two stable isobars, the isobar with the smaller number of excess neutrons has the greater nuclear abundance in the region of light masses.

In the region of large mass numbers, the curves of the sums of the abundances of isobars become more regular, and isobars with a larger number of excess neutrons turn out to be more abundant.

In order to try to understand this difference, two types of nuclear reactions should be considered:

1. Reactions leading to the formation of nuclei situated on the side of neutron-rich nuclei relative to the energy valley. These reactions predominated at large mass numbers and gave a “smoothed” distribution of abundances.

2. Reactions leading to the formation of nuclei situated on the side of nuclei with a deficiency of neutrons relative to the energy valley. These reactions predominated in the region of small masses and formed a “fine structure” in the abundance distribution.

It may be supposed that reactions of type 1 were “neutron capture, formation,” i.e. $(n\gamma)$ with subsequent $\beta$-decay, as postulated in the theory of neutron capture. To explain reactions of type 2, no suitable theory has yet been proposed; however, from the empirical data it is evident that reactions of this type are necessary, as shown below.

Any theory in which very high temperatures ($kT > 1$ MeV) are postulated for the transformation of nuclei with a given mass number into nuclei with another mass number must lead to the conclusion of a uniform change of abundance with mass number. In the case of a very high temperature, not only the ground state but also many excited states will be involved in the reaction, so that the effect of an abrupt change of some property of the ground states (for example, at a “magic” number)

will be “smeared out” as a result of the participation of excited states. The same will be true if the reactions leading to changes in mass numbers take place in the region where the β-unstable nuclei lie on the slopes of the energy trough, as is assumed in the theory of element formation by neutron capture (Alpher and Herman \(^{5,6,7}\)).

The sum rule for isotope abundances

In the region \(A > 70\), the isotope with the larger number of excess neutrons is almost always the more abundant one. The abundance of the isotope with the smaller neutron excess, the so-called “shielded” isotope, i.e., the isotope that has only one neutron above a closed shell, has a comparable value only when this isotope has a substantially larger binding energy than the unshielded isotope. In most cases the value of the sum of the abundances of these two isotopes coincides with the value interpolated between the values of the unshielded isotope at mass numbers \(A - 2\) and \(A + 2\).

Such a distribution gives the impression that, in this mass interval, shielded nuclei were formed from their shielded isobars after the mass distribution had been established. However, it can be shown that such a transformation could not have occurred by two successive β-decays starting from the level of thermal excitation. This can be proved by considering the isobaric pair \(\mathrm{In}^{115} — \mathrm{Sn}^{115}\), for which the following data are available.

The abundance ratio is \(\mathrm{In}^{115}/\mathrm{Sn}^{115} = 23\); the excited level in \(\mathrm{In}^{115}\): \(0.335\ \mathrm{Mev} = E^*\). The half-life in this state is 4.5 hours. The partial half-life for β-decay in this state is 70 hours. The spins of \(\mathrm{In}^{115}\) in the excited and normal states are \(^{9}/_{2}\) and \(^{1}/_{2}\). The number of \(\mathrm{In}^{115}\) nuclei in the excited state \(N^*\) at temperature \(T\) will be equal to \(N^* = (g^*/g) N \exp(-E^*/kT)\). From the experimental data cited it follows that natural indium could not have been at temperature \(T\) for more than \(1 \times e^{0.335/kT}\) hours, where \(kT\) is expressed in Mev.

This means that \(\mathrm{In}^{115}\) in nature could not have been at a temperature exceeding approximately \(0.3\ \mathrm{Mev} = kT\) for more than several hours; otherwise a large fraction of the nuclei with mass 115 would have had to be in the form of \(\mathrm{Sn}^{115}\). Comparing this result with the available data on excited states, one may conclude that it is impossible to explain the abundance of a shielded nucleus by assuming β-decay from levels of thermal excitation higher than the ground state of the intermediate odd-odd isobar. According to the theory of neutron capture, shielded nuclei are formed at a later stage of neutron formation, when the rate of neutron-capture processes becomes less than the average rate of β-decay, so that formation takes place in the region of stable nuclei. They will then be formed from nuclei with odd \(A\) that have a sufficiently long lifetime, or by stable \((n\gamma)\) capture followed by β-decay of odd-odd nuclei. However, it cannot be expected that these abundances will follow the distribution pattern required by the sum rule.

Light isotopes in the region of large masses

The theory of neutron capture does not explain the presence of such a type of shielded nuclei, which has a lower binding energy than their shielded isobars situated on the β\(^+\) side of the energy trough. This type of nucleus is, in general, approximately 10 times less abundant than that found in the more privileged energy state

type of screened nuclides. Their abundance does not correlate with their relative binding energies. This can be verified directly on the basis of the fact that, for a number of elements, the abundance of the lightest isotope is greater than the abundance of the next isotope by mass. Such a phenomenon occurs for Mo, Ru, Cd, Sn, Xe, and Ba. In the cases of Ce and Dy, the lightest isotope is only slightly inferior in abundance to the next one. Of course, the lightest isotope always has a lower binding energy than the next isotope by mass.

The most remarkable feature of the distribution of the abundances of these rare nuclides is that, over wide intervals of mass numbers, the values of their abundances, as functions of \(A\), apparently obey their own law of “smoothness.” This law is especially clearly manifested in the behavior of the abundances of \(\mathrm{Sn}^{112}\), \(\mathrm{Sn}^{114}\), \(\mathrm{Te}^{120}\), \(\mathrm{Xe}^{124}\), \(\mathrm{Xe}^{126}\), \(\mathrm{Ba}^{130}\), etc. Hence, apparently, the inevitable conclusion follows that, in these mass intervals, part of the nuclear matter must have been formed on the side of the \(\beta^{+}\)-energy trough in the region of unstable types of nuclei with a deficiency of neutrons and, moreover, by such a route as led to the formation of a “smooth” distribution of stable types of nuclei. It is possible that secondary spallation processes led to the formation of these nuclides in the required ratios.

Effects of magic numbers in the region of large masses

The first physicist to notice that the abundance of certain types of nuclei containing definite numbers of neutrons or protons is exceptionally large was Elsasser \(^{24,25}\). These numbers, or so-called “magic numbers,” are:

\[ 2,\ 8,\ 20,\ 28,\ 50,\ 82,\ 126,\ldots \]

They belong to two different arithmetic series:

1) \(2,\ 8,\ 20,\ 40,\ 70,\ 112,\ldots\)
2) \(2,\ 6,\ 14,\ 28,\ 50,\ 82,\ 126,\ldots\)

The first series is significant at small mass numbers, while the second predominates at mass numbers exceeding 40. The effects of magic numbers are at present well understood from the standpoint of the theory of the shell structure of the nucleus [Mayer and Jensen \(^{52}\)].

A magic number is characterized by a sudden drop in the binding energy of the next nucleon. However, the binding energy of the nearest nucleon is also a function of the number of excess neutrons. In the region of large mass numbers there is no obvious correlation between the abundances and the excess of neutrons; therefore one cannot expect a simple correlation between the abundance values and the fall in the binding energy of the last particle at a magic number.

Yuz and Sherman \(^{43}\) showed that the neutron-capture cross section of nuclei containing a magic number of neutrons is exceptionally small. This experimental result was taken as strict proof in favor of the theory of the origin of the elements by neutron capture, since, according to this theory, the large cosmic abundances of nuclei with a magic number of neutrons follow quite satisfactorily from the small neutron-capture cross sections. The process of neutron formation occurring in the region of stable nuclei leads, according to this theory, to a sharp rise at the value of the neutron number corresponding to the filling of the neutron shell, and to a gradual smooth leveling of the nuclear abundances in passing to large mass numbers. If neutron formation occurs in the region of neutron-rich \(\beta^{-}\)-unstable nuclei, then the expected maximum will be smoothed out and shifted toward smaller mass numbers.

It is possible that the broad maxima on the abundance curves near mass numbers 130 and 194 are effects of the magic numbers for the completion of shells at \(N\) equal to 82 and 126, as a result of neutron formation in regions where \(N-Z\) is equal to 34 and 54. With decreasing neutron density, the center of the neutron-formation reaction will shift toward smaller numbers of excess neutrons; thus the sharp maxima at \(A\) equal to 138 and 208 could have arisen after the formation of the bulk of the nuclei in this mass interval.

For the time being it is impossible to describe the kinetics of such reactions quantitatively in a more rigorous way and to determine what assumptions are necessary in order to explain the sharp minima near \(A\), equal to 135 and 206, immediately preceding \(N\), corresponding to the closed shells 82 and 126.

In the corresponding region preceding the completion of the shell at \(N\) equal to 50, there are indications of the detection of an analogous picture, although the picture in this region cannot be regarded as established as reliably as in the region before \(N\) equal to 82 and 126. At \(A\) equal to 120 and 121, a discontinuity is observed on the abundance curves, which cannot be smoothed by any means. The discontinuity, associated with a change in the character of the distribution of isotopic abundances, occurs at the point where the number of neutrons in the nucleus reaches 70. A discontinuity at this number is unexpected, but apparently one cannot avoid the conclusion that the large total spin of the neutrons in the \(6h_{11/2}\) shell must in some way be connected with this irregularity. At the corresponding point, at 112 neutrons, a slight change in the character of the distribution of abundances may be noticed; however, the discontinuity in the abundance curves which, possibly, exists at \(A\) equal to 186 and 187 can be smoothed without difficulty. Probably the filling of the neutron shell \(7i_{13/2}\) begins before the number of neutrons reaches 112.

Other irregularities in the region of large masses are less impressive and not so firmly established. The uncertainty of the relative abundances of the rare-earth elements makes it impossible to determine quantitatively the irregularity which, apparently, occurs in the region of \(A\) equal to 170, and to clarify the question of what configuration can be correlatively connected with the fact that the abundance values of hafnium isotopes with odd \(A\) do not correspond to the general trend of the abundance curve for odd \(A\). It may be noted that the sum rule is not obeyed at mass number 176. It would be tempting to correlate the long lifetime of natural \(Lu^{176}\) with this irregularity, but no acceptable basis can be proposed for such a connection.

Contrary to the widespread opinion, in the distribution of abundances one cannot detect any traces of such effects as could be unambiguously ascribed to completed proton shells.

Mass region \(70 < A < 90\)

From what was said in the preceding paragraph it may be concluded that in the region \(A > 90\) the greater part of nuclear matter must have been formed on the neutron-enriched side of the energy valley, and only a small fraction, of the order of \(1\%\), could have formed on the neutron-deficient \(\beta^+\)-side. In the following paragraph it is shown that the opposite situation is evidently valid for the region of light elements with mass numbers \(A < 70\), where the main mass of nuclear matter must have been formed in the form of \(\beta^+\)-active nuclides with a deficiency of neutrons. Proceeding from this, it would be reasonable to suspect that there must exist an intermediate region of mass numbers where nuclei were formed directly in the region

stable types of nuclei near the bottom of the energy trough. If, for example, it is assumed that the final abundance distribution was determined by the two opposing reactions considered above in such a way that at a later stage of development one reaction (“neutron formation”) predominated in the region of large masses, while the opposite reaction predominated in the region of small masses, then the abundance in the region of intermediate masses should reflect equilibrium conditions to a greater degree than the abundance in other mass regions. This, apparently, is what is found in the empirical abundance data. The abundances of odd \(A\) in the range of values \(A\) from 57 to 87 fall on a smooth curve. However, the abundances of even \(A\) exhibit strange, irregular behavior, and the rule of the sums of isobar abundances is clearly not obeyed. However, if the abundance values for nuclei with the same neutron excess are joined in the figure, another type of regularity immediately appears. In this case smooth curves are obtained. In the regions between closed shells the binding energy will be a smooth function of mass number for nuclei with the same neutron excess; therefore the smoothness of this configuration may serve as an indication of an internal connection between binding energy and the cosmic abundance of nuclei in this mass interval. An estimate of the temperature determining this connection gives a value of \(kT\) of the order of 1 MeV.

The fact that the abundance curve for odd \(A\) does not reveal an explicit correlation between abundances and neutron excess is not surprising, because the fraction of \(\beta\)-unstable isobars in the final abundances of stable nuclei is much larger in the case of odd mass numbers than in the case of even ones. In addition, small irregularities on the abundance curve of odd \(A\) could have been “smoothed out” in estimating the values of element abundances.

The iron peak and the region of small masses

The new value for the Fe/Si ratio, amounting to one third of the value accepted earlier, still leaves the abundance of \(\mathrm{Fe}^{56}\) greater than the sum of the abundances of all the other types of nuclei with mass numbers exceeding 40. No properties of the \(\mathrm{Fe}^{56}\) nucleus are known that could explain its predominance in nature. But \(\mathrm{Fe}^{56}\) is an isobar of the “doubly magic” unstable \(\mathrm{Ni}^{56}\), containing 28 protons and 28 neutrons. The expectation of a correlation between abundances and nuclear properties inevitably leads to the conclusion that \(\mathrm{Ni}^{56}\) was the primary nucleus from which \(\mathrm{Fe}^{56}\) was formed*), and that, consequently, nuclei in this mass interval were formed on that side of the energy trough where there is a deficiency of neutrons. The half-life of \(\mathrm{Ni}^{56}\), which is transformed by \(K\)-capture into \(\mathrm{Co}^{56}\) (80 d), has recently been determined as 6.5 days [Shellin and Stoughton\(^{83}\) and Worthington\(^{102}\)]. Consequently, the process leading to the excess abundance of mass 56 could not have lasted more than several days.

Together with Fe, the elements Cr, Ti, and Ca also exhibit an excessively large abundance of isotopes with the number of excess neutrons \(I(=2N-A)\) equal to 4. This may be regarded as an indication that throughout this mass interval nuclei with zero neutron excess \((N=Z)\) were first formed, and then decayed, turning into their isobars with \(I\) equal to 4. In general, nuclei with \(N=Z\) apparently possess a greater binding energy than that which would correspond to an ideally parabolic

* This idea was first expressed to one of the authors by Haxel in 1946 and was cited by Suess (1948) as a private communication.

in the energy trough, and this makes plausible a large initial abundance*). The fact that the abundance distribution was in fact established in less than a day is proved by the half-life of Fe$^{52}$, equal to 7.8 hours, as a result of which Fe$^{52}$ is transformed into Cr$^{52}$.

Undoubtedly, for $N = 8, 14$ and 20 magic-number effects are present, although the uncertainty in the abundance values and the rapid change of abundance with mass number in this interval somewhat obscure the character of these effects. The increased abundance of the nuclei Mg$^{30}$ and A$^{38}$ with $I$ equal to 2 indicates effects of shell closure of nuclei at $N$ equal to 12 and 20, respectively.

Harkins’ rule and the abundances of nuclei with odd $A$

According to Mattauch’s law, for each odd mass number there is only one stable isobar. But for every odd mass number exceeding 32 there exists at least one unstable isobar with a half-life greater than a day, i.e., with a half-life long in comparison with the time of establishment of the mass distribution. Obviously, in the case of odd mass numbers unstable isobars should, on the average, have participated to a relatively greater extent in the abundance of stable nuclei than in the case of even mass numbers. Hence one can understand why the abundance curve for odd $A$ is much smoother than the curve for even $A$. In other respects the difference between the abundances of even and odd nuclei can be only qualitative.

As follows from Harkins’ rule, there is always one isobar with even $A$ and with an abundance exceeding the geometric mean of the corresponding neighboring isobars with odd $A$. The difference in the abundances of elements with even and odd $A$, i.e. the even–odd effect of abundances, decreases with increasing mass numbers and disappears for several mass numbers near $A = 170$ and 190.

The even–odd effect of abundances, expressed by Harkins’ rule, cannot be a simple consequence of the difference in binding energies of nuclei with even and odd $A$, as had been assumed for many years. This effect does not follow from the theory of element formation by neutron capture; however, by introducing a number of refinements and additional assumptions, it is possible to explain this effect satisfactorily within the framework of the capture theory. Thus, for example, the rate of processes in a series of $\beta$-decays is on average somewhat greater for odd than for even mass numbers, so that nuclei with odd $A$, formed on the neutron-enriched slope of the energy trough, will decay, transforming into nuclei with a smaller neutron excess, somewhat faster than nuclei with even $A$. The neutron-capture cross section depends on the neutron excess and, for a given mass number, will be the larger the smaller the neutron excess; thus nuclei with odd $A$ will, by neutron capture, be transformed into even isotopes of the nearest larger mass number at a somewhat greater rate than even nuclei into odd ones.

Discussion of the general picture of the abundance distribution could be considerably continued. However, we hope that the points noted here will ultimately lead to an improvement of the theoretical basis and of the cosmological model, which in turn will facilitate the interpretation of the empirical features of the distribution of cosmic nuclear abundance.

*) See Blatt and Weisskopf, Theoretical Nuclear Physics, IL, 1951. The theoretically “symmetric” energy leads to two parabolas intersecting at $N = Z$.

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