it goes without saying that here one can speak only of the spectroscopic method of studying isotopes in stellar atmospheres. As is known, different isotopes of one and the same element are chemically completely identical, and therefore their spectra are also completely the same. However, because the nuclear masses of isotopes of one and the same element differ by one, two, or more neutrons, the spectra of the different isotopes of a given element will be shifted relative to one another by a very small amount; moreover, the lighter the element, the greater this isotopic shift will be. The maximum effect will obviously be for hydrogen, where for H\(_2\) it reaches a considerable value—1.2 Å. Under present instrumental conditions it has not yet been possible to detect isotopes from the atomic spectra of stars. Such attempts, however, have not been made, which can hardly be justified. Perhaps even now it would be possible to observe the atomic spectrum of heavy hydrogen—deuterium—if its relative concentration were not too small. In the future, it may be possible to detect the atomic spectra of isotopes of the lightest elements.

However, isotopes are much easier to detect from molecular than from atomic spectra. At the same time it is obvious that the smaller the difference between the masses of the components of a molecule and the smaller their mass, the greater the vibrational part of the isotopic shift will be. This is evident from the fact that the isotope effect is determined by the ratio of the reduced masses of the ordinary and heavy molecules or atoms:

\[ \Delta v=(p-1)(\omega'_e u' - \omega''_e u'')-(p^2-1)(x'_e\omega'_e u'^2-x''_e\omega''_e u''^2)+\ldots, \]

where

\[ u=v+\frac{1}{2}, \qquad p=\sqrt{\frac{MM'}{M+M'}}:\sqrt{\frac{MM'_1}{M+M'_1}} . \]

Twenty years ago Sanford and Menzel\(^1\) first suggested that two rather prominent bands in the spectra of the so-called carbon stars of classes N and R could be identified with bands of the heavy carbon molecule, which had just been discovered in the laboratory by King and Birge\(^2\). This was the first indication of the presence of isotopes in stars. However, in the spectra of cool stars, rich in numerous molecular bands, an identification based on two bands is always unreliable, since it may be the result of a chance coincidence.

Indeed, this result was largely forgotten for a decade until 1939–1940, when the Simeiz Observatory began to study this problem. Although our instrumental resources were modest, already in 1940 we could rather confidently

could detect in the spectra of carbon stars not two bands of the heavy carbon molecule, but 12 bands[^3], adding to the two known bands ten previously unknown bands of the heavy molecules \(C^{13}C^{12}\) and \(C^{13}C^{13}\). The result should have seemed convincing, because the identification was based not only on satisfactory agreement in wavelengths between observation and calculation. We were able to detect new bands for different sequences on different sides of the zero sequence and to obtain isotopic shifts of different signs on both sides of the zero sequence. Thus, a considerable number of new bands, agreement with theory with respect to the absolute value and sign of the isotopic shift, and also satisfactory agreement with respect to the expected course of the band intensities of the ordinary and heavy molecules gave what was already quite convincing evidence in favor of the presence of the isotope \(C^{13}\) in the atmospheres of carbon stars.

Another result on which we insisted in the first paper was the assertion that the concentration of \(C^{13}\) relative to \(C^{12}\) varies within wide limits from 0.05 to 0.50, at its maximum exceeding, in individual stars, by almost 40 times the value following from laboratory determinations of the effective cross sections for the capture of protons by the nuclei \(C^{12}\) and \(C^{13}\), and also the value of the concentration of \(C^{13}\) observed on the Earth[^3]. In the first paper we investigated the sequences \(+1\), \(-1\), \(-2\). In order to judge how reliable our observational material may be considered, we give here, for illustration, in Figs. 1 and 2, photographs of small regions of the spectrum covering the sequences \(-1\) and \(-2\). Arrows indicate the positions of the ordinary and heavy molecules \(C^{12}C^{12}\), \(C^{12}C^{13}\), and \(C^{13}C^{13}\).

After the appearance of this work, papers on isotopes in stellar atmospheres began to appear in America, Canada, and France[^4]. In turn, we also continued the work and over the course of a number of recent years were able significantly to expand the results obtained by us. We were able to find evidence in favor of the presence not only of the heavy carbon molecules \(C^{13}C^{12}\) and \(C^{13}C^{13}\), but also of the heavy cyanogen molecule \(C^{13}N^{14}\) for the violet system \({}^{2}\Sigma \to {}^{2}\Sigma\), and also, earlier than others, to find a very considerable number of new bands of the heavy cyanogen molecule for the red system \({}^{2}\Pi \to {}^{2}\Sigma\)[^5]. For these systems the number of new bands found by us already ran into the dozens. For illustration we give Fig. 3, which presents a photograph and a microphotogram obtained in Simeiz for the bands \(C^{13}N^{14}\) and \(C^{12}N^{14}\) (3.0 and 4.1) in the red-infrared region of the spectrum. The doubleness of the bands is expressed here quite distinctly, and there is no doubt that, alongside the bands of the ordinary cyanogen molecule \(C^{12}N^{14}\), we have here bands of the heavy cyanogen molecule \(C^{13}N^{14}\)[^6].

On the basis of abundant observational material it was possible to arrive at the firm conclusion that the isotope \(C^{13}\) is not only present in the atmospheres of carbon stars, but that it is sometimes present in a quite unexpectedly large concentration.

Fig. 1. Spectra of class N stars in the region of the Swan bands (sequence \(-1\)). The arrows indicate the positions of the bands \(C^{12}C^{13}\), \(C^{13}C^{12}\), \(C^{13}C^{13}\), \(C^{13}\) being especially abundant in Y. Can. Ven.

Fig. 2. Spectrum of RJ Draconis in the region of the Swan bands (sequence \(-2\)).

As a result of work carried out at several large observatories over the last 6–7 years, the unexpected result—one that had seemed incredible—of a very high relative concentration of the heavy isotope \(C^{13}\) was confirmed. At first this seemed improbable, and this circumstance was the reason for such interest in the isotopes.

But this result was not immediately accepted. In one physics journal doubt was expressed as to its reality. However, after both McKellar and Herzberg, on the basis of different

Fig. 3. Spectrum and microphotogram of J Canum Venaticorum in the region of the cyanogen bands.

material, also found in some carbon stars a very high concentration of \(C^{13}\), all doubts had to fall away. In the end the generally accepted point of view became that in some carbon stars the concentration reaches at least 0.35.

This result should have embarrassed physicists, who had found from measurements of the effective cross sections of the nuclei of carbon isotopes a value of \(C^{13}:C^{12}\) at least 20 times smaller. This result also contradicts what is observed on Earth (the ratio of the concentrations of \(C^{13}\) and \(C^{12}\) is close to \(1:90\)). This result was also in contradiction with the ratio \(C^{13}:C^{12}\) adopted for stellar interiors by Bethe in his thermonuclear hypothesis concerning the sources of the energy of the stars and the Sun. Thus, in this problem of such fundamental importance, very serious contradictions were revealed.

It is therefore not surprising that, in connection with this contradiction, and also in order to test Bethe’s hypothesis, quite recently, already in 1950, in the radiation laboratory of the California Institute of Technology, Hall and Fowler carried out experimental work on determining the effective cross section for the radioactive capture of protons by carbon nuclei at an energy of about 100 kev—in conditions already more closely approximating those that occur inside stars. As a result, these authors, quite unexpectedly, obtained for the effective cross section of \(C^{12}\) nuclei a value many times larger than had previously been found.\(^1\) Passing from these new values of the capture cross section to the ratio \(C^{13}:C^{12}\) that interests us, we obtain a value close to 0.15 or even 0.20. Such a relative concentration of \(C^{13}\) is approximately 10–15 times greater than what is observed on Earth and what Bethe had adopted for stellar interiors, and is only 2–3 times less than what we found at the maximum in the atmospheres of carbon stars. This radically changes the situation, provided that there is no error in the experiment mentioned.

Thus, it is now no longer the result for carbon stars that appears incomprehensible from the physical point of view; rather, the very small relative concentration of the heavy isotope \(C^{13}\) on Earth becomes incomprehensible. At the same time, that part of Bethe’s hypothesis which concerns the former estimate of the ratio \(C^{13}:C^{12}\) in the interiors of stars and the Sun must be revised.

In the light of the results obtained above, the fact of the very small relative concentration of \(C^{13}\) on Earth stands out especially clearly. When, in our first paper, we found a very large concentration of \(C^{13}\) in the atmospheres of carbon stars, we, emphasizing the extreme discrepancy with the concentration of \(C^{13}\) on Earth, attempted to make a rough estimate of at least the upper limit of the concentration of \(C^{13}\) in the solar atmosphere. This was done by us in our paper,\(^3\) where we used for this purpose Rowland’s tables of wavelengths. An analysis of the wavelengths of weak lines in the region of the location of the \((0,0)\) band of the carbon molecule, as well as of the cyanogen molecule, made it completely clear that the isotopic components of the rotational structure are not detected in the spectrum of the Sun. From this was

a reliable conclusion was drawn that the concentration of the molecule $C^{13}$ is in any case much less than 0.1. In February 1950, after 8 years, similar work was repeated on Mount Wilson, and three authors—Greenstein, Richardson, and Schwarzschild—came to the same conclusion, that in the solar spectrum the band lines of the heavy molecule $C^{13}N^{14}$ are practically not observed. These authors also try to estimate the upper limit of the ratio $C^{13}:C^{12}$ and find that it is less than $1:36$.

Thus, we must come to the conclusion that in the solar atmosphere the concentration of $C^{13}$ is very small and, perhaps, approaches the terrestrial value (about $1:90$).

On the other hand, the concentration of $C^{13}$ is found to be very large in the atmospheres of the so-called carbon stars, and must also be large in the interiors of stars, if one proceeds from the new laboratory determinations of the effective cross sections for the capture of protons by carbon nuclei. Thus, the problem seems to have entered a new phase. Now the non-carbon stars stand quite apart, since the value of $C^{13}:C^{12}$ may already not differ so strongly from what the laboratory data give for the nuclear reaction $C^{12}(p,\gamma)$. In order to preserve Bethe’s hypothesis on the source of energy for the Sun, there remains the alternative: the observed relative concentration of the heavy isotope $C^{13}$ in the solar atmosphere (of the order of 1–2%) differs very strongly from the relative concentration of the heavy isotope $C^{13}$ (of the order of 20%) in the interior of the Sun. The significance of this result for cosmogony and for the problem of the internal structure of stars cannot be underestimated.

This work may serve as an illustration of useful and effective cooperation even between observational astrophysics and experimental nuclear physics. In the example given, we saw how results obtained in astrophysics forced physicists to reconsider earlier results and to obtain new ones, very different from the former. Taking into account the extremely great consequences of a fundamental character that follow from the acceptance of one or another result in this field, we are entitled to expect that experimental determinations of the effective cross sections for the capture of protons by carbon nuclei will be repeated. One may also hope that, in connection with the great astrophysical interest in Bethe’s cyclic scheme, physicists may try to test experimentally not only its first link.

At the same time, astrophysicists must devote ever greater attention to the problem of isotopes in astrophysics. As we have seen, isotope spectroscopy in astrophysics can have a fairly reliable basis. The determination of isotope concentrations in stellar atmospheres and other investigations connected with isotopes evidently constitute an interesting and, in essence, new field of research for certain astrophysical problems of great fundamental significance.

References

1. Sanford, Menzel, Publ. Astron. Soc. Pacific. 41, 271 (1929); 42, 34 (1930).
2. Birge, King, Astroph. J. 72, 19 (1930).
3. G. Shain, Vestnik AN SSSR No. 10, 52 (1940); Bull. Abastum. Observ. No. 6, 1 (1942).
4. McKellar, Publ. Astron. Soc. Pacific 59, 186 (1947); 61, 34 (1949); 61, 199 (1949); 62, 110 (1950).
5. G. A. Shain, V. F. Gaze, Izvest. Crimean Astrophys. Observ. 2, 131 (1948).
6. G. A. Shain, V. F. Gaze, Izvest. Crimean Astrophys. Observ. 5, 24 (1950).
7. Hall, Fowler, Phys. Rev. 77, 197 (1950).
8. Grunstein, Richardson, Schwarzchild, Publ. Astron. Soc. Pacific 62, 15 (1950).