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The History and Impact of the CNO Cycles in Nuclear Astrophysics


The carbon cycle, or Bethe-Weizsäcker cycle, plays an important role in astrophysics as one of the most important energy sources for quiescent and explosive hydrogen burning in stars. This paper presents the intellectual and historical background of the idea of the correlation between stellar energy production and the synthesis of the chemical elements in stars on the example of this cycle. In particular, it addresses the contributions of Carl Friedrich von Weizsäcker and Hans Bethe, who provided the first predictions of the carbon cycle. Further, the experimental verification of the predicted process as it developed over the following decades is discussed, as well as the extension of the initial carbon cycle to the carbon-nitrogen-oxygen (CNO) multi-cycles and the hot CNO cycles. This development emerged from the detailed experimental studies of the associated nuclear reactions over more than seven decades. Finally, the impact of the experimental and theoretical results on our present understanding of hydrogen burning in different stellar environments is presented, as well as the impact on our understanding of the chemical evolution of our universe.

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  1. The modern terminology for nuclear reactions follows the scheme A(a,b)B, with A being the target nucleus, a the projectile, b the reaction product, and B the nuclear recoil nucleus.


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  9. Hufbauer, “Stellar-Energy Problem” (ref. 3).

  10. Archbishop James Ussher calculated the age of the world by summing the ages of the biblical figures in the genesis.

  11. Eddington, “Internal Constitution of Stars” (ref. 8).

  12. Eddington, “Internal Constitution of Stars” (ref. 8).

  13. Robert E. Atkinson and Fritz G. Houtermans, “Zur Frage der Aufbaumöglichkeit der Elemente in Sternen,” Zeitschrift für Physik 54 (1929), 656–65.

  14. George Gamow, “Zur Quantentheorie des Atomkernes,” Zeitschrift für Physik 51 (1928), 204–12.

  15. Carl Friedrich von Weizsäcker, Die Atomkerne, Grundlagen und Anwendungen ihrer Theorie (Leipzig: Akademische Verlagsgesellschaft, 1937), 163–66.

  16. Weizsäcker, “Die Atomkerne” (ref. 15).

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  25. Weizsäcker in his 1978 interview with Karl Hufbauer ( remains somewhat ambivalent in this point: “The things I remember are quite limited. At that time I had the idea of the carbon cycle, and I felt that this was the solution, and Gamow came and told me that Bethe had probably found the solution to the problem and that it was the carbon cycle. Then I said, ‘Well, I think he’s right, I found it too,’ and my paper at that time was perhaps already in print, I don’t remember. In any case, I felt that I had already done it and submitted it for print. But on the other hand, it was very good if Bethe had done it too, and it was not the first time I had done something parallel with Bethe. It had been the same thing with the mass-defect formula for the atomic nuclei, of which I spoke before. Then I felt that at least he should tell Bethe that I had done it. And I might even have written a letter to Bethe about that. But since Bethe didn’t have it, perhaps I didn’t. Perhaps I asked Gamow to tell him. Then I was a little bit disturbed by the fact that Bethe’s paper didn’t appear earlier—because it was delayed, because it was submitted for some Festschrift—because that gave the impression that I had true priority, while I would say that we were just independent.” The two known letters of Weizsäcker to Bethe from September 30, 1936, and September 24, 1937, respectively are mainly concerned with nuclear physics questions related to his first hypothesis, in particular the question of the possible existence or longevity of 4H, 4Li, 5He, and 5Li, which was of existential importance for his theory of element formation.

  26. Hans A. Bethe and Charles L. Critchfield, “The Formation of Deuterons by Proton Combination,” Physical Review 54 (1938), 248–54.

  27. In modern nuclear physics terminology, this reaction sequence would be formulated as: 12C(p,γ)13N(β + ν)13C(p,γ)14N(p,γ)15O(β + ν)15N(p,α)12C.

  28. Weizsäcker, “Über Elementumwandlungen II” (ref. 11), 639.

  29. Weizsäcker, “Über Elementumwandlungen II” (ref. 11), 639.

  30. Karl Hufbauer does not agree with this thesis. On the basis of Weizsäcker’s statements in the 1978 interview (, he believes that between January and May 1938, Weizsäcker came independently to the realization that the structural hypothesis is untenable and must be replaced by an alternative process, such as the carbon cycle. Karl Hufbauer, “Stellar Structure and Evolution 1924–1939,” Journal for the History of Astronomy 37 (2006), 203–27.

  31. Carl Friedrich von Weizsäcker, “Über die Entstehung des Planetensystems,” Zeitschrift für Astrophysik 22 (1943), 319–55.

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  33. Subrahmanyan Chandrasekhar, An Introduction to the Study of Stellar Structure (1958; New York: Dover, 1967), 468–86.

  34. Strömgren stayed only for two years at Yerkes. In 1939 he was offered a professorship in Copenhagen and spent the following years there. He maintained scientific connections with his German counterparts and was the only Danish scientist to take part in the DPG meeting in Copenhagen in 1941 to meet his former friends Heisenberg and Weizsäcker.

  35. Teller stayed there until 1941 and was then recruited by Bethe to Los Alamos to participate in the Manhattan Project. After the war in 1949 he instigated and supervised the development of the hydrogen bomb at the newly founded Livermore National Laboratory.

  36. This was a second article of a three-part series of works that Bethe had published in the 1930s. Following the example of Weizsäcker’s monograph Der Atomkern, Bethe wanted to summarize in this series all the knowledge on the physics of atomic nuclei. Still famous today, this work is referred to as the “Bethe Bible.” Hans Bethe, “Nuclear Physics B. Nuclear Dynamics, Theoretical,” Review of Modern Physics 9 (1937), 69–246.

  37. Sylvan S. Schweber, “The Happy Thirties,” in Hans Bethe and His Physics, ed. Gerald E. Brown and Chang-Hwan Lee, 131–45 (Singapore: World Scientific, 2006).

  38. George Gamow, My World Line (New York: Viking, 1970), 136.

  39. Sylvan S. Schweber, Nuclear Forces: The Making of the Physicist Hans Bethe (Cambridge, MA: Harvard University Press, 2012), 315–60.

  40. George Gamow, The Birth and Death of the Sun (New York: Viking, 1940), 112–13.

  41. Hans A. Bethe, “My Life in Astrophysics,” in Hans Bethe (ref. 37), 22–47.

  42. Neutrinos had been postulated by Wolfgang Pauli (1900–1958) as early as 1930, but found their way into astrophysics only after the war.

  43. Bethe and Critchfield, “Formation of Deuterons” (ref. 26).

  44. Hans A. Bethe and Robert E. Marshak, “The Physics of Stellar Interiors and Stellar Evolution,” Reports on Progress in Physics 6 (1939), 1–15.

  45. Hans A. Bethe, “Energy Production in Stars,” Physical Review 55 (1939), 434–56.

  46. Karl Hufbauer, “Stellar Structure and Evolution, 1924–1939,” Journal for the History of Astronomy 37, no. 2 (2006), 203–22, and Giora Shaviv, The Life of Stars: The Controversial Inception and Emergence of the Theory of Stellar Structure (Heidelberg: Springer, 2009).

  47. Even today there is no experimental confirmation of the p + p fusion rate; the cross section is simply too low. However, it is argued that the theory of weak interaction is sufficiently known, and the last calculation of the rate of Bahcall is reliable. Measurements of the solar neutrinos generated by the p + p reaction in the sun are indeed in agreement with the theoretically calculated rate within the framework of the standard solar model. Marc Kamionkowski and John N. Bahcall, “The Rate of the Proton-Proton Reaction,” The Astrophysical Journal 420 (1994), 884–91.

  48. In modern nuclear physics terminology, these reactions would be formulated as: 2H(p,γ)3He; 2H(p,n)21H, 2H(d,p)3H; 2H(d,γ)4He.

  49. In modern nuclear physics terminology, this is formulated as: 1H(p,νγ)2H; 2H(p,γ)3He; and 3He(τ,2p)4He.

  50. Edwin E. Salpeter, “Energy Production in Stars,” Annual Review of Nuclear Science 2 (1953), 41–62.

  51. Bethe, “Nuclear Physics, B” (ref. 36).

  52. Hans A. Bethe, “Recent Evidence on the Nuclear Reactions in the Carbon Cycle,” Astrophysical Journal 92 (1940), 118–21.

  53. The principle of the electrostatic accelerator was well known and was based on the technique of generating a high potential for an electrically isolated ion source by charge transport on a rubber band. The charged particles were accelerated over the potential difference between the ion source and the target region. Merle Tuve at the Carnegie Institute experimented with such machines at an early stage. With the introduction of the high-pressure tank by Ray Herb at Wisconsin, far higher potential differences and thus particle energies could be generated than with machines operating under atmospheric conditions. While he obtained a first patent, the primacy of the invention by Van de Graff is therefore controversial.

  54. Marshall G. Hollowell, Hans, A. Bethe, “Cross Section on the Reaction 15N(p,α)12C,” Physical Review 57 (1940), 747–47.

  55. Raymond G. Herb, D. B. Parkinson, and D. W. Kerst, “A Van de Graaff Electrostatic Generator Operating Under High Air Pressure,” Review of Scientific Instruments 6 (1935), 261–65.

  56. Tom Lauritsen, Charles C. Lauritsen, William A. Fowler, “Application of a Pressure Electrostatic Generator to the Transmutation of Light Elements by Protons,” Physical Review 59 (1941), 241–52.

  57. A more detailed account of the development of experimental nuclear astrophysics at Caltech is given by: John L. Greenberg and Judith R. Goldstein, “The Origins of Nuclear Astrophysics at Caltech,” History of Science Annual Meeting, Norwalk, October 29, 1983, HumsWP-0097.

  58. The role of nuclear physicists in the Manhattan project has been extensively discussed in the literature on the history of science. Notably is the book of Robert Jungk, published in Germany in 1955, Brighter than a Thousand Suns, Robert Jungk, Heller als tausend Sonnen: Das Schicksal der Atomforscher (Bern: Scherz Verlag 1956), as well as a more recent book by Richard Rhodes, The Making of the Atomic Bomb (New York: Simon and Schuster, 1986).

  59. William A. Fowler, Charles Lauritsen, and Tom Lauritsen, “Gamma-Radiation from Excited States of Light Nuclei,” Review of Modern Physics 20 (1948), 236–77.

  60. This information, to the extent that it did not remain classified, has been partially published in the so-called Manhattan Nuclear Energy Series (Manhattan Project Technical Section), which for years have been an important source of various experimental techniques.

  61. William A. Fowler, “Experimental and Theoretical Results on Nuclear Reactions in Stars,” in Les Processus Nucléaires dans les Astres, Communications présentées au cinquième Colloque International d’Astrophysique tenu à Liège les 10–12 Septembre, 1953, ed. Geert Ceuterick, Mémoires de la Société Royale des Sciences de Liège 14, 88–112 (Louvain: Société royale des sciences de Liège, 1954).

  62. William A. Fowler, George R. Burbidge, and E. Margaret Burbidge, “Stellar Evolution and the Synthesis of the Elements,” Astrophysical Journal 122 (1955), 271–85.

  63. This work reflects the original concept of the structural hypothesis on the origin of the heavy elements by Weizsäcker, which, however, has not been cited in either this or in other Anglo-Saxon work.

  64. George R. Burbidge, E. Margaret Burbidge, William A. Fowler, and Fred Hoyle, “Synthesis of the Elements in Stars,” Review of Modern Physics 29 (1957), 547–650.

  65. At the same time, a young Canadian physicist, Al Cameron (1925–2005), published his work in Chalk River as a report of the Atomic Energy of Canada Limited. Albert G. W. Cameron, Stellar Evolution, Nuclear Astrophysics, and Nucleogenesis, 2nd ed., AECL-454 (Chalk River, Ontario: Atomic Energy of Canada Limited, 1957),

  66. Fowler, “Nuclear Reactions in Stars” (ref. 61).

  67. Edwin E. Salpeter, “Nuclear Reactions in Stars. II. Protons on Light Nuclei,” Physical Review 97 (1955), 1237–44.

  68. Claus R. Rolfs, “Spectroscopic Factors from Radiative Capture Reactions,” Nuclear Physics A 217 (1973), 29–70.

  69. In modern terminology: 17O(p,γ)18F(β + ν)18O(p,α)15N.

  70. Claus R. Rolfs and William S. Rodney, “Proton Capture by 15N at Stellar Energies,” Astrophysical Journal Letters 194 (1974), L63–L66.

  71. In modern terminology: 18O(p,γ)19F(p,α)16O.

  72. Michael Wiescher, H. W. Becker, J. Görres, K.-U. Kettner, H. P. Trautvetter, W. E. Kieser, C. Rolfs, R. E. Azuma, et al., “Nuclear and Astrophysical Aspects of 18O(p,γ)19F,” Nuclear Physics A 349 (1980), 165–216.

  73. David Dearborn and David N. Schramm, “CNO Tri-Cycling as an 17O Enrichment Mechanism,” Astrophysical Journal Letters 194 (1974), L67–L70.

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  77. Michael Wiescher, Joachim Görres and Hendrik Schatz, “The Hot and Cold CNO Cycles,” Annual Review of Nuclear and Particle Science 60 (2010), 381–404.

  78. The astronomers define metallicity as the fraction of all elements with masses above helium in the elemental abundance distribution of stars. Looking at the solar element abundance distribution, the metallicity essentially refers to the abundance of CNO elements.

  79. Wiescher, Görres, and Schatz, “Hot and Cold CNO” (ref. 78).

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  82. Wick C. Haxton, R. G. Hamish Robertson, and Aldo M. Serenelli, “Solar Neutrinos: Status and Prospects,” Annual Review of Astronomy and Astrophysics 51 (2013), 21–61.

  83. These detectors measured also geothermal neutrinos, which are generated by radioactive decay processes in the earth itself. This is a direct proof of the long-term high radioactivity of the earth’s interior.

  84. Wick C. Haxton and Aldo M. Serenelli, “CN Cycle Solar Neutrinos and the Sun’s Primordial Core Metallicity,” The Astrophysical Journal 687 (2008), 678–91.

  85. Wiescher, Görres, and Schatz, “Hot and Cold CNO” (ref. 78).

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  87. John N. Bahcall, “Solar Models: An Historical Overview,” Nuclear Physics B 118 (2003), 22–86.

  88. Preparations for such measurements are currently being made at the Italian-American Borexino detector located in a highway tunnel under the Gran Sasso massif in the Apennines and at the Canadian SNO detector in Sudbury Mine, Ontario.

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  101. Cosmic ray–induced radiation is a dominant background component over the entire energy range in of γ ray detectors that are being used in low energy reaction studies. Further components are the low-energy γ radiation resulting from the natural decay processes in materials, as well as the γ radiation, which is generated by nuclear reactions to target impurities in the experiment.

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  111. This metaphor of dwarfs standing on the shoulders of giants has been traced to the twelfth century, attributed to Bernard of Chartres. Isaac Newton used it in 1676 in a letter to Robert Hooke: “If I have seen further, it is by standing on the shoulders of giants,” Digital Library,

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This article is based on a presentation the author gave at the symposium in honor of the 100th birthday of Carl Friedrich von Weizsäcker, and was published in German, in the Proceedings of the Leopoldina Academy.112 This is a revised and extended version for the English-speaking audience. My special gratitude goes to Professor Karl Hufbauer for helpful discussions and his willingness to provide unpublished work and information on the history of the power generation in stars. Thanks also to Joachim Görres and Karl-Ulrich Kettner for multiple discussions of the topic and for bringing up useful information and memories on earlier days of experimental study of CNO and NeNa reactions.

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Correspondence to Michael Wiescher.

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Michael Wiescher is the Freimann Professor of Physics in the Department of Physics, University of Notre Dame.

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Wiescher, M. The History and Impact of the CNO Cycles in Nuclear Astrophysics. Phys. Perspect. 20, 124–158 (2018).

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