Skip to main content

How Nature Overcomes Its Own Barriers

  • Chapter
  • First Online:
The Synthesis of the Elements

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 387))

  • 1661 Accesses

Abstract

FigureĀ 8.1 shows the light nuclei arranged in the \((Z,N)\) plane, where \(Z\) is the number of protons and \(N\) the number of neutrons. We see that there are no stable nuclei for \(A=Z+N=5\) and \(A=Z+N=8\). This means that hydrogen cannot fuse with helium to form any \(A=5\) nucleus and helium cannot fuse with another helium to form an \(A=8\) nucleus. These are the \(A=5\) and 8 nuclear barriers. But we know that the nuclei heavier than helium are synthesized. So how does this come about?

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    von Weizsacker, C.F., Astrophys. J. 114, 165 (1951).

  2. 2.

    Jordan, P., Die herkunft der Sterne, 1947, p. 38.

  3. 3.

    Richardson, R.S. and Schwarzschild, M., Astrophys. J. 108, 373 (1948); Gamow, G. and Teller, E., Phys. Rev. 55, 791 (1939); Gamow, G. and Keller, G., Rev. Mod. Phys. 17, 125 (1945); Gamow, G. Phys. Rev. 67, 120 (1945).

  4. 4.

    Chandrasekhar, S., MNRAS 95, 207, 226, 676 (1935).

  5. 5.

    Nuclear densities are densities at which the nuclei touch each other. The radius of the nucleus is about \(10^{-5}\) times the radius of the atom, taking the latter to be the radius of the outer occupied electronic shells. The atom has an infinite number of electronic shells with radius increasing to infinity. But as the number of electrons in each atom is finite, they occupy only the lowest energy levels and for this reason any particular atom has a finite radius, the radius of the highest occupied level. Normal matter densities on the Earth are \({\sim }1\,\mathrm{ g/cm}^{3}\). If the matter is compressed to densities as high as \(10^{15}\,\mathrm{ g/cm}^{3}\), the nuclei touch each other and form one gigantic nucleus. This is nuclear matter.

  6. 6.

    Gamow. G., Rev. Mod. Phys. 21, 367 (1949).

  7. 7.

    Gamow, G., The Creation of the Universe, Viking press, New York, 1952.

  8. 8.

    Harkins, W.D., J. Am. Chem. Soc. 39, 856 (1917); Phys. Rev. 15, 85 (1920).

  9. 9.

    Lauritsen C.C. and Crane, H.R., PRL 46, 537 (1934).

  10. 10.

    Feenberg, E., Phys. Rev. 49, 328 (1936).

  11. 11.

    Crane, H.R., Delsasso, L.A., Fowler, W.A., and Lauritsen, C.C., Phys. Rev. 48, 100, 102, 125 (1935).

  12. 12.

    Margenau, H., PRL 53, 198 (1938).

  13. 13.

    Rutherford, E., Proc. Roy. Soc. A131, 684 (1931); Rutherford, E., Lewis, W.B., and Bowden, B.V., Proc. Roy. Soc. A142, 347 (1933).

  14. 14.

    Gamow, G., Nature 131, 433 (1933).

  15. 15.

    Wilson, H.A., PRL 44, 858 (1934).

  16. 16.

    Glƶckle, W., and Kamada, H., PRL 71, 971 (1993). See also Nogga, A., Kamada, H., Glƶckle, W., and Barrett, B.R., arXiv:nucl-th/0112026v2, 28 May 2002.

  17. 17.

    In Jensen, J.H.D., in Nobel Foundation, Nobel Lectures 4, Physics, 1963ā€“1970, Elsevier, Amsterdam, 1972.

  18. 18.

    Mang, H.J., Phys. Rev. 119, 1069 (1960).

  19. 19.

    Lewis, G.N., Livingston, M.S., and Lawrence, E.O., PRL 44, 55 (1933).

  20. 20.

    Lawrence, E.O., McMillan, E., and Henderson, M.C., Phys. Rev. 47, 273 (1935).

  21. 21.

    Bothe, W., and Becker, H., Zeits. f. Physik 76, 421 (1932).

  22. 22.

    Crane, H.R., and Lauritsen, C.C., Phys. Rev. 45, 497 (1934).

  23. 23.

    Crane, H.R., Delsasso, L.A., Fowler, and Lauritsen, C.C., Phys. Rev. 46, 1109 (1934).

  24. 24.

    Bethe, H.A., Rev. Mod. Phys. 9, 69 (1937). This extensive review of nuclear physics justifiably earned the title ā€˜Betheā€™s Bibleā€™.

  25. 25.

    Gaerttner, E.R., and Pardue, L.A., Phys. Rev. 57, 386 (1940).

  26. 26.

    The relevant particles are those with energies equal to the Gamow peak, and not those with the average energy.

  27. 27.

    Holloway, M.G., and Moore, B.L., Phys. Rev. 58, 847 (1940).

  28. 28.

    Not every transition which is energetically possible actually takes place. As well as energy conservation, the transition between any two energy levels must satisfy all other conservation laws, and in particular momentum and angular momentum conservation. The selection rules tell us which transition is possible and which is forbidden owing to violation of at least one conservation law.

  29. 29.

    Guggenheimer, K.M., Heitler, H., and Powell, C.F., Proc. Roy. Soc. London A190, 196 (1947).

  30. 30.

    Gibson, W.M., Proc. Phys. Soc. London A62, 586 (1949).

  31. 31.

    Malm, R., and Buechner, W.W., Phys. Rev. 81, 519 (1951).

  32. 32.

    Terrell, J., Phys. Rev. 80, 1076 (1950).

  33. 33.

    Johnson, V.R., Phys. Rev. 86, 302 (1952).

  34. 34.

    Tollestrup, A.V., Fowler, W.A., and Lauritsen, C.C., Phys. Rev. 76, 428 (1949).

  35. 35.

    The figure in the paper has a small error. The level at 7 should be 7.1 as given in the text.

  36. 36.

    Pringle, R.W., Roulston, K.I., and Standil, S., Phys. Rev. 78, 627 (1950).

  37. 37.

    Bradford, C.E., and Bennett, W.E., Phys. Rev. 77, 753 (1950).

  38. 38.

    Shaviv, G., The Life of Stars, The Controversial Inception and Emergence of the Theory of Stellar Structure, Springer and Magnes Pub., 2009.

  39. 39.

    Miller, C., and Cameron, A.G.W., Phys. Rev. 81, 316 (1951).

  40. 40.

    A nuclear emulsion plate is a photographic plate with a thick emulsion layer. The ionized particles ionize the grains of the emulsion and in this way leave the imprints of their track in the emulsion.

  41. 41.

    Wilkins, J.J. and Goward, F.K., Proc. Phys. Soc. 63A, 1173 (1950).

  42. 42.

    Ɩpik E. Proc. Roy. Irish Acad. A54, 49 (1951). The paper was published over a year after it was read before the Irish Academy.

  43. 43.

    If one assumes, as Ɩpik did, that the stars in a given location of the HR diagram are burning helium, then the number of stars in this location relative to their number along the main sequence is a good estimate of the ratio of the times the stars take to consume their nuclear source.

  44. 44.

    Salpeter, E.E., when he discussed the history of nuclear astrophysics before 1957, Pub. Astron. Soc. Australia 25, 1 (2008). The Astrophysical Data System (ADS) is not very accurate with the citations, and I found two citations to Ɩpik which were not included in the ADS, for example, Dunbar et al., Phys. Rev. 92, 649 (1953). So ADS results should be treated with caution.

  45. 45.

    Wrubel, M.H., Irish AJS 10, 77 (1972).

  46. 46.

    Guier, W.H., and Roberts, J.H., Phys. Rev. 79, 719 (1950).

  47. 47.

    Guier, W.H., Bertini, H.W., and Roberts, J.H., Phys. Rev. 8, 426 (1952).

  48. 48.

    Hornyak, W.F., Lauritsen, T., Morrison, P., and Fowler, W.A., Rev. Mod. Phys. 22, 291 (1950).

  49. 49.

    Azjenberg, F. and Lauritsen, T., Rev. Mod. Phys. 24, 321 (1952), published October 1952. The authorsā€™ affiliation was with the Kellog Radiation Laboratory, CalTech. Thomas Lauritsen (1915ā€“1973) was the son of Charles Lauritsen (1892ā€“1968m) who established the Kellogg laboratory and was the director from its establishment until his retirement in 1962.

  50. 50.

    In 1950, Azjenberg and Lauritsen had the level at 7.Ā MeV and it is not clear why the level ā€˜movedā€™ half an MeV upward.

  51. 51.

    Crane, H.R., Delsasso, L.A., Fowler, W.A., and Lauritsen, C.C., Phys. Rev. 48, 100 (1935).

  52. 52.

    Salpeter, E.E., Astrophys. J. 115, 326 (1952).

  53. 53.

    Gamow, G., Phys. Rev. 53, 595 (1938).

  54. 54.

    The details of this story were checked personally with Salpeter during my stay at Cornell.

  55. 55.

    The Kellogg value was from Tollestrup, A.V., Fowler, W.A., and Lauritsen, C.C., Phys. Rev. 76, 428 (1949).

  56. 56.

    According to Salpeter in Nuclear Physics Before 1957, Fowler considered all previous reports on the existence of such a level as wrong. In this way, he disagreed with Lauritsen and Azjenberg from his own laboratory.

  57. 57.

    Carbon stars are giant stars containing a higher abundance of carbon than oxygen. In most stars the carbon abundance is lower than that of oxygen.

  58. 58.

    Ɩpik, E.J., MSRSL 1, 131 (1954), Les processus nuclĆ©aires dans les astres, Communications prĆ©sentĆ©es au cinquiĆØme Colloque International dā€™Astrophysique tenu Ć  LiĆØge les 10ā€“12 septembre.

  59. 59.

    Here Ɩpik cited Franzinetti and Payne, Nature 161, 735 (1948). These researchers investigated high energy cosmic ray induced reactions which led to the emission of \(\upalpha \) particles from the decay of \(\mathrm{ ^8Be}\), which in turn was the product of the decay of \(\mathrm{ ^8Li}\).

  60. 60.

    Ɩpik cited Carlsonā€™s result, which was the lowest of all the results. But the idea of a dynamic equilibrium, as suggested by Salpeter, is independent of the exact energy. The exact energy only slightly changes the concentration of \(\mathrm{ ^8Be}\) in equilibrium.

  61. 61.

    Burbidge, E.M., Burbidge, G.R., Fowler, W.A., and Hoyle, F., Rev. Mod. Phys. 29, 547 (1957).

  62. 62.

    Beghian, L.E., Halban, H.H., Husain, T., and Sanders, L.G., PRL 90, 1129 (1953), submitted April 1953 and published June 1953.

  63. 63.

    Hoyle, F., Astrophys. J. Suppl. 1, 121 (1954).

  64. 64.

    Salpeter, E.E., Publ. Astron. Soc. Australia 25, 1 (2008).

  65. 65.

    Hoyle, F., Dunbar, D.N.F., Wenzel, W.A., and Whaling, W., Phys. Rev. 92, 1095 (1953).

  66. 66.

    Dunbar, D.N.F., Pixley, R.E., Wenzel, W.A., and Whaling, W., Phys. Rev. 92, 649 (1953).

  67. 67.

    Hoyle, F., Astrophys. J. Suppl. 1, 121 (1954).

  68. 68.

    Hoyle, F., MNRAS 106, 343 (1946).

  69. 69.

    The anthropic principle is a philosophical claim that the Universe must be compatible with the existence of life as it is observed.

  70. 70.

    Cook, C.W., Fowler, W.A., Lauritsen, C.C., and Lauritsen, T., Phys. Rev. 107, 508 (1957).

  71. 71.

    Recall that nuclear reactions under astrophysical conditions are usually very slow because the energies are low. So \(\mathrm{ ^8Be}+\upalpha \) yielding \(^{12}\mathrm{ C}\) and decaying back to the products was hopelessly slow, and hence not observed.

  72. 72.

    Uebergang, R.G., Aust. J. Phys. 7, 279 (1954).

  73. 73.

    Steffen, K.G., Hinrichs, O., and Neuert, H., Zeit. F. Phys. 145, 156 (1956).

  74. 74.

    Bent, R.D., Bonner, T.W., McCrary, J.H., Ranken, W.A., Phys. Rev. 100, 771 (1955).

  75. 75.

    Hornyak, W.F., Bull. Am. Phys. Soc. Ser. II 1, 197 (1956).

  76. 76.

    Russell, J.L., Phillips, G.C., and Reich, C.W., Phys. Rev. 104, 135, 143 (1956).

  77. 77.

    Heydenburg, N.P. and Temmer, G.M., Phys. Rev. 104, 123 (1956).

  78. 78.

    Salpeter, E.E., Phys. Rev. 107, 516 (1957).

  79. 79.

    Fregeau, J.H., and Hofstadter, R., Phys. Rev. 99, 1503 (1955); ibid. 104, 225 (1956).

  80. 80.

    The citation of the prize read:

    For his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons.

  81. 81.

    The most recent result, viz., Chemykh, M., and 5 authors, Proc. 13th Intl. Symposium Capture Gamma-Ray Spect., AIP Conf. Proc. 2009 is \(\Gamma _{\mathrm{ e}^\pm }=6.2\times 10^{-5}\)Ā eV.

  82. 82.

    Blatt, J., and Weisskopf, V., Theoretical Nuclear Physics, Wiley, NY, 1952.

  83. 83.

    Salpeter, E.E., Phys. Rev. 98, 1183 (1955).

  84. 84.

    Hayakawa, S., Hayashi, C., Imoto, M., and Kikuchi, K., Prog. Theor. Phys. 16, 507 (1956).

  85. 85.

    Fowler, W.A., Interviewed by Greenberg and Buge, 1984, CalTech Archives. In his Nobel lecture, Fowler claimed that Hoyle was convinced from his work with Schwarzschild and previous work by Sandage and Schwarzschild, that helium burning should commence in red giants at about \(1\times 10^8\)Ā K and not at \(2\times 10^8\)Ā K, as the old reaction rate by Salpeter had yielded (see Fowler, 1983 Nobel prize lecture).

  86. 86.

    Almqvist, E., Bromley, D.A., Ferguson, A.J., Gove, H.E., and Litherland, A.E., Phys. Rev. 114, 1040 (1959).

  87. 87.

    According to the uncertainty principle, the width of the level is connected to the lifetime of the system in that level. From a nuclear reaction point of view, this means that, if the energy of the colliding particles is within the wide range of the level and not just equal to the prescribed energy, the reaction can proceed.

  88. 88.

    Freer, M., Wuosmaa, A.H., Betts, R.R., Henderson, D.J., Wilt, P., Zurmuhle, R.W., Balamuth, D.P., Barrow, S., Benton, D., Li, Q., Liu, Z., and Miao, Y., Phys. Rev. C 49, 1751 (1994).

  89. 89.

    Alburger, D.E., Phys. Rev. 124, 193 (1961), who used the reaction \(\mathrm{ ^{10} B}+\mathrm{ ^3 He}\rightarrow \mathrm{ ^{12} C} +\mathrm{ p}\).

  90. 90.

    Hall and Tanner, Nucl. Phys. 53, 673 (1964), who used the reaction \(\mathrm{ ^{10} B}+ \mathrm{ ^3He} \rightarrow \mathrm{ ^{12} C} +\mathrm{ p}\).

  91. 91.

    Seeger, P.A., and Kavanagh, R.W., Nucl. Phys. 46, 577 (1963), who used the reaction \(\mathrm{ ^{14} N}+\mathrm{ ^2 D}\rightarrow \mathrm{ ^{12} C} +\upalpha \).

  92. 92.

    Mak, H.-B., and 4 coauthors, Phys. Rev. C 12, 1158 (1975).

  93. 93.

    Freeman, J.M., and Baxter, A.S., Nature 162, 696 (1948); Burcham, W.E., and Freeman, J.M., Phys. Rev. 75, 1756 (1949).

  94. 94.

    Millar, C.H., Bartholomew, G.A., and Kinsey, B.B., PRL 81, 150 (1951).

  95. 95.

    Chao, C.Y., Tollestrup, A.V., Fowler, W.A., and Lauritsen, C.C., Phys. Rev. 79, 108 (1950).

  96. 96.

    Dyer, P. and Barnes, C.A., Nucl. Phys. A233 (1974).

  97. 97.

    Kettner, K.U., and 8 coauthors, Z. Phys. A 308, 73 (1982).

  98. 98.

    Langanke, K. and Koonin, S.E., Nucl. Phys. A410, 334 (1983); ibid., Nucl. Phys. A439, 384 (1985). The first paper was published when Langanke was still in Munster. The second paper was published after he joined Koonin in Caltech.

  99. 99.

    The probability for this reaction to take place at thermal energies (\(T=2\times 10^8\) or 300Ā keV) was given by \(S(300\,\mathrm{ keV})= 350\)Ā keVĀ barn (MĆ¼nster), 240Ā keVĀ barn (Caltech), and 80Ā keVĀ barn in standard nucleosynthesis calculations at that time.

  100. 100.

    Arnett, W.D., and Thielemann, F-K., Astrophys. J. 295, 589 (1985).

  101. 101.

    Metcalfe, T.S., Winget, D.E., and Charbonneau, P., Astrophys. J. 557, 1021 (2001).

  102. 102.

    The oscillations depend on the C/O ratio which is the result of helium burning.

  103. 103.

    Nuclear astrophysicists write the probability of a nuclear reaction as

    $$\begin{aligned} \sigma (E)=\frac{S(E)}{E}\exp \left[-\left(\frac{E_\mathrm{ G}}{E}\right)^{1/2}\right], \end{aligned}$$

    where \(E_\mathrm{ G}\) is the energy of the Gamow peak. The exponent takes care of the tunneling factor and all the nuclear physics resides in the fator \(S(E)\). At low energies, what matters is \(S(0)\). The unit ā€˜barnā€™ for probability of absorption has its own history. During WWII research on the atomic bomb, American physicists at Purdue University who were bombarding uranium nuclei with neutrons to check the absorption of neutrons, described the uranium nucleus as being ā€˜as big as a barnā€™, i.e., a superb absorber of neutrons. Physicists working on the project adopted the name ā€˜barnā€™ for a unit equal to \(10^{-24}\)Ā cm\(^2\). Initially, they hoped the American slang name would obscure any reference to the study of nuclear structure, but eventually the word became a standard unit in particle physics. Wackeroth and Belkora (eds.), Cross Section. High Energy Physics Made Painless, Fermilab Science Education Office. Retrieved 2009-03-13.

  104. 104.

    Kunz, R., and 7 coauthors, Astrophys. J. 567, 643 (2002).

  105. 105.

    Kunz, R. 2002, Ph.D. thesis, Stuttgart.

  106. 106.

    Caughlan, G.R. and Fowler, W.A., Atomic Data and Nuclear Data Tables 40, 283 (1988).

  107. 107.

    SchĆ¼rmann, D., and 16 coauthors, Eur. Phys. J. A26, 301 (2005).

  108. 108.

    Schlattl, H., and 4 coauthors, A., astro-ph/0307528v2, 30 October 2003; Astrophys. Space Sci. 291, 27 (2004).

  109. 109.

    Bujarrabal, V. and Cernicharo, J., Astron. Astrophys. 288, 551 (1994).

  110. 110.

    Wang, W. and Liu, X.-W., MNRAS 381, 669 (2007).

  111. 111.

    Wahlin, R., and 6 coauthors, Memorie della Societa Astronomica Italiana 77, 955 (2006).

  112. 112.

    Cohen, M. and Barlow, M.J., MNRAS 362, 1199 (2005).

  113. 113.

    Brink, in The Alpha Particle Model of Light Nuclei, Proc. Enrico Fermi school course XXXVII, Varenna, 1966.

  114. 114.

    Takigawa, N., and Arima, A., Nucl. Phys. A168, 593 (1971).

  115. 115.

    Pichler, R., Oberhummer, H., Csoto, A., Moskowski, S.A., Nucl. Phys. A618, 55 (1997).

  116. 116.

    Ajzenberg-Selove, F., Nucl. Phys. A506, 1 (1990).

  117. 117.

    Angulo, C., et al., Nucl. Phys. A656, 3 (1999).

  118. 118.

    Fynbo, J., et al. Nature 433, 136 (2005).

  119. 119.

    Diget and 20 coauthors, Nucl. Phys. 760, 3 (2005).

  120. 120.

    Barrow, J.D. and Tipler, F.J., The Anthropic Cosmological Principle, Oxford University Press, LC 87-28148, ISBN 9780192821478 (2009).

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

Ā© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Shaviv, G. (2012). How Nature Overcomes Its Own Barriers. In: The Synthesis of the Elements. Astrophysics and Space Science Library, vol 387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28385-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28385-7_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28384-0

  • Online ISBN: 978-3-642-28385-7

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics