The Heavy Quanta Theory of Nuclear and Cosmic Ray Phenomena

  • Frederik Jozef Belinfante

Abstract

In 1935 Yukawa suggested in a paper in the Proceedings of the Physico-Mathematical Society of Japan 1) that the exchange forces between heavy particles (protons and neutrons) must be attributed to the action of an intervening field and, in particular, may be regarded as a second order effect due to the consecutive emission and absorption of charged “heavy quanta”, just as the electromagnetic interaction between two charged particles can be described by the quantized electromagnetic field. In order to explain the range of about 2 × 10−13 cm of the nuclear forces, he assumed that this quantum had a mass about 200 times as large as the electron mass: m ≈ 200 m. In his original theory this field was tentatively regarded as a scalar field. Then, however, it turned out 2) that, if the energy of the field of heavy quanta was assumed to be positive, the exchange force between a proton and a neutron became repulsive in a 3S state, in contradiction to the fact that this is the ground state of the deuteron. Since in the mean time experiments on cosmic ray phenomena 3) 4) 5) 6) had suggested the existence of a charged particle just having a mass of the order of magnitude 200 m, which might be identified with the quantum of Yukaw a’s theory 7), Yukawa expressed his intention to investigate whether this difficulty with the sign of the proton-neutron force could be removed by introducing a non-scalar heavy quantum field 2).

Keywords

Matrix Element Commutation Relation Canonical Variable Light Particle Symmetrical Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1).
    H. Y u k a w a, Proc. phys. math. Soc. Japan 17, 48, 1935.Google Scholar
  2. 2).
    H. Yukawa and S. SSakata, Proc. phys. math. Soc. Japan 19, 1084, 1937.Google Scholar
  3. 3).
    C.D. Anderson and S. H. Neddermeyer, Phys.Rev. 50, 273, 1936.CrossRefGoogle Scholar
  4. 4).
    C.D. Anderson and S.H. Neddermeyer, Phys. Rev. 51, 884, 1937.CrossRefGoogle Scholar
  5. 5).
    C. G. and D. D. M o n t g o m e r y, Phys. Rev. 50, 975, 1936.CrossRefGoogle Scholar
  6. 6).
    J. C. Street and E. C. Stevenson, Phys. Rev. 51, 1005, 1937.Google Scholar
  7. 7.
    H. Y u k a w a, Proc. phys. math. Soc. Japan 19, 712, 1937.Google Scholar
  8. 8).
    N. Kemmer, Nature 141, 116, 1938.CrossRefGoogle Scholar
  9. 9).
    H. J. Bhabha, Nature 141, 117, 1938.CrossRefGoogle Scholar
  10. 10).
    N. Kemmer, Proc. roy. Soc. A 166, 127, 1938.Google Scholar
  11. 11).
    C. Moller and L. Rosenfeld, Nature 143, 241, 1939.CrossRefGoogle Scholar
  12. 12).
    F. J. B e l i n f ant e, Physica 6 1939, (in the press). Second chapter of this thesis, referred to by [M.F.].Google Scholar
  13. 13).
    H. J. B h a b h a, Nature 143, 276, 1939.CrossRefGoogle Scholar
  14. 14).
    C. G. Darwin, Nature 143, 602, 1939.CrossRefGoogle Scholar
  15. 15).
    W. Pauli and V. Weisskopf, Heiv. phys. Acta 7, 709, 1934.Google Scholar
  16. 16).
    A. Proc a, J. Phys. Radium 7, 347, 1936; 8, 23, 1937.Google Scholar
  17. 17).
    E. Durandin and A. Erschow, Phys. Z. Sowjet Un. 12, 466, 1937.Google Scholar
  18. 18).
    H. J. Bhabha, Proc. roy. Soc. A 166, 501, 1938.CrossRefGoogle Scholar
  19. 19).
    H. Fröhlich, W. Héitier and N. Kemmer, Proc. roy. Soc. A 166, 154, 1938.CrossRefGoogle Scholar
  20. 20).
    W. Pauli, Z. Phys. 43, 601, 1927.CrossRefGoogle Scholar
  21. 21).
    H. Yukawa, S. Sakata and M. Taketani, Proc. phys. math. Soc. Japan 20, 319, 1938.Google Scholar
  22. 22).
    N. K Kemmer, Heiv. phys. Acta 10, 47, 1937.Google Scholar
  23. 23).
    H. Yukawa, S. Sakata, M. Kobayasi and M. Taketani, Proc. phys. math. Soc. Japan 20, 720, 1938.Google Scholar
  24. 24).
    A. H. W i 1 s o n, Proc. Cambr. phil. Soc. 34, 365, 1938.Google Scholar
  25. 25).
    R. G. Sachs and M. Goeppert-Mayer, Phys. Rev. 53, 991, 1938.CrossRefGoogle Scholar
  26. 26).
    R.G. Herb, D.W. Kerst, D.B. Parkinson and G. J. Plain, Phys. Rev. 55, 998, 1939.CrossRefGoogle Scholar
  27. 27).
    N. P. Heydenburg, L. R. Hafstad and M. A. Tuve, Phys. Rev. 55, 603, 1939.Google Scholar
  28. 28).
    G. Breit, L.E. Hoisington, S.S. Share andH.M. Thaxton, Phys. Rev. 55, 1103, 1939.CrossRefGoogle Scholar
  29. 29).
    L. Simon s, Phys. Rev. 55, 792, 1939.CrossRefGoogle Scholar
  30. 30).
    N. Kemmer, Proc. Cambr. phil. Soc. 34, 354, 1938.Google Scholar
  31. 31).
    F. J. B e l i n f ant e, Physica 6 1939, (in the press). First chapter of this thesis, referred to by [U.C.].Google Scholar
  32. 32).
    H. A. Beth e, Phys. Rev. 55, 1261, 1939.CrossRefGoogle Scholar
  33. 33).
    W. Heisenberg and W. Pauli, Z. Phys. 56, 1, 1929; 63, 574, 1930.Google Scholar
  34. 34).
    W. Heisenberg and W. Paul i, Z. Phys. 59, 168, 1929.Google Scholar
  35. 35).
    E. Fermi, Rend. R. Accad. Lincei (Cl. Sc. fis. mat. nat.) 9, 881, 1929.Google Scholar
  36. 36).
    E. Fermi, Rev. mod. Phys. 4, 87, 1932.CrossRefGoogle Scholar
  37. 37).
    E. C. G. St neck e l b erg, Nature 143, 560, 1939.Google Scholar
  38. 38).
    E. Fermi, Rend. R. Accad. Lincei (Cl. Sc. fis. mat. nat.) 12, 431, 1930.Google Scholar
  39. 39).
    W. Pauli and M. Fier z, Heiv. phys. Acta 12, 297, 1939.Google Scholar
  40. 40).
    F. J. B e l i n f an te, „0n the Spin Angular Momentum of Mesons“ Physica 6 1939, (in the press).Google Scholar
  41. 41).
    E. Fermi, Z. Phys. 88, 161, 1934.CrossRefGoogle Scholar
  42. 42).
    E.J. Konopinski and G. E. Uhlenbeck, Phys. Rev. 48, 7, 1935.CrossRefGoogle Scholar
  43. 43).
    L. Rosenfeld, Ann. Physik 5, 113, 1930.CrossRefGoogle Scholar
  44. 44).
    L. R Rosenfeld, Ann. Inst. H. Poincaré 2, 24, 1932.Google Scholar
  45. 45).
    M. Kobayasi and T. Okayama, Proc. phys. math. Soc. Japan 21, 1, 1939.Google Scholar
  46. 46).
    J. W. G i h b s, „Vector Analysis“ (by E. B. WiIson), chap. 4. ( Yale Bicentennial Publ., New York-London, 1902 ).Google Scholar
  47. 47).
    K. F. N o v Kobat z k y, Z. Phys. 111, 292, 1939.Google Scholar
  48. 48).
    H. A. Kramer s, Proc. roy. Acad. Amsterdam 40, 814, 1937.Google Scholar
  49. 49).
    W. H Heitler, Proc. roy. Soc. A 166, 529, 1938.CrossRefGoogle Scholar
  50. 50).
    W. H Heitler, The Quantum Theory of Radiation“, chap. 3. ( Clarendon Pr., Oxford, 1936 ).Google Scholar
  51. 51).
    G. Brei t, Phys. Rev. 39, 616, 1932.CrossRefGoogle Scholar
  52. 52).
    D. I w a n e n k o, Nature 144, 77, 1939.CrossRefGoogle Scholar
  53. 53).
    H. A. Kramer s, Hand-u. Jahrb. chem. Phys. 1, § 65, 1937.Google Scholar
  54. 54).
    J.M.B. Kellogg, I.I. Rabi, N.F. Ramsey and J. R. Zacharias, Phys. Rev. 55, 318, 1939.CrossRefGoogle Scholar
  55. 55).
    H. A. Beth e, Handb. Physik 24/1, 275–277 and 551–560, 1933.Google Scholar
  56. 56).
    H. A. Kramer s, Hand-u. Jahrb. chem. Phys. 1, § 45, 1933.Google Scholar
  57. 57).
    W. Heisenberg, Ann. Physik 32, 20, 1938.CrossRefGoogle Scholar
  58. 58).
    J.M.B. Kellogg, I.I. Rabi, N.F. Ramsey and J.R. Zacharias, Phys. Rev. 55, 595, 1939.CrossRefGoogle Scholar
  59. 59).
    I. Est ermann, O. C. Simpson and O. Stern, Phys. Rev. 53, 535, 1937.CrossRefGoogle Scholar
  60. 60).
    F. Bloch, Phys. Rev. 50, 259, 1936; 51, 994, 1937.Google Scholar
  61. 61).
    R. Frisch, H. von H alb an jun. and J. Koch, Nature 140, 360, 1937.Google Scholar
  62. 62).
    F.Bloch, H. von Halban jun. and J. Koch, Nature 140, 360, 1937Google Scholar
  63. 63).
    V. W. Cohen, H. H. Goldsmith and J. Schwinger, Phys. Rev. 55, 106, 1939.CrossRefGoogle Scholar
  64. 64).
    C. F. von Weizsäcker, „Die Atomkerne“, p. 135. ( Akad. Verl. Ges., Leipzig 1937 ).Google Scholar
  65. 65).
    H. A. Be the and R. P e i e r 1 s, Proc. roy. Soc. A 148, 146, 1935.Google Scholar
  66. 66).
    G. Breit, H. M. Th axton and L. Eisenbud, Phys. Rev. 55, 1018, 1939.CrossRefGoogle Scholar
  67. 67).
    H. Yukawa and S. Sakata, Nature 143, 761, 1939 and Proc. phys. math. Soc. Japan 21, 138, 1939.Google Scholar
  68. 68).
    H. Eu1er, Naturwiss. 26, 382, 1938.CrossRefGoogle Scholar
  69. 69).
    P. E h r e n test and A. Fréon, C. R. Paris 207, 853, 1938.Google Scholar
  70. 70).
    L. W. Nordheim, Phys. Rev. 55, 506, 1939.CrossRefGoogle Scholar
  71. 71).
    L. W. Nordheim and F. L. Yost, Phys. Rev. 51, 942, 1937.CrossRefGoogle Scholar
  72. 72).
    L.W. Nordheim, Phys. Rev. 55, 506, 1939.CrossRefGoogle Scholar
  73. 73).
    L. W. Nordheim and F.L. Yost, Phys Rev. 51, 942, 1937CrossRefGoogle Scholar
  74. 74).
    G.E. Uhlenbeck and H. Kuiper, Physica 4, 601, 1937.CrossRefGoogle Scholar
  75. 75).
    Y. Nisina, M. Takeuti and T. Itimiy a, Phys. Rev. 55, 585, 1939.CrossRefGoogle Scholar
  76. 76).
    O. L a p or t e, Phys. Rev. 54, 905, 1938.CrossRefGoogle Scholar
  77. 77).
    S. Sakata and Y. Tanikaw a, Proc. phys. math. Soc. Japan 21, 58, 1939.Google Scholar
  78. 78).
    G. Wentze1, Phys. Rev. 54, 869, 1938.CrossRefGoogle Scholar
  79. 79).
    L. W. and G. Nor d heim, Phys. Rev. 54, 254, 1938.CrossRefGoogle Scholar
  80. 80).
    H. Maass, Ann. Physik 27, 507, 1936.CrossRefGoogle Scholar
  81. 81).
    N. Arley and W. Reitle r, Nature 142, 158, 1938.Google Scholar
  82. 82).
    S. Gorodetzkv, C. R. Paris 208, 1987, 1939.Google Scholar
  83. 83).
    K. Schmeiser and W. Bothe, Ann. Physik 32, 161, 1938.CrossRefGoogle Scholar
  84. 84).
    H. A. Kramers, Hand-u. Jahrb. chem. Phys. 1, § 89, 1937.Google Scholar
  85. 85).
    Scherze r, Ann. Physik 34, 585, 1939.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1939

Authors and Affiliations

  • Frederik Jozef Belinfante
    • 1
  1. 1.Geboren te ’S-GravenhageNiederlande

Personalised recommendations