Enhancement of fusion rates due to quantum effects in the particles momentum distribution in nonideal plasma media

  • N.J. Fisch
  • M.G. GladushEmail author
  • Y.V. Petrushevich
  • P. Quarati
  • A.N. Starostin
Regular Article


This study concerns a situation when measurements of the nonresonant cross-section of nuclear reactions appear highly dependent on the environment in which the particles interact. An appealing example discussed in the paper is the interaction of a deuteron beam with a target of deuterated metal Ta. In these experiments, the reaction cross section for d(d, p)t was shown to be orders of magnitude greater than what the conventional model predicts for the low-energy particles. In this paper we take into account the influence of quantum effects due to the Heisenberg uncertainty principle for particles in a non-ideal plasma medium elastically interacting with the medium particles. In order to calculate the nuclear reaction rate in the non-ideal environment we apply both the Monte Carlo technique and approximate analytical calculation of the Feynman diagram using nonrelativistic kinetic Green’s functions in the medium which correspond to the generalized energy and momentum distribution functions of interacting particles. We show a possibility to reduce the 12-fold integral corresponding to this diagram to a fivefold integral. This can significantly speed up the computation and control accuracy. Our calculations show that quantum effects significantly influence reaction rates such as p +7Be, 3He +4He, p +7Li, and 12C +12C. The new reaction rates may be much higher than the classical ones for the interior of the Sun and supernova stars. The possibility to observe the theoretical predictions under laboratory conditions is discussed.


Plasma Physics 


  1. 1.
    V.M. Galitsky, A.B. Migdal, Zh. Eksp. Teor. Fiz. (USSR) 34, 139 (1958)Google Scholar
  2. 2.
    L.P. Kadanoff, G. Baym, Quantum statistical mechanics (Benjamin, New York, 1962)Google Scholar
  3. 3.
    A.V. Eletskii, A.N. Starostin, M.D. Taran, Phys. Usp. 48, 281 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    E. Wigner, Phys. Rev. 40, 749 (1932)ADSCrossRefGoogle Scholar
  5. 5.
    G.E. Uhlenbeck, L. Gropper, Phys. Rev. 41, 79 (1932)ADSCrossRefzbMATHGoogle Scholar
  6. 6.
    L.D. Landau, E.M. Lifshitz, Statistical Physics (Butterworth-Heinemann, 1980), Vol. 5Google Scholar
  7. 7.
    N.N. Bogoliubov, Izv. Academii Nauk USSR 11, 77 (1947)Google Scholar
  8. 8.
    L.P. Pitaevskii, E.M. Lifshitz,Statistical Physics (Butterworth-Heinemann, 1980), Part 2, Vol. 9Google Scholar
  9. 9.
    V.A. Belyakov, Zh. Eksp. Teor. Fiz. (USSR) 40, 1210 (1961) Google Scholar
  10. 10.
    E. Daniel, S.H. Vosko, Phys. Rev. 120, 2041 (1960)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    V.M. Galitski, V.V. Yakimets, Zh. Eksp. Teor. Fiz. (USSR) 51, 957 (1966)Google Scholar
  12. 12.
    J.C. Kimball, J. Phys. A 8, 1513 (1975)ADSCrossRefGoogle Scholar
  13. 13.
    A.N. Starostin, V.I. Savchenko, N.J. Fisch, Phys. Lett. A 274, 64 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    M. Coraddu, G. Mezzorani, Yu.V. Petrushevich, P. Quarati, A.N. Starostin, Physica A 340, 496 (2004) ADSCrossRefGoogle Scholar
  15. 15.
    A.N. Starostin, A.G. Leonov, Yu.V. Petrushevich, Vl.K. Rerikh, Plasma Phys. Rep. 31, 123 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    A.L. Zubarev, J. Phys. A 41, 312004 (2008) ADSCrossRefGoogle Scholar
  17. 17.
    J.N. Bahcall, L.S. Brown, A. Gruzinov, R.F. Sawyer, A&A 383, 291 (2002) ADSCrossRefGoogle Scholar
  18. 18.
    N.L. Aleksandrov, A.N. Starostin, J. Exp. Theor. Phys. 86, 903 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    S. Ichimaru, Rev. Mod. Phys. 65, 255 (1993)ADSCrossRefGoogle Scholar
  20. 20.
    A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski,Quantum Field Theoretical Methods in Statistical Physics, 2nd edn. (Pergamon, 1965)Google Scholar
  21. 21.
    E.E. Salpeter, Aust. J. Phys. 7, 373 (1954)ADSCrossRefzbMATHGoogle Scholar
  22. 22.
    A.I. Chugunov, H.E. DeWitt, D.G. Yakovlev, Phys. Rev. D 76, 025028 (2007) ADSCrossRefGoogle Scholar
  23. 23.
    L.S. Brown, R.F. Sawyer, Rev. Mod. Phys. 69, 411 (1997)ADSCrossRefGoogle Scholar
  24. 24.
    A.B. Balantekin, N. Takigawa, Rev. Mod. Phys. 70, 77 (1998)ADSCrossRefGoogle Scholar
  25. 25.
    M. Aliotta, C. Spitaleri, M. Lattuada, A. Musumarra, R.G. Pizzone, A. Tumino, C. Rolfs, F. Strieder, Eur. Phys. J. A 9, 435 (2000)ADSCrossRefGoogle Scholar
  26. 26.
    F. Strieder, C. Rolfs, C. Spitaleri, P. Corvisiero, Naturwissenschaften 88, 461 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    F. Raiola, P. Migliardi, G. Gyurky, M. Aliotta, A. Formicola, R. Bonetti, C. Broggini, L. Campajola, P. Corvisiero, H. Costantini, J. Cruz, A. D’Onofrio, Z. Fulop, G. Gervino, L. Gialanella, A. Guglielmetti, G. Imbriani, C. Gustavino, A.P. Jesus, M. Junker, R.W. Kavanagh, P.G.P. Moroni, A. Ordine, J.V. Pinto, P. Prati, V. Roca, J.P. Ribeiro, D. Rogalla, C. Rolfs, M. Romano, F. Schumann, D. Schurmann, E. Somorjai, F. Strieder, F. Terrasi, H.P. Trautvetter, S. Zavatarelli, Eur. Phys. J. A 13, 377 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    Int. Conf. on Cold Fusion (Cambridge, MA, 2003)Google Scholar
  29. 29.
    K. Czerski, A. Huke, P. Heide, G. Ruprecht, Eur. Phys. J. A 27, 83 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    A. Huke, K. Czerski, P. Heide, Nucl. Instrum. Meth. Phys. Res. B 256, 599 (2007) ADSCrossRefGoogle Scholar
  31. 31.
    E.G. Adelberger, S.M. Austin, J.N. Bahcall, A.B. Balantekin, G. Bogaert, L.S. Brown, L. Buchmann, F. Edward Cecil, A.E. Champagne, L. de Braeckeleer, C.A. Duba, S.R. Elliott, S.J. Freedman, M. Gai, G. Goldring, Christopher R. Gould, A. Gruzinov, W.C. Haxton, K.M. Heeger, E. Henley, C.W. Johnson, M. Kamionkowski, R.W. Kavanagh, S.E. Koonin, K. Kubodera, K. Langanke, T. Motobayashi, V. Pandharipande, P. Parker, R.G.H. Robertson, C. Rolfs, R.F. Sawyer, N. Shaviv, T.D. Shoppa, K.A. Snover, E. Swanson, R.E. Tribble, S. Turck-Chièze, J.F. Wilkerson, Rev. Mod. Phys. 70, 1265 (1998) ADSCrossRefGoogle Scholar
  32. 32.
    G.A. Caughlan, W.A. Fowler,At. Data Nucl. Data Tables 40 (1998)Google Scholar
  33. 33.
    A. Lavagno, P. Quarati, Phys. Lett. B 498, 47 (2001)ADSCrossRefGoogle Scholar
  34. 34.
    V. Fortov, V. Ternovoi, M. Zhernokletov, M. Mochalov, A. Mikhailov, A. Filimonov, A. Pyalling, V. Mintsev, V. Gryaznov, I. Iosilevskii, J. Exp. Theor. Phys. 97, 259 (2003)ADSCrossRefGoogle Scholar
  35. 35.
    S. Grishechkin, S. Gruzdev, V. Gryaznov, M. Zhernokletov, R. Ilkaev, I. Iosilevskii, G. Kashintseva, S. Kirshanov, S. Manachkin, V. Mintsev, A. Mikhailov, A. Mezhevov, M. Mochalov, V. Fortov, V. Khrustalev, A. Shuikin, A. Yukhimchuk, JETP Lett. 80, 398 (2004)ADSCrossRefGoogle Scholar
  36. 36.
    V.E. Fortov, R.I. Ilkaev, V.A. Arinin, V.V. Burtzev, V.A. Golubev, I.L. Iosilevskiy, V.V. Khrustalev, A.L. Mikhailov, M.A. Mochalov, V.Ya. Ternovoi, M.V. Zhernokletov, Phys. Rev. Lett. 99, 185001 (2007) ADSCrossRefGoogle Scholar
  37. 37.
    J.D. Huba, NRL plasma formulary (Naval Research Laboratory, Washington, DC, 2002), revised editionGoogle Scholar
  38. 38.
    Max Krook, Tai Tsun Wu, Phys. Rev. Lett. 36, 1107 (1976)ADSCrossRefGoogle Scholar
  39. 39.
    C.M Ermakov, G.A. Mikhailov,Statisticheskoe Modelirovanie (in Russian) (Nauka, Moscow, 1982)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • N.J. Fisch
    • 1
  • M.G. Gladush
    • 2
    Email author
  • Y.V. Petrushevich
    • 3
  • P. Quarati
    • 4
    • 5
  • A.N. Starostin
    • 3
  1. 1.Department of Astrophysical SciencesPrinceton UniversityPrincetonUSA
  2. 2.Institute for Spectroscopy of the Russian Academy of SciencesTroitsk, Moscow regionRussia
  3. 3.SRC RF Troitsk Institute for Innovation and Fusion Research Troitsk, Moscow regionRussia
  4. 4.Politecnico di Torino Department of PhysicsTorinoItaly
  5. 5.INFNSezione di CagliariItaly

Personalised recommendations