Jpn. J. Appl. Phys. 12 (1973) pp. 1611-1620  |Next Article|  |Table of Contents|
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Neutron Thermalization as a Fluctuation of the Nonequilibrium Steady State

Hideo Hayasaka

(Received March 1, 1973)

Neutron thermalization problem has been reconsidered as a fluctuation of a steady state in an absorbing medium. If energy dependent neutron density distributions are chosen as random variables, the thermalization process can be treated as a Markoffian random process in which an incompletely thermalized neutron field approaches the steady state.
It is shown that the thermalization matrix corresponds to the first moment-drift vector-, and that the diffusion constant is represented by a generalized Einstein relation. Since the loss of energy of the neutron per collision with a heavy moderator nucleus is very small in the thermalization process, the Smoluchowski integral equation is converted into the Fokker-Planck equation. The quasi-Onsager reciprocal relation is obtained with respect to the steady state of the neutron thermalization process, in which neutrons are supplied, scattered and captured.

URL: http://jjap.jsap.jp/link?JJAP/12/1611/
DOI: 10.1143/JJAP.12.1611

References | Citing Articles (3)

1. E. Amaldi: Handbuch der Physik (Springer, Berlin, 1954) Vol. 38, §95–112.
2. N. Corngold, ed.: U.S. Atomic Energy Commission Report, BNL-719, (U.S.A.E.C., Washington D. C, 1962).
3. E. P. Wigner and J. E. Wilkins: U.S. Atomic Energy Commission Report, AECD-2275, (U.S.A. E.C., Washington D. C, 1944).
4. K. H. Beckurts and K. Wirtz: Neutron Physics (Springer, Berlin, 1964), p. 180.
5. V. F. Turchin: Slow Neutrons (Sivan Press, Jerusalem, 1965) p. 220.
6. K. Andersen and K. E. Shuler: J. Chem. Phys. 40 (1964) 633[AIP Scitation].
7. N. Corngold: Ann. Phys. 6 (1959) 368.
8. C. S. Shapiro and N. Corngold: Phys. Rev. 137 (1965) A1686[APS].
9. M. S. Green: Proceeding of the International Symposium on Transport Process in Statistical Mechanics, Brussels, 1956 (Interscience, New York, 1958) p. 8.
10. J. G. Kirkwood and J. Ross: Proceeding of the International Symposium on Transport Process in Statistical Mechanics, Brussels, 1956 (Interscience, New York, 1958) p. 1.
11. I. Prigogine and R. Brout: Proceeding of the International Symposium on Transport Process in Statistical Mechanics, Brussels, 1956 (Interscience, New York, 1958) p. 25.
12. I. Prigogine: Non-Equilibrium Statistical Mechanics (Wiley, New York, 1963) p. 136.
13. R. Brout: Physica 22 (1956) 509[CrossRef].
14. I. Prigogine: Physica 15 (1949) 271[Elsevier].
15. H. G. Reik: Z. Physik 148 (1957) 156.
16. R. H. Fowler: Statistical Mechanics (Cambridge Univ. Press, London, 1936).
17. S. R. Grout: Thermodynamics of Irreversible Process (Interscience Publishers, Inc., New York, 1951) p. 13.
18. L. D. Landau and E. M. Lifshitz: Statistical Physics (Pergamon Press, London, 1958) p. 343.
19. S. Chandrasekher: Rev. Mod. Phys. 15 (1948) 1[APS].
20. M. C. Wang and G. E. Uhlenbeck: Rev. Mod. Phys. 17 (1945) 323[APS].
21. R. F. Greene and H. B. Callen: Phys. Rev. 83 (1951) 1231[APS].
22. M. Lax: Rev. Mod. Phys. 32 (1960) 25[APS].
23. R. K. Osborn and S. Yip: Foundations of Neutron Transport Theory (Gordon and Breach Science Publishers, Inc., New York, 1966) p. 13.
24. R. K. Osborn and M. Natelson: J. Nuclear Energy 19 (1965) 619.
25. M. N. Moore: Nuclear Sci. Engng. 6 (1959) 448.
26. C. E. Cohn: Nuclear Sci. Engng. 5 (1959) 331.
27. K. Saito: Nuclear Sci. Engng. 28 (1967) 452.
28. K. Saito and Y. Taji: Nuclear Sci. Engng. 30 (1967) 54.
29. A. Einstein: Ann. Physik 33 (1910) 1275.
30. A. D. Fokker: Ann. Physik 43 (1914) 812.
31. M. S. Green: J. Chem. Phys. 20 (1952) 1281[CrossRef]; 22 (1954) 398[CrossRef].
32. L. Onsager: Phys. Rev. 37 (1931) 405[APS]; 38 (1931) 2265[APS].