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Correction of the Fermi Pseudopotential Concept in the Theory of Dynamic Thermal-Neutron Scattering

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Abstract

The propagation of thermal neutrons through media characterized by different degrees of ordering is analyzed. It is shown that the standard Fermi pseudopotential concept should be modified in order to obtain a unified description of thermal-neutron propagation in crystalline and amorphous media. It is found that satisfactory results are obtained upon employing a pseudopotential that correctly reproduces the amplitude of scattering on a single center in the second order of perturbation theory rather in the first order. General formulas that describe thermal-neutron propagation through media of arbitrary degree of ordering are derived.

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REFERENCES

  1. I. I. Gurevich and L. V. Tarasov, Low-Energy Neutron Physics (Nauka, Moscow, 1965; North-Holland, Amsterdam, 1968).

  2. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1989; Pergamon, New York, 1977).

  3. A. Abragam and M. Goldman, Nuclear Magnetism: Order and Disorder, The International Series of Monographs on Physics (Oxford Univ. Press, New York, 1982), Vol. 2.

    Google Scholar 

  4. A. L. Barabanov and S. T. Belyaev, Eur. Phys. J. B 15, 59 (2000).

    Article  ADS  Google Scholar 

  5. V. V. Fedorov, Neutron Physics (PIYaF, St. Petersburg, 2004) [in Russian].

  6. M. Utsuro and V. K. Ignatovich, Handbook of Neutron Optics (Wiley-VCH, Weinheim, 2010).

    Book  Google Scholar 

  7. F. S. Dzheparov and D. V. L’vov, Condensed Matter Neutron Studies (NIYaU MIFI, Moscow, 2012) [in Russian].

  8. E. Fermi, Ricerca Sci. 2, 13 (1936).

    Google Scholar 

  9. J. Ziman, Principles of the Theory of Solids (Cambridge Univ. Press, Cambridge, 1976).

    MATH  Google Scholar 

  10. O. Madelung, Introduction to Solid State Theory (Springer, Berlin, 1978).

    Book  Google Scholar 

  11. M. L. Goldberger and F. Seitz, Phys. Rev. 71, 294 (1947).

    Article  ADS  Google Scholar 

  12. M. D. Whitacker and H. G. Beyer, Phys. Rev. 55, 1101 (1939).

    Article  ADS  Google Scholar 

  13. L. J. Rainwater, W. W. Havens, Jr., J. R. Dunning, and C. S. Wu, Phys. Rev. 73, 733 (1948).

    Article  ADS  Google Scholar 

  14. V. F. Sears, Phys. Rep. 82, 1 (1982).

    Article  ADS  Google Scholar 

  15. H. Rauch and S. A. Werner, Neutron Interferometry (Oxford Univ. Press, Oxford, 2015).

    Book  Google Scholar 

  16. M. Lax, Phys. Rev. 85, 621 (1952).

    Article  ADS  Google Scholar 

  17. V. F. Sears, Phys. B (Amsterdam) 151, 156 (1988).

    Article  Google Scholar 

  18. H. Ekstein, Phys. Rev. 83, 721 (1951).

    Article  ADS  MathSciNet  Google Scholar 

  19. G. V. Kulin, A. N. Strepetov, A. I. Frank, P. Geltenbort, S. V. Goryunov, M. Jentschel, and D. V. Kustov, Phys. Lett. A 378, 2553 (2014).

    Article  ADS  Google Scholar 

  20. A. Akhiezer and I. Pomeranchuk, Some Problems of Nuclear Theory (Gos. Izdat. Tekh.-Teor. Liter., Moscow, Leningrad, 1950) [in Russian].

    Google Scholar 

  21. F. S. Dzheparov and D. V. L’vov, JETP Lett. 72, 360 (2000).

    Article  ADS  Google Scholar 

  22. N. March, W. Young, and S. Sampanthar, The Many-Body Problem in Quantum Mechanics (Dover, New York, 2012).

    Google Scholar 

  23. D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (W. A. Benjamin, New York, 1975).

    Google Scholar 

  24. F. S. Dzheparov and D. V. Lvov, Appl. Magn. Reson. 48, 989 (2017).

    Article  Google Scholar 

  25. L. Lanz and B. Vacchini, Phys. Rev. A 56, 4826 (1997).

    Article  ADS  Google Scholar 

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ACKNOWLEDGMENTS

We are grateful to L.N. Bogdanova, A.D. Gulko, B.L. Ioffe, B.O. Kerbikov, V.V. Fedorov, and A.I. Frank for stimulating discussions.

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Dzheparov, F.S., Lvov, D.V. Correction of the Fermi Pseudopotential Concept in the Theory of Dynamic Thermal-Neutron Scattering. Phys. Atom. Nuclei 83, 621–628 (2020). https://doi.org/10.1134/S1063778820030060

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  • DOI: https://doi.org/10.1134/S1063778820030060

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