A CONVECTIVE MODEL OF A ROTON
Keywords:
superfluid helium, convection, elementary convective cell, roton, energy spectrum of helium II, density of the normal component of helium II, neutron scattering, light scattering, dipole momentum
Abstract
A convective model describing the nature and structure of the roton is proposed. According to the model, the roton is a cylindrical convective cell with free horizontal boundaries. On the basis of the model, the characteristic geometric dimensions of the roton are estimated, and the spatial distribution of the velocity of the helium atoms and the perturbed temperature inside are described. It is assumed that the spatial distribution of rotons has a horizontally multilayer periodic structure, from which follows the quantization of the energy spectrum of rotons. The noted quantization allows us to adequately describe the energy spectrum of rotons. The convective model is quantitatively confirmed by experimental data on the measurement of the density of the normal component of helium II, the scattering of neutrons and light by helium II. The use of a convective model for describing the scattering of light by helium II made it possible to estimate the dipole moment of the roton, as well as the number of helium atoms participating in the formation of the roton.
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References
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2. Соhen M., Feуnman R.P. Theory of Inelastic Scattering of Cold Neutrons from Liquid Helium // Phys. Rev. – 1957. - Vol. 107. – No.1. – P.13-24.
3. Palevsky H., Otnes K., Larsson K.E. Excitation of Rotons in Helium II by Cold Neutrons // Phys. Rev. – 1958. – Vol. 112. – No. 1. – P.11-18.
4. Υаrnell J.L., Arnοld G.P., Вendt P.J., Кеrr E.С. Excitations in Liquid Helium: Neutron Scattering Measurements // Phys. Rev. – 1959. – Vol.113. - No.6. – P.1379-1386.
5. Fizicheskaya encyklopedia [Physical encyclopedia] / Gl. red. А. М. Prohorov. Red.kol. D.M. Alekseev, А. М. Baldin, А. М. Bonch-Bruevich, A.S. Borovik-Romanov i dr. – М.: Sov. encyclopedia. T.I. Aaronova – Boma effekt – Dlinnie linii. - 1988. 704 p. (in Russian)
6. Feynman R.P. Atomic Theory of the Two-Fluid Model of Liquid Helium // Physiсal Review. – 1954. – Vol. 94. – No.2. – P. 262-277.
7. Kruglov V.I., Collett M.J. Roton Excitation Spectrum in Liquid Helium II // Phys. Rev. Lett. – 2001. – Vol. 87. – No.18. – P.185302.
8. Landau L.D. Teoriya sverhtekuchesti geliya-ІІ [The theory of superfluidity of helium-II] // GETF. – 1941. – Vol. 11. – P.592-616. (in Russian)
9. Halatnikov I.M. Teoriya sverhtekuchesti [The theory of superfluidity]. – М.: Nauka, 1971. – 320p. (in Russian)
10. Bozbiei L.S., Borts B.V., Kostikov A.O., Tkachenko V.I. Formation of Elementary Convective Cell in Horizontal Layer of Viscous Incompressible Fluid // East European J. of Phys.. – 2014. – Vol.1. – No.4. – P. 49-56.
11. Andronikashvili E.L. Issledovanie teplovoj strukturi geliya ІІ s pomoschjyu rasseyaniya holodnih nejtronov [Study of the thermal structure of helium II using cold neutron scattering] // UFN. – 1960 – Vol. 72. – Iss. 4. - P. 697-710. (in Russian)
12. Gershuni G.Z., Zguhovitskij E.M. Konvektivnaya ustojchivost neszgimaemoj zgidkosti [Convective stability of an incompressible fluid]. – М: Nauka, 1972. – 393p. (in Russian)
13. Getling A.V. Formirovanie prostranstvennih struktur konvekcii Releya-Benara [Formation of Rayleigh-Benard's spatial convection structures] // UFN. –1991. – Vol.161. – Iss. 9. – P. 1–80. (in Russian)
14. Daunt Dzh.G, Smit P.S. Sovremennoe sostoyanie problemi zhidkogo geliya [The current state of the problem of liquid helium] // UFN. – 1955. – Vol. 56. – Iss. 3. – P. 249-416. (in Russian)
15. Kapitsa P.L. Sverhtekuchest geliya – II [Superfluidity of helium-II] // UFN. – 1967. – Vol. 93. – Iss. 11. – P. 481–494. (in Russian)
16. Meyer L., Mellink J.H. The Thermomechanical Effects in Liquid Helium II // Physica. – Vol. 13. – Iss. 4–5. – P. 197-215.
17. Svojstva elementov. Ch. І. Fizicheskie svojstva. Spravochnik [Properties of elements. Part I. Physical properties. Reference book]. Pod red. G.V. Samsonova. – М.: Metallurgiya, 1976. – 600p. (in Russian)
18. Polezgaev V.I., Soboleva E.B. Konvekciya Releya-Benara v okolokriticheskoj zgidkosti vblizi poroga ustojchivosti [Rayleigh-Benard convection in a near-critical fluid near the stability threshold] // Izv. RAN. Mehanika zgidkosti i gaza. – 2005. - No. 2. – P. 48-61. (in Russian)
19. Royal Society Mathematical Tables: Vol. 7. Bessel functions, P. Ш. Zeros and associated values. – Cambridge: Cambridge Univ. Press, I960. Russkij perevod: Tablici nulej Besselya. – М.: VC AN SSSR, 1967. – BМТ; Iss. 44.
20. Donnelly R.J., Barenghi C.F. The Observed Properties of Liquid Helium at the Saturated Vapor Pressure // J. Phys. Chem. Ref. Data. – 1998. – Vol. 27. – No. 6. – P. 1217-1274.
21. Fizicheskaya encyklopedia [Physical encyclopedia] / Gl. red. А.М. Prohorov. Red.kol. D.M. Alekseev, А.М. Baldin, А.М. Bonch-Bruevich, A.S. Borovik-Romanov i dr. – М.: Bolschaya Rossijskaya encyclopedia. Vol. 3. Magnitoplazmennij – Pojntinga teorema. – 1992. 672 p. (in Russian)
22. Greytak T.J., Yan J. Light Scattering From Rotons In Liquid Helium // Physical Review Letter. – 1969. – Vol. 22. – No. 19. – P. 987 – 990.
23. Greytak T.J. Light Scattering from Superfluid Helium. Quantum Liquids. Lectures presented at the International School of Low Temperature Physics. Edited by J. Ruvalds and T. Regge. Erice, Italy, June 11-25, 1977.
24. Greytak T. J., Woerner R., Yan J., Benjamin R. Experimental Evidence for a Two-Roton Bound State in Superfluid Helium // Physical Review Letters. – 1970. – Vol. 25. – No. 22. – P.1547 - 1550.
25. Melnikovsky L.A. Polarization of Dielectrics by Acceleration // J. Low Temp. Phys. – 2007. – Vol. 148. – P. 559-564.
26. Spravochnik himika. Tom 1. Obschie svedeniya, stroenie veschestva, svojstva vazgnejshih veschestv, laboratrnaya tehnika [Reference book of the chemist. Volume 1. General information, the structure of matter, the properties of critical substances, laboratory equipment] / Pod red. B.P. Nikolskogo. – М.-L.: Himiya, 1966 – 1071 p. (in Russian)
27. Poluektov Yu.M., Savchenko V.N. On Electric Polarization of Helium Atoms by Acceleration / PAST, Series: Nuclear Physics Investigations (57) – 2012. – No. 1. – P. 299-301.
28. Smirnova N.A. Metodi statisticheskoj termodinamiki v fizicheskoj himii [Methods of statistical thermodynamics in physical chemistry]. – М.: Vish. Shkola, 1982. – 455p. (in Russian)
29. Fabelinskij I.L. Otkritie kombinatcionnogo rasseyaniya sveta [The discovery of Raman scattering of light] // UFN. – 1978. – Vol. 126. – Iss. 1. – P. 124 - 152. (in Russian)
Published
2017-05-13
Cited
How to Cite
Tkachenko, V. I. (2017). A CONVECTIVE MODEL OF A ROTON. East European Journal of Physics, 4(1), 28-46. https://doi.org/10.26565/2312-4334-2017-1-02
Section
Original Papers
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