Abstract
The interaction of rotons is studied by a direct examination of their orbital dynamics. It is found that upon representing rotons as point dipoles in the superfluid, obeying the Landau dispersion relation, negative energy states occur, some of which are stable and some unstable. The binding energy and effective mass of these states are found, but are too large to agree with experiment. Improvements in the Hamiltonian are explored which recognize the actual dispersion curve as well as higher moments in the interaction. Both modifications lead to binding energy and effective mass in better agreement with experiment. Scattering is also examined, and one finds that a representative roton-roton cross section may be obtained in the dipole approximation, again using Landau dispersion. The scattering cross section is shown to be in satisfactory agreement with neutron linewidths in the roton-dominated region, as well as the roton contribution to the shear viscosity.
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References
T. J. Greytak, R. Woerner, J. Yan, and R. Benjamin,Phys. Rev. Letters 25, 1547 (1970).
I. M. Khalatnikov,An Introduction to the Theory of Superfluidity (Benjamin, New York and Amsterdam, 1965).
A. Zawadowski, J. Ruvalds, and J. Solana,Phys. Rev. A 5, 399 (1972).
J. Yau and M. J. Stephen,Phys. Rev. Letters 27, 482 (1971).
R. P. Feynman, inProgress in Low Temperature Physics, Vol. I, C. J. Gorter, ed. (North Holland, Amsterdam, 1955).
R. J. Donnelly and P. H. Roberts,Phys. Letters 43A, 199 (1973).
P. H. Roberts and R. J. Donnelly,Phys. Letters 43A, 1 (1973).
J. S. Brooks,The Properties of Superfluid Helium below 1.6 Degrees Kelvin, Ph.D. Thesis, University of Oregon, 1973.
R. J. Arms and F. R. Hama,Phys. Fluids 8, 553 (1965).
L. E. Fraenkel,Proc. Roy. Soc. (London)A316, 29 (1970);J. Fluid Mech. 51, 119 (1972).
J. Norbury,Proc. Camb. Phil. Soc. 72, 253 (1972);J. Fluid Mech. 57, 417 (1973).
P. H. Roberts and R. J. Donnelly,Phys. Letters 31A, 137 (1970).
P. H. Roberts,Mathematika 19, 169 (1972).
P. H. Roberts and J. Grant,J. Phys. 4, 55 (1971).
R. J. Donnelly and P. H. Roberts,Phil. Trans. Roy. Soc. A271, 41 (1971).
R. A. Cowley and A. D. B. Woods,Can. J. Phys. 49, 177 (1971).
J. L. Yarnell, G. P. Arnold, P. J. Bendt, and E. C. Kerr,Phys. Rev. 113, 1379 (1959).
O. W. Dietrich, E. H. Graf, C. H. Huang, and L. Passell,Phys. Rev. A 5, 1377 (1972).
R. J. Donnelly,Physics Letters 39A, 221 (1972).
M. J. Stephen,Phys. Rev. 187, 279 (1969); D. Baeriswyl,Phys. Letters 41A, 297 (1972); R. A. Cowley,J. Phys. C: 5, L287 (1972).
D. F. Brewer and D. O. Edwards, inProc. 8th Int. Conf. Low Temp. Phys., Davies, ed. (Butterworths, 1963), p. 96; J. Wilks,Liquid and Solid Helium (Clarendon Press, Oxford, 1967), p. 72.
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Research supported by the Air Force Office of Scientific Research, Grant AF-AFOSR-71-1999 and by the National Science Foundation, Grant NSF-GH-35898.
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Roberts, P.H., Donnelly, R.J. Scattering and binding of rotons. J Low Temp Phys 15, 1–27 (1974). https://doi.org/10.1007/BF00655620
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DOI: https://doi.org/10.1007/BF00655620