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Table 1 : : 2 : : 3 : : 4 : : 5

The Calculated Thermodynamic Properties of Superfluid Helium-4
James S. Brooks and Russell J. Donnelly

7. References

[1] Landau, L. D., The Theory of Superfluidity of Helium II, J. Phys. 5, 71 (1941); On the Theory of Superfluidity of Helium II, J. Phys. 11, 91 (1947).

[21 Cowley, R. A., and Woods, A. D. B., Inelastic Scattering of Thermal Neutrons From Liquid Helium, Can. J. Phys. 49, 177 (1971).

[3] Dietrich, 0. W., Graf, E. H., Huang, C. H., and Passell, L, Neutron Scattering by Rotons in Liquid Helium, Phys. Rev. A 5, 1377 (1972); also unpublished data provided by O. W. Dietrich.

[4] Henshaw, D. G., and Woods, A. D. B., Modes of Atomic Motions in Liquid Helium by Inelastic Scattering of Neutrons, in Proc. Seventh Int. Conf. on Low Ten Physics, G. M. Graham and A. C. Hollis Hallet, eds.,' p. 539, University of Toronto Press, Toronto (1961).

[5] Henshaw, D. G., and Woods, A. D. B, Modes of Atomic Motions in Liquid Helium by Inelastic Scattering of Neutrons, Phys. Rev. 121, 1266 (1961).

[6] Graf, E. H., Minkiewicz, V. J., Møller, H. B., and Passell, L.,

Neutron-Scattering Study of Collective Excitations in Superfluid Helium, Phys. Rev. A 10, 1748 (1974).

[7] Svensson, E. C., Woods, A. D. B., and Martel, P., Phonon Dispersion in Liquid Helium under Pressure, Phys. Rev. Lett. 29, 1148 (1972).

[8] Woods, A. D. B., and Cowley, R. A., Structure and Excitations of Liquid Helium, Rep. Prog. Phys. 36, 1135 (1973).

[9] Yarnell, J. L., Arnold, G. P., Bendt, P. J., and Kerr, E. C., Excitations in Liquid Helium: Neutron Scattering Measurements, Phys. Rev. 113, 1379 (1959).

[10] Bendt, P. J., Cowan, R. D., and Yarnell, J. L., Excitations in Liquid Helium: Thermodynamic Calculations, Phys. Rev. 113, 1386 (1959).

[11] Wilke, J., The Properties of Liquid and Solid Helium, Clarendon Press, Oxford (1967).

[12] Donnelly, R. J., Experimental Superfluidity, Chicago Lectures in Physics Series, notes compiled by W. I. Glaberson and P. E. Parks, University of Chicago Press (1967).

[13] McCarty, R. D., Thermodynamic Properties of Helium 4 from 2 to 1500 K at Pressures to 108 Pa, J. Phys. Chem. Ref Data 2, 923 (1973).

[14] Angus, S., de Renck, K. M., and McCarty, R. D., Final Report on IUPAC Helium4 Tables. Part I: Text, IUPAC Thermodynamic Tables Project Centre, Dept. of Chemical Engineering and Chemical Technology, Imperial College of Science and Technology, London (1975)

[15] Donnelly, R. J., The Landau Parameters in Helium II , Phys. Lett. 39A, 221 (1972).

[16] Brooks, J.,S., and Donnelly, R. J., Model Dispersion Curves for Helium II, in,Low Temperature Physics-LT13, Vol. 1, K. D. Timmerhaus, W. J. O'Sullivan, and E. F. Hammel, eds., Plenum Publishing, New York (1974).

[17] Brooks, J. S., and Donnelly, R. J., Excitation Spectrum of Helium II: A Series Representation, Phys. Lett. 46A, 111 (1973).

[18] Brooks, J. S., The Properties of Superfluid Helium Below 1.6 Degrees Kelvin, Ph.D. Thesis, University of Oregon, Eugene, Oregon (1973).

[19] Brooks, J. S., and Donnelly, R. J., The Calculated Properties of Helium II. A Technical Report, University of Oregon, Eugene (1973,).

[20]. Van Degrift, C. T., Dielectric Constant, Density, and Expansion Coefficient of Liquid He4 at Vapor Pressure Below 4.4 K, Ph.D. Thesis, University of California, Irvine (1974).

[21] Heiserman, J., Hulin, J. P., Maynard. J., and Rudnick, I., Precision Sound Velocity Measurements in He II, Phys. Rev. (submitted); Maynard. J., Determination of the Thermodynamics of He II from Sound Velocity Data, Phys. Rev. (submitted).

[22] Goodstein, D. L., Brooks, J. S., Donnelly, R. J., and Roberts, P. H., Quasiparticles and Thermal Expansion, Phys. Lett. 54A, 281 (1975).

[23] Roberts, P. H., and Donnelly, R. J., Simple Theory of Temperature-Dependent Energy Levels: Application to He II Phys. Lett. 55A, 443 (1976)

[24] Donnelly, R. J., and Roberts, P. H. "A Theory of Temperature-Dependent Energy Levels: Thermodynamic Properties of HeII" J. Low Temp. Phys. 27, 687-736 (1977)..

[25] Keller, W. E., Helium-3 and Helium4, Plenum Press, New York (1969).

[26] Khalatnikov, I. M., An Introduction to the Theory of Superfluidity, W. A. Benjamin, New York (1965).

[27] Feenberg, E., Comments on Long-Wavelength Excitations and Structure Functions in the Theory of Liquid 4He at T =0, Phys. Rev. Lett. 26, 301 (1971); also Theory of Quantum Fluids, Academic Press, New York (1969).

[28] Phillips, N. E., Waterfield, C. G., and Hoffer, J. K., Calorimetric Evidence for Positive Phonon Dispersion in Liquid Hehum-4, Phys. Rev. Lett. 25, 1260 (1970).

[29] Pitaevskii, L. P., Properties of the Spectrum of Elementary Excitations Near the Disintegration Threshold of the Excitations, J. Exptl. Theoret. Phys. (USSR) 36, 1168 (1959). Engl. trans.: Soviet Phys. JETP 9, 830 (1959).

[30] Brooks, J. S., and Donnelly, R. J., Influence of Phonon Dispersion on the Velocity of Second Sound in He II, Phys. Rev. A 9, 1444 (1974).

[31] Abraham, B. M., Eckstein, Y., Ketterson, J. B., Kuchnir, M., and Roach, P. R., Velocity of Sound, Density, and Grüneisen Constant in Liquid 4He, Phys. Rev. Al, 250 (1970); Errata, Phys. Rev. A2, 550 (1970).

[32] Boghosian, C., and Meyer, H., Density, Coefficient of Thermal Expansion, and Entropy of Compression of Liquid He' Under Pressure Below 1.4oK, Phys. Rev. 152, 200 (1966); Errata, Phys. Rev. 163, 206 (1967).

[33] Elwell, D. L., and Meyer, H., Molar Volume, Coefficient of Thermal Expansion, and Related Properties of Liquid He4 Under Pressure, Phys. Rev. 164, 245 (1967).

[34] Kerr, E. C., and Taylor, R. D., The Molar Volume and Expansion Coefficient of Liquid He4, Ann. Phys. 26, 292 (1964).

[35] Van den Meijdenberg, C. J. N., Taconis, K. W., and Ouboter, R. De Bruyn, The Entropy of Helium II Under Pressure from Measurements on the Fountain Effect, Physics 27, 197 (1961).

[36] Wiebes,J., Ph.D. Thesis, Kammerlingh Onnes Laboratory, Leiden (1969). Caloric Measurements on Liquid and Melting Helium below 1.5 Kelvin.

[37] Roberts, P. H., and Donnelly, R. J., Scattering and Binding of Rotons, J. Low Temp. Phys. 15, 1 (1974).

[38] Greytak, T. J., Woerner, R., Yan, J., and Benjamin, R., Experimental Evidence for a Two- Roton Bound State in Superfluid Helium, Phys. Rev. Lett. 25, 1547 (1970); and Murray, C. A., Woerner, R. L., and Greytak, T. J., High Resolution Raman Study of the Two- Roton Bound State, J. Phys. C8 (6), L90-94 (1975).

[39] Roberts, P. H., and Pardee, W. J., Bound States of the Two-roton Schrödinger Equation, J. Phys. A7, 1283 (1974).

[40] Putterman, S. J., Superfluid Hydrodynamics, North-Holland/ American Elsevier, New York (1974), Chapter I, Section 7.

[41] Rudnick, I., Physical Acoustics at UCLA in the Study of Superfluid Helium, in New Directions in Physical Acoustics, International School of Physics "Enrico Fermi." XLIII Corso (In press).

[42] Grilly, E.R., Compressibility of Liquid He4 as a Function of Pressure, Phys. Rev. 149, 97 (1966).

[43] Keesom, W. H., Helium, Elsevier, Amsterdam (1942).

[44] Tough, J. T., McCormick, W. D., and Dash, J. G., Viscosity of Liquid He II, Phys. Rev. 132, 2373 (1963).

[45] Romer. R. H., and Duffy, R. J., Normal-Fluid Densities in Liquid Helium II Under Pressure, Phys. Rev. 186, 255 (1969).

[46] Maurer, R. D., and Herlin, M. A., Pressure Dependence of Second Sound Velocity in Liquid Helium II, Phys. Rev. 81, 444 (1951).

[47] Watson, G. E., Reppy, J. D., and Richardson, R. C., Low Temperature Density and Solubility of He4 in Liquid He4 Under Pressure, Phys. Rev. 188, 384 (1969).

[48] Grilly, E. R., Pressure-Volume-Temperature Relations in Liquid and Solid 4He, J. Low Temp. Phys. 11, 33 (1973).

[49] Whitney, W. M., and Chase, C. E., Ultrasonic Velocity and Dispersion in Liquid Helium II from 0.15 to 1.8'K, Phys. Rev. 158, 200 (1967).

[50] Atkins, K. R., and Stasior, R. A., First Sound in Liquid Helium at High Pressures, Can. J. Phys. 31, 1156 (1953).

[51] Vignos, J. H., and Fairbank, H. A., Sound Measurements in Liquid and Solid He3, He4, and He3-He4 Mixtures, Phys. Rev. 147, 185 (1966).

[52] Barmatz, M., and Rudnick, I., Velocity and Attenuation of First Sound Near the ? Point of Helium, Phys. Rev. 170, 224 (1968).

[53] Atkins, K. R., and Edwards, M. H., Coefficient of Expansion of Liquid Helium II , Phys. Rev. 97, 1429 (1955).

[54] Kierstead, H. A., Lambda Transformation of Liquid He* at High Pressures, Phys. Rev. 153, 258 (1967).

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