Abstract
The Galitskii-Feynman T matrix, which sums the infinite ladder series in a many-fermion system for both particle-particle and hole-hole scattering, is studied in detail for a family of realistic He-He interactions. The structure of the S-wave bound-state singularity, reported previously, and its dependence on the bare interaction are documented at length. Special attention is devoted to the T matrix in the scattering region, where the c.m. energy of the interacting pair is positive. In particular, the on-energy-shell T matrix in this region is parametrized in terms of real “effective” phase shifts incorporating many-body effects. The critical behavior discussed previously in the bound-state region manifests itself clearly in the zero-energy limit of these phase shifts for the S wave. Below (above) a certain critical density, which is a function of both temperature and c.m. momentum, this limit approaches the value 0(−π) radians. A generalized Levinson's theorem relates this behavior to the existence of fermion-fermion pairing. An especially striking feature of these many-body phase shifts is the cusp behavior exhibited at the Fermi surface in the lowtemperature limit, which turns out to arise essentially from the structure of the particle and hole occupation probabilities. Throughout this study the temperature dependence of the T matrix is particularly emphasized.
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References
A. A. Abrikosov and I. M. Khalatnikov, Rep. Prog. Phys. 22, 329 (1959).
P. Nozieres, Theory of Interacting Fermi Systems (Benjamin, New York, 1964); D. Pines and P. Nozieres, The Theory of Quantum Liquids (Benjamin, New York, 1966), Vol. I.
A. L. Stewart, Advan. Phys. 12, 299 (1963).
R. H. Sherman and F. D. Edeskuty, Ann. Phys. (N.Y.) 9, 522 (1960).
E. Feenberg, Theory of Quantum Fluids (Academic Press, New York, 1969).
F. Mohling, Phys. Rev. 122, 1043 (1961), and many other papers; E. R. Tuttle and F. Mohling, Ann. Phys. (N.Y.) 38, 510 (1966); A. Ford, F. Mohling, and J. C. Rainwater, Ann. Phys. (N.Y.) 84, 80 (1974).
T. D. Lee and C. N. Yang, Phys. Rev. 113, 1165 (1959).
B. Kahn, On the Theory of the Equation of State (Dissertation, University of Utrecht), (North-Holland, Amsterdam, 1938). Reprinted in Studies in Statistical Mechanics, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1965), Vol. III, p. 277.
B. D. Day, Rev. Mod. Phys. 39, 719 (1967); H. A. Bethe, Ann. Rev. Nucl. Sci. 21, 93 (1971).
V. M. Galitskii and A. B. Migdal, Sov. Phys.—JETP 7, 96 (1958); V. M. Galitskii, Sov. Phys.—JETP 7, 104 (1958).
A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
R. F. Bishop, M. R. Strayer, and J. M. Irvine, Phys. Rev. A 10, 2423 (1974); R. F. Bishop, M. R. Strayer, and J. M. Irvine, J. Low Temp. Phys. 20, 571 (1975).
M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, London, 1964); R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).
Y. Yamaguchi, Prog. Theor. Phys. (Kyoto) —Supplement (1959).
N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, 3rd ed. (Clarendon Press, Oxford, 1965).
M. I. Haftel and F. Tabakin, Nucl. Phys. A158, 1 (1970).
H. B, Ghassib, R. H. Ibarra, and J. M. Irvine, Ann. Phys. (N.Y.) 85, 378 (1974); H. B. Ghassib and J. M. Irvine, J. Low Temp. Phys. 18, 201 (1975).
I. R. Rao and Y. S. T. Rao, preprint, Tata Institute, Bombay, 1975.
A. I. Ahonen, M. T. Haikala, M. Krusius, and O. V. Lounasmaa, Phys. Rev. Lett. 33, 628 (1974).
A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975); J. C. Wheatley, Rev. Mod. Phys. 47, 415 (1975).
R. F. Bishop, Phys. Rev. C 7, 479 (1973).
R. F. Bishop, H. B. Ghassib, and M. R. Strayer, Phys. Rev. A (to be published).
L. W. Bruch and I. J. McGee, J. Chem. Phys. 46, 2959 (1967); J. Chem. Phys. 52, 5884 (1970).
D. E. Beck, Mol. Phys. 14, 311 (1968); Mol. Phys. 15, 332 (1968); J. Chem. Phys. 50, 541 (1969).
G. Sposito, J. Low Temp. Phys. 3, 491 (1970); G. Sposito and E. Hukoveh, J. Low Temp. Phys. 9, 495 (1972).
A. A. Frost and B. Musulin, J. Chem. Phys. 22, 1017 (1954).
R. F. Bishop, H. B. Ghassib, and M. R. Strayer (to be published).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover Publications, New York, 1965), pp. 332, 334, 556.
A. C. Anderson, D. O. Edwards, W. R. Roach, R. E. Sarwinski, and J. C. Wheatley, Phys. Rev. Lett. 17, 367 (1966).
J. Wilks, The Properties of Liquid and Solid Helium (Clarendon Press, Oxford, 1967), p. 1.
W. M. Frank, D. J. Land, and R. M. Spector, Rev. Mod. Phys. 43, 36 (1971).
W. Kohn and D. Sherrington, Rev. Mod. Phys. 42, 1 (1970).
R. Kubo and T. Nagamiya, eds., Solid State Physics (McGraw-Hill, New York, 1969).
C. N. Yang, Rev. Mod. Phys. 34, 694 (1962).
R. F. Sawyer and D. J. Scalapino, Phys. Rev. D 7, 953 (1973); D. F. Goble, Ann. Phys. (N. Y.) 90, 295 (1975).
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Ghassib, H.B., Bishop, R.F. & Strayer, M.R. A study of the Galitskii-Feynman T matrix for liquid 3He. J Low Temp Phys 23, 393–410 (1976). https://doi.org/10.1007/BF00116928
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DOI: https://doi.org/10.1007/BF00116928