Influence of Collisions on the Magnetic Susceptibility of an Electron Gas. I

R. B. Thomas, Jr

doi:10.1103/PhysRev.155.577

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Influence of Collisions on the Magnetic Susceptibility of an Electron Gas. I

R. B. Thomas, Jr.

Space Sciences Laboratory, General Electric Company, Valley Forge, Pennsylvania

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Phys. Rev. 155, 577 – Published 15 March, 1967

DOI: https://doi.org/10.1103/PhysRev.155.577

Abstract

Using a simple model, a determination is made of the influence of collisions on the magnetic susceptibility of an electron gas without assuming the existence of a relaxation time. The model consists of noninteracting free electrons being elastically scattered by randomly distributed impurity centers in the presence of a strong uniform magnetic field. The free energy for this simple system is expanded in ascending powers of the strength of the scattering potential and is evaluated for impurities represented by a screened Coulomb potential. The result for the oscillatory part of the magnetic susceptibility is in agreement with that obtained by Dingle to the order considered and provides an explicit expression for the collision relaxation time and the corresponding Dingle temperature.

References (15)

L. Landau, Z. Physik 64, 629 (1930)
A. H. Wilson, The Theory of Metals (Cambridge University Press, London, 1953), 2nd ed., Chap. 6, p. 160
R. E. Peierls, Z. Physik 80, 763 (1933)
R. E. Peierls, Quantum Theory of Solids (Oxford University Press, London, 1955), Chap. 7, p. 155
R. B. Dingle, Proc. Roy. Soc. (London) A211, 517 (1952)
G. H. Wannier and D. R. Fredkin, Phys. Rev. 125, 1910 (1962)
[2], p. 329
L. D. Landau and E. M. Lifshitz, Statistical Physics (Addison-Wesley Publishing Company, Reading, Massachusetts, 1958), p. 93
W. Kohn and J. M. Luttinger, Phys. Rev. 108, 590 (1957)
N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, London, 1936), Chap. II, Sec. 5, p. 86
M. J. Stephen, Phys. Rev. 129, 997 (1963)
N. D. Mermin and E. Canel, Am. J. Phys. (N. Y.) 26, 247 (1964)
V. Celli and N. D. Mermin, Phys. Rev. 140, A839 (1965)
F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940), p. 585
E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford University Press, London, 1937), p. 60

[c1] L. Landau, Z. Physik 64, 629 (1930)

[c2] A. H. Wilson, The Theory of Metals (Cambridge University Press, London, 1953), 2nd ed., Chap. 6, p. 160

[c3] R. E. Peierls, Z. Physik 80, 763 (1933)

[c4] R. E. Peierls, Quantum Theory of Solids (Oxford University Press, London, 1955), Chap. 7, p. 155

[c5] R. B. Dingle, Proc. Roy. Soc. (London) A211, 517 (1952)

[c6] G. H. Wannier and D. R. Fredkin, Phys. Rev. 125, 1910 (1962)

[c7] [2], p. 329

[c8] L. D. Landau and E. M. Lifshitz, Statistical Physics (Addison-Wesley Publishing Company, Reading, Massachusetts, 1958), p. 93

[c9] W. Kohn and J. M. Luttinger, Phys. Rev. 108, 590 (1957)

[c10] N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, London, 1936), Chap. II, Sec. 5, p. 86

[c11] M. J. Stephen, Phys. Rev. 129, 997 (1963)

[c12] N. D. Mermin and E. Canel, Am. J. Phys. (N. Y.) 26, 247 (1964)

[c13] V. Celli and N. D. Mermin, Phys. Rev. 140, A839 (1965)

[c14] F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940), p. 585

[c15] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford University Press, London, 1937), p. 60

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Influence of Collisions on the Magnetic Susceptibility of an Electron Gas. I

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Influence of Collisions on the Magnetic Susceptibility of an Electron Gas. II. The Constant Susceptibility

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