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The effect of the electron-electron interactions on diamagnetic susceptibility is investigated using the Green's-function formalism. General expressions for the Green's function and eigenvalues of the effective one-particle Hamiltonian of the Coulomb gas are developed through second order in the magnetic field strength. Specializing to the Hartree-Fock approximation, the Sampson-Seitz prescription is proven: The susceptibility is given by the Landau-Peierls formula applied to the quasiparticle energy. Energy-band electrons are treated in the Hartree-Fock approximation, yielding a quasiparticle term plus an explicit many-body correction to the orbital paramagnetism. The quasiparticle term corresponds to treating the self-energy operator as a nonlocal pseudopotential. The explicit many-body correction is shown to be small for sodium and bismuth.
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Philippas et al. (1972) studied this question.
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