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Problem 7

Consider the electron gas within the Hartree-Fock approximation with screened Coulomb interaction:

(a) Show that this description of the electron gas is consistent with Fermi liquid theory

(b) Find an expression for the effective mass m^*

(c) Find expressions for the Landau parameters F_0^s, F_0^a, F_1^s, F_1^a

(d) Verify that the relation m^*/m=1+F_1^s/3 holds

(e) Find expressions for the compressibility and the magnetic susceptibility

(f) Find numerical values for m^*/m for r_s=2,3,4,5, and 6.

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