A note on the momentum distribution function for an electron gas

The one-electron momentum distribution function 〈a_kσ^†a_kσ〉 for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that 〈a_kσ^†a_kσ〉 has the following exact asymptotic form for large k (k ≫ p_F; p_F, the Fermi momentum): 〈a_kσ^†a_kσ〉 = 4 9( αr_s π)²×( p_F⁸ k⁸) g{double arrow, left up, right down}(0) + ⋯, where g{double arrow, left up, right down}(0) is the zero-distance value of the spin-up-spin-down pair correlation function. The physical implications of the above asymptotic form are discussed.