A note on the momentum distribution function for an electron gas

The one-electron momentum distribution function 〈akσ†akσ〉 for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that 〈akσ†akσ〉 has the following exact asymptotic form for large k (k ⪢ pF; pF, the Fermi momentum): 〈akσ†akσ〉 = 49(αrsπ)2×(pF8k8) g⇅(0) + ⋯, where g⇅(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.