On the short-range correlation in electron gas

The structure factor $\text{S(}\text{q}\text{) = (1/n)〈ϱqϱ−q〈}$ of an electron gas is investigated by a diagrammatic analysis of perturbation theory. By generalizing the theoretical treatment in a previous paper, it is shown that S(q) has the following exact dominant asymptotic form for large q (q ⪢ p_F; p_F, the Fermi momentum): $\text{S(}\text{q}\text{)= 1 −}\text{4}\text{3}\text{(αr}{}_{\mathrm{s}}\text{/π) (p}{}^4{}_{\mathrm{<mtext>F</mtext>}}\text{/q}{}^4\text{) g}\textcolor{red}{}\text{(0) +hellip;}$, where g (0) is th e exact value of the spin-up-spin-down pair correlation function at the origin. It is therein clarified that “electron-electron” ladder interactions which are included in the Goldstone energy diagrams as a part, play an essential role in determining the above coefficient of the order q⁻⁴ of S(q).