Lawrence Dunne
Dear Chao,
Elman's answer is excellent but we can also view screening at a deeper level.
It goes back to the famous study of the electron gas by David Bohm and David Pines at the University of Illinois in the 1950's.
When the Coulomb potential is decomposed into Fourier components it turns out that the long-wavelength part goes into collective PLASMON modes which are very difficult to excite and effectively drop out of the low-energy dynamics.
This leaves only a short-range screened interaction of the type given above by Elman but includes a long-range Friedel type oscillatory term.
The book by Haug " Theoretical Solid State Physics" vol. 1 ( Pergamon press). p 202 gives an extended discussion of this.
Best wishes- Lawrence Dunne
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