@article{oai:kyutech.repo.nii.ac.jp:00000101,
 author = {Nazarov, V. U. and Nishigaki, Satoshi},
 issue = {9},
 journal = {Physical review B. Condensed matter and materials physics},
 month = {Feb},
 note = {Although the nonlinear response of solids in such phenomena as ion slowing and second harmonic generation has been studied since long ago, to our knowledge there has not existed a quantum theory of the inelastic scattering of charges by solids beyond the first Born approximation. In this paper we relate the inelastic cross section in the second Born approximation to the order Z3 to the quadratic retarded density-response function in the same (but far less trivial) fashion it has been known for the first Born approximation, deriving by this a formula applicable to describe the electron and positron energy-loss spectroscopy. The complete account of recoil is preserved. Our general formalism neither relies on a specific approximation to the dielectric response (such as the random phase approximation) nor is it restricted to scattering by a homogeneous electron gas: it is “exact” in the sense of inclusion of exchange and correlation and is applicable to targets of arbitrary symmetry. Based on this formalism, we perform explicit calculations of the Z3 contribution to plasmon excitation by electrons and positrons in a simple hydrodynamic model of electron gas and discuss the results, which prove to be instructive in the general case too.},
 pages = {094303-1--094303-11},
 title = {Z3-order theory of quantum inelastic scattering of charges by solids},
 volume = {65},
 year = {2002}
}