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Actually, the source mentioned in my question does answer partially the question. Consider a monatomic gas with an electron cloud. Its response to an electric field is typically given in terms of an expansion. $P(t) = \varepsilon_0\Big[\chi^{(1)}E(t)+\chi^{(2)}E^2(t)+\chi^{(3)}E^3(t)+..\Big]$ When there is spherical symmetry, for a monatomic case, we can ...


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Higher harmonic generation always takes place within a nonlinear transparent medium and the summetry constraints are always due to the symmetry properties of the medium. There are vastly different symmetries between homogeneous gases and nonlinear crystal structures. This is what your sources are referring to. To go into the symmetry constraints of a ...


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