= Radial induced-charge screening kernel
{title2=$g(q)=q[1-\epsilon(q)^{-1}]/(2\pi^2)$}
For a point source $Ze$ and the <Fourier transform> convention $\rho(\mathbf q)=\int e^{-i\mathbf q\cdot\mathbf r}\rho(\mathbf r)d^3r$, self-consistent screening gives $\rho_{\rm ind}(q)=Ze[\epsilon(q)^{-1}-1]$. Angular inversion yields $\rho_{\rm ind}(r)=-(Ze/r)\int_0^\infty g(q)\sin(qr)dq$. The factor $1/(2\pi^2)$ includes the inverse-transform normalization and spherical angular integral. Perfect long-wavelength screening implies total induced charge $-Ze$.
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