The Coulomb correction (difference from the 1st Born approximation) to the Moli`{e}re screening angle in multiple Coulomb scattering theory is evaluated with the allowance for inelastic contribution. The controversy between dominance of close- or remote-collision contributions to Coulomb correction is discussed. For scattering centres represented by a Coulomb potential with a generic (not necessarily spherically symmetric) creening function, the Coulomb correction is proven to be screening-independent, by virtue of the eikonal phase cancellation in regions distant from the Coulomb singularity. Treating the atom %more self-consistently, as an assembly of pointlike electrons and the nucleus, and summing the scattering probability over all the final atom states, it is shown that besides the Coulomb correction due to close encounters of the incident charged particle with atomic nuclei, there are similar corrections due to close encounters with atomic electrons (an analog of Bloch correction). For low $Z eq1$ the latter contribution can reach $sim 25%$, but its observation is partly obscured by multiple scattering effects.
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