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The main contribution to the effective shear modulus of neutron star crustcan be calculated within Coulomb solid model and can be approximated by simpleanalytical expression for arbitrary (even multicomponent) composition. Here Iconsider correction associated with electron screening within Thomas-Fermiapproximation. In particular, I demonstrate that for relativistic electrons(density $\rho>10^6$ g\,cm$^{-3}$) this correction can be estimated as $\delta\mu_\mathrm{eff}^\mathrm{V}= -9.4\times 10^{-4}\sum_Z n_Z Z^{7/3}e^2/a_\mathrm{e}$, where summation is taken over ion species, $n_Z$ is numberdensity of ions with charge $Ze$, $k_\mathrm{TF}$ is Thomas-Fermi screeningwave number. Finally, $a_\mathrm{e}=(4 \pi n_\mathrm{e}/3)^{-1/3}$ is electronsphere radius. Quasineutrality condition $n_\mathrm{e}=\sum_Z Z n_Z$ isassumed. This result holds true for arbitrary (even multicomponent andamorphous) matter and can be applied for neutron star crust and (dense) coresof white dwarfs. For example, the screening correction reduces shear modulus by$\sim 9$\% for $Z\sim40$, which is typical for inner layers of neutron starcrust.

Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus