Charge density of the fermionic vacuum

We examine the properties of the matter vacuum in the absence of fermion-photon interactions. We calculate the spatial distribution of the vacuum’s charge density associated with model nuclear interactions and show that even in the absence of photons, the fermionic vacuum can screen off the Coulomb field around a nucleus. For force fields that vary on spatial scales larger than the electron’s Compton wavelength, the resulting charge density is proportional to the spatial derivative of the nuclear force field. As a result we can estimate the electric permeability of the one-dimensional fermionic vacuum to be 5.1 × 10^?7.