The induced electron density at the position of a single point charge Z embedded in a three-dimensional degenerate electron gas is studied at high densities. The perturbative, plane-wave-based treatment developed within the framework of density matrices by March and Murray (Phys Rev 120: 830, 1960, [1]) is applied here up to second order in Z. Comparison with the result obtained by considering the exact scattering enhancement in a bare Coulomb field is made. The small numerical difference found in the second-order term of the induced density at contact is analyzed following Wigner’s (Phys Rev 94: 77, 1954, [2]) similar perturbative treatment of the proton field in the hydrogen atom. The impact of the many-body screening is discussed as well.
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