The spurious self-interaction energy, which is one-half the integrated electrostatic interaction energy of a normalized electronic charge distribution with the potential field generated by itself, is calculated analytically for a is-like electron charge distribution governed by an attractive screened Hulthen-type model potential. The exact result obtained is used, via an energetic cancellation constraint and a convenient Holder's integral inequality, to deduce an analytical lower bound for the screening-dependent positive coefficient of a negative exchange-like energy term applied routinely in the local-density approximation to density functional theory with Coulomb potentials. The bare Coulomb case is investigated by Sobolev's integral inequality as well.
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