  We consider two nonlocal variational models arising in physical contexts. The
first is the Thomas-Fermi-Dirac-von Weiz\"{a}cker (TFDW) model, introduced in
the study of ionization of atoms and molecules, and the second is the liquid
drop model with external potential, proposed by Gamow in the context of nuclear
structure. It has been observed that the two models exhibit many of the same
properties, especially in regard to the existence and nonexistence of
minimizers. We show that, under a "sharp interface" scaling of the coefficients
and constrained mass, the TFDW energy Gamma-converges to the Liquid Drop model,
for a general class of external potentials. Finally, we present some
consequences for global minimization of each model.
