  We consider a variant of Gamow's liquid drop model with an anisotropic
surface energy. Under suitable regularity and ellipticity assumptions on the
surface tension, Wulff shapes are minimizers in this problem if and only if the
surface energy is isotropic. We show that for smooth anisotropies, in the small
nonlocality regime, minimizers converge to the Wulff shape in $C^1$-norm and
quantify the rate of convergence. We also obtain a quantitative extension of
the energy of any minimizer around the energy of a Wulff shape yielding a
geometric stability result. For certain crystalline surface tensions we can
determine the global minimizer and obtain its exact energy expansion in terms
of the nonlocality parameter.
