In models of N interacting particles in \BbbR d as in Density Functional Theory or crowd motion, the repulsive cost is usually described by a two-point function c\varepsilon (x,y) = \ell (| x - y| ) where \varepsilon \ell : \BbbR + \rightarrow [0, \infty ] is decreasing to zero at infinity and parameter \varepsilon > 0 scales the interaction distance. In this paper we identify the limit energy of such a model in the short-range regime \varepsilon \ll 1 under the sole assumption that \exists r0 > 0 : \int \infty \ell (r)rd - 1 dr < +\infty . This extends recent results [D. Hardin, r0 E. B. Saff, and O. Vlasiuk, Asymptotic Properties of Short-Range Interaction Functionals, preprint, https://arxiv.org/abs/2010.11937, 2021], [D. P. Hardin, T. Lebl\'e, E. B. Saff, and S. Serfaty, Constr. Approx., 48 (2018), pp. 61-100], [M. Lewin, J. Math. Phys., 63 (2022), 061101] obtained in the homogeneous case \ell (r) = r - s where s > d.