Riesz external field problems on the hypersphere and optimal point separation

We consider discrete minimal energy problems on the unit sphere S^d in the Euclidean space R^{d+1} in thepresence of an external field Q, where the interaction is via Riesz kernel 1/r^s, s \u3e d-2. In particular we show that (Q,s)-Fekete points that minimize the discrete weighted s-energy when Q is the Riesz potential of a signed measure are well separated