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The van der Waals-London's law, for a collection of atoms at largeseparation, states that their interaction energy is pairwise attractive anddecays proportionally to one over their distance to the sixth. The firstrigorous result in this direction was obtained by Lieb and Thirring [LT], byproving an upper bound which confirms this law. Recently the van derWaals-London's law was proven under some assumptions by I.M. Sigal and theauthor [AS]. Following the strategy of [AS] and reworking the approachappropriately, we prove estimates on the remainder of the interaction energy.Furthermore, using an appropriate test function, we prove an upper bound forthe interaction energy, which is sharp to leading order. For the upper bound,our assumptions are weaker, the remainder estimates stronger and the proof issimpler. The upper bound, for the cases it applies, improves considerably theupper bound of Lieb and Thirring. However, their bound is much more general.Here we consider only spinless Fermions.

Remainder estimates for the Long Range Behavior of the van der Waals interaction energy