We consider a multi-atomic system where the nuclei are assumed to be point charges
at fixed positions. Particles interact via Coulomb potential and electrons have
pseudorelativistic kinetic energy. We prove the van der Waals–London law, which states
that the interaction energy between neutral atoms decays as the sixth power of the distance
between the
atoms. In the many-atom case, we rigorously compute all the terms in the binding energy up to the
order
with error
term of order
.
This yields the first proof of the famous Axilrod–Teller–Muto three-body
correction to the van der Waals–London interaction, which plays an important
role in atomic physics. As intermediate steps we prove exponential decay of
eigenfunctions of multiparticle Schrödinger operators with permutation symmetry
imposed by the Pauli principle and new estimates of the localization error.
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