Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 9, 2997–3369
Issue 8, 2619–2996
Issue 7, 2247–2618
Issue 6, 1871–2245
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
This article is available for purchase or by subscription. See below.
Van der Waals–London interaction of atoms with pseudorelativistic kinetic energy

Jean-Marie Barbaroux, Michael C. Hartig, Dirk Hundertmark and Semjon Vugalter

Vol. 15 (2022), No. 6, 1375–1428
Abstract

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 |D| between the atoms. In the many-atom case, we rigorously compute all the terms in the binding energy up to the order |D|9 with error term of order 𝒪(|D|10). 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.

PDF Access Denied

We have not been able to recognize your IP address 44.210.149.218 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
van der Waals–London force, Axilrod–Teller–Muto correction, pseudorelativistic kinetic energy, exponential decay, localization error, Herbst operator
Mathematical Subject Classification 2010
Primary: 81Q10
Secondary: 46N50, 34L15, 47A10, 35P15
Milestones
Received: 24 January 2019
Revised: 10 January 2021
Accepted: 15 February 2021
Published: 10 November 2022
Authors
Jean-Marie Barbaroux
Aix-Marseille Université, Université de Toulon, CNRS, CPT
Marseille
France
Michael C. Hartig
Aix Marseille Université, Université de Toulon, CNRS, CPT
Marseille
France
Dirk Hundertmark
Institute for Analysis
Karlsruhe Institute of Technology
Karlsruhe
Germany
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Semjon Vugalter
Institute for Analysis
Karlsruhe Institute of Technology
Karlsruhe
Germany