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Applied Mathematics Research eXpress Advance Access originally published online on August 20, 2009
Applied Mathematics Research eXpress (2009) 2009:1-27, doi:10.1093/amrx/abp002 published on November 6, 2009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Minimum Energy Configurations of Classical Charges: Large N Asymptotics

Stephane Capet and Gero Friesecke

Center for Mathematics, Technische Universität München, 85747 Garching, Germany

Correspondence: Correspondence to be sent to: gf{at}ma.tum.de

We study the minimum energy configurations of N particles in Formula of charge –1 ("electrons") in the potential of M particles of charges Z{alpha} > 0 ("atomic nuclei"). In a suitable large-N limit, we determine the asymptotic electron distribution explicitly, showing in particular that the number of electrons surrounding each nucleus is asymptotic to the nuclear charge ("screening"). The proof proceeds by establishing, via Gamma-convergence, a coarse-grained variational principle for the limit distribution, which can be solved explicitly.


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