Asymptotics for Two-Dimensional Atoms
2012 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 13, no 2, 333-362 p.Article in journal (Refereed) Published
We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge Z > 0 and N quantum electrons of charge -1 is E(N, Z) = - 1/2 Z(2) lnZ + ( E-TF (lambda) + 1/2 c(H))Z(2) + o(Z(2)) when Z -> a and N/Z -> lambda, where E (TF)(lambda) is given by a Thomas-Fermi type variational problem and c (H) a parts per thousand -2.2339 is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when Z -> a, which is contrary to the expected behavior of three-dimensional atoms.
Place, publisher, year, edition, pages
2012. Vol. 13, no 2, 333-362 p.
IdentifiersURN: urn:nbn:se:kth:diva-91245DOI: 10.1007/s00023-011-0123-2ISI: 000300279900004ScopusID: 2-s2.0-84856744468OAI: oai:DiVA.org:kth-91245DiVA: diva2:509297
QC 201203122012-03-122012-03-122014-05-20Bibliographically approved