Asymptotics for Two-dimensional Atoms
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Asymptotics for Two-dimensional Atoms. / Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip.
I: Annales Henri Poincare, Bind 13, Nr. 2, 2012, s. 333-362.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Asymptotics for Two-dimensional Atoms
AU - Nam, Phan Thanh
AU - Portmann, Fabian
AU - Solovej, Jan Philip
PY - 2012
Y1 - 2012
N2 - 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 $E(N,Z)=-{1/2}Z^2\ln Z+(E^{\TF}(\lambda)+{1/2}c^{\rm H})Z^2+o(Z^2)$ when $Z\to \infty$ and $N/Z\to \lambda$, where $E^{\TF}(\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\rm H}\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\to \infty$, which is contrary to the expected behavior of three-dimensional atoms.
AB - 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 $E(N,Z)=-{1/2}Z^2\ln Z+(E^{\TF}(\lambda)+{1/2}c^{\rm H})Z^2+o(Z^2)$ when $Z\to \infty$ and $N/Z\to \lambda$, where $E^{\TF}(\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\rm H}\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\to \infty$, which is contrary to the expected behavior of three-dimensional atoms.
KW - Faculty of Science
KW - Mathematical Phyics
U2 - 10.1007/s00023-011-0123-2
DO - 10.1007/s00023-011-0123-2
M3 - Journal article
VL - 13
SP - 333
EP - 362
JO - Annales Henri Poincare
JF - Annales Henri Poincare
SN - 1424-0637
IS - 2
ER -
ID: 37759675