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 -