Asymptotics for Two-dimensional Atoms

TY - JOUR

T1 - Asymptotics for Two-dimensional Atoms

AU - Nam, Phan Thanh

AU - Portmann, Fabian

AU - Solovej, Jan Philip

PY - 2012/3

Y1 - 2012/3

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) = -1/2Z 2lnZ + (E TF(λ) + 1/2c H)Z 2 + o(Z 2) when Z → ∞ and N/Z → λ, where E TF(λ) is given by a Thomas-Fermi type variational problem and c H ≈ -2.2339 is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when Z → ∞, 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) = -1/2Z 2lnZ + (E TF(λ) + 1/2c H)Z 2 + o(Z 2) when Z → ∞ and N/Z → λ, where E TF(λ) is given by a Thomas-Fermi type variational problem and c H ≈ -2.2339 is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when Z → ∞, 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

SN - 1424-0637

VL - 13

SP - 333

EP - 362

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 2

ER -