An upper bound on the ionic ground state density at the nucleus
An upper bound on the electronic ground-state density of an \(N\)-electron Hamiltonian is proved. More precisely, it is shown that \[ \limsup_{Z\to\infty} {\rho_d(0)\over Z^3}\leq {\pi\over 48} q, \] where \(\rho_d\) is the corresponding density, \(Z\) is the charge of the nucleus and \(q\) is the number of spin states of a single electron. The authors provide a short proof for the above estimates which generalizes known results on neutral atoms. The main ingredients in the proof are an inequality of Hoffmann-Ostenhof et. al. for \(\rho_d(0)\) and Lieb-Thirring's estimate on the correlation energy.
scientific article; zbMATH DE number 1087267