arXiv subjects
Publications and source records attributed to Konstantin Merz.
We prove the convergence of the density on the scale $Z^{-1}$ to the density of the Bohr atom (with infinitely many electrons) (strong Scott conjecture) for a model that is known to describe heavy atoms accurately.
We consider a large neutral atom of atomic number $Z$, taking relativistic effects into account by assuming the dispersion relation $\sqrt{c^2p^2+c^4}$. We study the behavior of the one-particle ground state density on the length scale $Z^{-1}$ in the limit $Z,c\to\infty$ keeping $Z/c$ fixed and find that the spherically averaged density as well as all individual angular momentum densities separately converge to the relativistic hydrogenic ones. This proves the generalization of the strong Scott conjecture for relativistic atoms and shows, in particular, that relativistic effects occur close to the nucleus. Along the way we prove upper bounds on the relativistic hydrogenic density.
We consider a large neutral atom of atomic number $Z$, modeled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably rescaled one-particle ground state density on the Thomas--Fermi length scale $Z^{-1/3}$. Using an observation by Fefferman and Seco (1989), we find that the density on this scale converges to the minimizer of the Thomas--Fermi functional of hydrogen as $Z\to\infty$ when $Z/c$ is fixed to a value not exceeding $2/π$. This shows that the electron density on the Thomas--Fermi length scale does not exhibit any relativistic effects.