Mathematical Physics Seminar

The infimum of the spectrum of the (non-relativistic) atomic Schrödinger operators with large nuclear charge $Z$ is given by the Thomas-Fermi-Energy (Lieb and Simon 1977). Later it was shown that it should be augmented by $Z^2/4$ (Scott correction) which originates from electrons close to the nucleus. However, for large $Z$ the Schrödinger model becomes physically questionable, since the innermost electrons move very fast, i.e., relativistic dynamics becomes important for a correct description. Relativistic models that -- in some qualitative way -- describe atoms have been investigated, establishing that the leading energy is still given by the Thomas-Fermi energy and that the Scott correction should be lowered. However, all of those models are oversimplifications; none is expected to give quantitative correct result.

In this talk we will present the no-pair Hamiltonian in the Furry picture, short Furry Hamiltonian. It is known to give numerically results agreeing with measured data and it is supported by Schwinger's derivation of the Scott correction in the relativistic context (Schwinger 1981). We will show that the Furry Hamiltonian has a Scott correction and that it agrees reasonably with the measured and semi-empirical data.

The talk is based on joint work with Michael Handrek, Munich.