Methods of calculating ionization energies of multielectron (five or more) isoelectronic atomic ions

We have previously used simple empirical equations to reproduce the literature values of the ionization energies of isoelectronic sequences of up to four electrons which gave very good agreement. We reproduce here a kinetic energy expression with corrections for relativity and Lamb shift effects which give excellent agreement with the literature values. These equations become more complex as the number of electrons in the system increases. Alternative simple quadratic expressions for calculating ionization energies of multielectron ions are discussed. A set of coefficients when substituted into a simple expression produces very good agreement with the literature values. Our work shows that Slater's rules are not appropriate for predicting trends or screening constants. This work provides very strong evidence that ionization energies are not functions of complete squares, and when calculating ionization energies electron transition/relaxation has to be taken into account. We demonstrate clearly that for particular isoelectronic sequences, the ionizing electrons may occupy different orbitals and in such cases more than one set of constants are needed to calculate the ionization energies

Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model

We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model. We consider a) the Wilson-Dirac operator at the critical value of the hopping parameter; b) Neuberger's overlap operator; c) the fixed point operator. We test chiral properties of the spectrum, dispersion relations and rotational invariance of the mesonic bound state propagators.Comment: Revised version; 13 pages (LaTeX), 3 figures (EPS

Decomposition of Optical Flow on the Sphere

We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are motivated by recent trends in image analysis. In particular we treat $u+v$ decomposition as well as hierarchical decomposition. Helmholtz decomposition of motion fields is obtained as a natural by-product of the chosen numerical method based on vector spherical harmonics. All models are tested on time-lapse microscopy data depicting fluorescently labelled endodermal cells of a zebrafish embryo.Comment: The final publication is available at link.springer.co

Impure Thoughts on Inelastic Dark Matter

The inelastic dark matter scenario was proposed to reconcile the DAMA annual modulation with null results from other experiments. In this scenario, WIMPs scatter into an excited state, split from the ground state by an energy delta comparable to the available kinetic energy of a Galactic WIMP. We note that for large splittings delta, the dominant scattering at DAMA can occur off of thallium nuclei, with A~205, which are present as a dopant at the 10^-3 level in NaI(Tl) crystals. For a WIMP mass m~100GeV and delta~200keV, we find a region in delta-m-parameter space which is consistent with all experiments. These parameters in particular can be probed in experiments with thallium in their targets, such as KIMS, but are inaccessible to lighter target experiments. Depending on the tail of the WIMP velocity distribution, a highly modulated signal may or may not appear at CRESST-II.Comment: 3 pages, 1 figure, accepted for publication in Physical Review Letter