Calculation of the energy levels of Ge, Sn, Pb and their ions in the VN−4V^{N-4} approximation

Energy levels of germanium, tin and lead together with their single, double and triple ionized positive ions have been calculated using the $V^{N-M}$ approximation suggested in the previous work (Dzuba, physics/0501032) (M=4 - number of valence electrons). Initial Hartree-Fock calculations are done for the quadruply ionized ions with all valence electrons removed. The core-valence correlations are included beyond the second-order of the many-body perturbation theory. Interaction between valence electrons is treated by means of the configuration interaction technique. It is demonstrated that accurate treatment of the core-valence correlations lead to systematic improvement of the accuracy of calculations for all ions and neutral atoms.Comment: 7 pages, 3 figures, 3 tables; submitted to Phys. Rev.

Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains

Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is subdiffusion. Many models of subdiffusion include a history dependence. This greatly confounds efforts to incorporate domain growth. Here we derive the fractional partial differential equations that govern subdiffusion on a growing domain, based on a Continuous Time Random Walk. This requires the introduction of a new, comoving, fractional derivative.Comment: 12 pages, 1 figur

Precision isotope shift measurements in Ca+^+ using highly sensitive detection schemes

We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with non-closed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a co-trapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the $^{2}$D$_{3/2}$ $\rightarrow$ $^{2}$P$_{1/2}$ transition in $^{40}$Ca$^{+}$, resulting in a transition frequency of $f=346\, 000\, 234\, 867(96)$ kHz. Furthermore, we determine the isotope shift of this transition and the $^{2}$S$_{1/2}$ $\rightarrow$ $^{2}$P$_{1/2}$ transition for $^{42}$Ca$^{+}$, $^{44}$Ca$^{+}$ and $^{48}$Ca$^{+}$ ions relative to $^{40}$Ca$^{+}$ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data

An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.Comment: 13 pages, 4 figure

Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains

Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a one-dimensional domain that is evolving. The model equations, which have been derived from generalized continuous time random walks, can incorporate complexities such as subdiffusive transport and inhomogeneous domain stretching and shrinking. A method for constructing analytic expressions for short time moments of the position of the particles is developed and moments calculated from this approach are shown to compare favourably with results from random walk simulations and numerical integration of the reaction transport equation. The results show the important role played by the initial condition. In particular, it strongly affects the time dependence of the moments in the short time regime by introducing additional drift and diffusion terms. We also discuss how our reaction transport equation could be applied to study the spreading of a population on an evolving interface.Comment: 38 pages, 10 figure

Microstructural asymmetry of the corticospinal tracts predicts right-left differences in circle drawing skill in right-handed adolescents

Most humans show a strong preference to use their right hand, but strong preference for the right hand does not necessarily imply a strong right–left asymmetry in manual proficiency (i.e., dexterity). Here we tested the hypothesis that intra-individual asymmetry of manual proficiency would be reflected in microstructural differences between the right and left corticospinal tract (CST) in a cohort of 52 right-handed typically-developing adolescents (11–16 years). Participants were asked to fluently draw superimposed circles with their right dominant and left non-dominant hand. Temporal regularity of circle drawing movements was assessed for each hand using a digitizing tablet. Although all participants were right-handed, there was substantial inter-individual variation regarding the relative right-hand advantage for fluent circle drawing. All subjects underwent whole-brain diffusion tensor imaging at 3 Tesla. The right and left CST were defined as regions-of-interest and mean fractional anisotropy (FA) and diffusivity values were calculated for right and left CST. On average, mean FA values were higher in the left CST relative to right CST. The degree of right–left FA asymmetry showed a linear relationship with right–left asymmetry in fluent circle drawing after correction for age and gender. The higher the mean FA values were in the left dominant CST relative to the right non-dominant CST, the stronger was the relative right-hand advantage for regular circle drawing. These findings show that right–left differences in manual proficiency are highly variable in right-handed adolescents and that this variation is associated with a right-left microstructural asymmetry of the CST

A New Option for a Search for Alpha Variation: Narrow Transitions with Enhanced Sensitivity

We consider several transitions between narrow lines that have an enhanced sensitivity to a possible variation of the fine structure constant, alpha. This enhancement may allow a search to be performed with an effective suppression of the systematic sources of uncertainty that are unavoidable in conventional high-resolution spectroscopic measurements. In the future this may provide the strongest laboratory constraints on alpha variation