Electron corrected Lorentz forces in solids and molecules in magnetic field

We describe the effective Lorentz forces on the ions of a generic insulating system in an magnetic field, in the context of Born-Oppenheimer ab-initio molecular dynamics. The force on each ion includes an important contribution of electronic origin, which depends explicitly on the velocity of all other ions. It is formulated in terms of a Berry curvature, in a form directly suitable for future first principles classical dynamics simulations based {\it e.g.,} on density functional methods. As a preliminary analytical demonstration we present the dynamics of an H$_2$ molecule in a field of intermediate strength, approximately describing the electrons through Slater's variational wavefunction.Comment: 5 pages, 2 figures; to appear in Phys. Rev.

Spectroscopic Constraints on the Surface Magnetic Field of the Accreting Neutron Star EXO 0748-676

Gravitationally redshifted absorption lines of Fe XXVI, Fe XXV, and O VIII were inferred recently in the X-ray spectrum of the bursting neutron star EXO 0748-676. We place an upper limit on the stellar magnetic field based on the iron lines. The oxygen absorption feature shows a multiple component profile that is consistent with Zeeman splitting in a magnetic field of ~(1-2)x10^9 gauss, and for which the corresponding Zeeman components of the iron lines are expected to be blended together. In other systems, a field strength >5x10^{10} gauss could induce a blueshift of the line centroids that would counteract gravitational redshift and complicate the derivation of constraints on the equation of state of the neutron star.Comment: 5 pages, submitted to Phys. Rev. Let

Lithium in strong magnetic fields

The electronic structure of the lithium atom in a strong magnetic field 0 <= gamma <= 10 is investigated. Our computational approach is a full configuration interaction method based on a set of anisotropic Gaussian orbitals that is nonlinearly optimized for each field strength. Accurate results for the total energies and one-electron ionization energies for the ground and several excited states for each of the symmetries ^20^+, ^2(-1)^+, ^4(-1)^+, ^4(-1)^-, ^2(-2)^+, ^4(-2)^+, $^4(-3)^{+}$ are presented. The behaviour of these energies as a function of the field strength is discussed and classified. Transition wave lengths for linear and circular polarized transitions are presented as well.Comment: 12 pages, 13 figures, accepted for publication in Phys. Rev.

Electronic Structure of Atoms in Magnetic Quadrupole Traps

We investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. The spin-spatial as well as generalized time reversal symmetries are established and shown to lead to a two-fold degeneracy of the electronic states in the presence of the field. Low-lying as well as highly excited Rydberg states are computed and analyzed for a broad regime of field gradients. The delicate interplay between the Coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. Electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and in particular the transition wavelengths and corresponding dipole strengths. The peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.Comment: 17 pages, 13 figures, accepted for publication in PR

Hydrogen and Helium atoms in strong magnetic fields

The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.Comment: 15 pages, 6 figure

Relationship of Foot Strike Pattern and Landing Impacts during a Marathon

Purpose: Foot strike patterns influence landing mechanics, with rearfoot strike (RFS) runners exhibiting higher impact loading than forefoot strike (FFS) runners. The few studies that included midfoot strike (MFS) runners have typically grouped them together with FFS. Additionally, most running studies have been conducted in laboratories. Advances in wearable technology now allow the measurement of runners' mechanics in their natural environment. The purpose of this study was to examine the relationship between foot strike pattern and impacts across a marathon race. Methods: 222 healthy runners (119 M, 103 F; 44.1±10.8 years) running a marathon race were included. A treadmill assessment was undertaken to determine foot strike pattern (FSP). An ankle mounted accelerometer recorded tibial shock (TS) over the course of the marathon. TS was compared between RFS, MFS and FFS. Correlations between speed and impacts were examined between FSPs. TS was also compared at the 10km and 40km race points. Results: RFS and MFS runners exhibited similar TS (12.24±3.59g vs. 11.82±2.68g, p=0.46) that was significantly higher (p<0.001 and p<0.01, respectively) than FFS runners (9.88±2.51g). Additionally, TS increased with speed for both RFS (r=0.54, p=0.01) and MFS (r=0.42, p=0.02) runners, but not FFS (r=0.05, p=0.83). Finally, both speed (p<0.001) and TS (p<0.001) were reduced between the 10km and 40km race points. However, when normalized for speed, TS was not different (p= 0.84). Conclusions: RFS and MFS exhibit higher TS than FFS. Additionally, RFS and MFS increase TS with speed, while FFS do not. These results suggest that the impact loading of MFS is more like RFS than FFS. Finally, TS, when normalized for speed, is similar between the beginning and end of the race

The helium atom in a strong magnetic field

We investigate the electronic structure of the helium atom in a magnetic field b etween B=0 and B=100a.u. The atom is treated as a nonrelativistic system with two interactin g electrons and a fixed nucleus. Scaling laws are provided connecting the fixed-nucleus Hamiltonia n to the one for the case of finite nuclear mass. Respecting the symmetries of the electronic Ham iltonian in the presence of a magnetic field, we represent this Hamiltonian as a matrix with res pect to a two-particle basis composed of one-particle states of a Gaussian basis set. The corresponding generalized eigenvalue problem is solved numerically, providing in the present paper results for vanish ing magnetic quantum number M=0 and even or odd z-parity, each for both singlet and triplet spin symmetry. Total electronic energies of the ground state and the first few excitations in each su bspace as well as their one-electron ionization energies are presented as a function of the magnetic fie ld, and their behaviour is discussed. Energy values for electromagnetic transitions within the M=0 sub space are shown, and a complete table of wavelengths at all the detected stationary points with respect to their field dependence is given, thereby providing a basis for a comparison with observed ab sorption spectra of magnetic white dwarfs.Comment: 21 pages, 4 Figures, acc.f.publ.in J.Phys.

Using structure-based organic chemistry online tutorials with automated correction for student practice and review

This article describes the development and implementation of an open-access organic chemistry question bank for online tutorials and assessments at University College Cork and Dublin Institute of Technology. SOCOT (structure-based organic chemistry online tutorials) may be used to supplement traditional small-group tutorials, thereby allowing students to develop essential problem-solving skills in organic chemistry. This online approach may be used for both formative and summative assessment. Students complete one problem set weekly or fortnightly, which consists of a number of questions of varying difficulty. A wide range of question types is possible; for example, prediction of reaction products, identification of reaction intermediates or reagents, and retrosynthetic analyses. Questions involving stereochemistry may be also be incorporated. The implementation is described, along with several sample questions and advice for creating questions. This approach is suitable for all levels of undergraduates, from introductory nonmajors to final-year chemistry students. Student feedback was overwhelmingly positive, and in particular, students found SOCOT to be a quite useful tool for review purposes. Our approach uses MarvinSketch, which is free for academic purposes, and the SMILES algorithm, which converts chemical structures into a text string and is compatible with any learning management system