Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory

The density of an atom in a state of well-defined angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and Local Density Approximations, generally violate this feature. We analyze, by means of perturbation theory, the degree of this violation and show that it is small. The correct symmetry of the density can be assured by a constrained-search formulation without significantly altering the calculated energies. We compare our procedure to the (different) common practice of spherically averaging the self-consistent potential. Kohn-Sham density functional theory with the exact exchange-correlation potential has the correct finite spherical harmonic content in its density; but the corresponding exact single particle potential and wavefunctions contain an infinite number of spherical harmonics.Comment: 11 pages, 6 figures. Expanded discussion of spherical harmonic expansion of Hartree density. Some typos corrected, references adde

Geographical and temporal distribution of SARS-CoV-2 clades in the WHO European Region, January to June 2020

We show the distribution of SARS-CoV-2 genetic clades over time and between countries and outline potential genomic surveillance objectives. We applied three available genomic nomenclature systems for SARS-CoV-2 to all sequence data from the WHO European Region available during the COVID-19 pandemic until 10 July 2020. We highlight the importance of real-time sequencing and data dissemination in a pandemic situation. We provide a comparison of the nomenclatures and lay a foundation for future European genomic surveillance of SARS-CoV-2.Peer reviewe

Decay spectroscopy at the two-proton drip line: radioactivity of the new nuclides 160Os and 156W

The radioactivity of 76160Os84 and 74156W82 that lie at the two-proton drip line have been measured in an experiment performed at the Accelerator Laboratory of the University of Jyväskylä. The 160Os nuclei were produced using fusion-evaporation reactions induced by a beam of 310 MeV 58Ni ions bombarding a 106Cd target. The 160Os ions were separated in flight using the recoil separator MARA and implanted into a double-sided silicon strip detector, which was used to measure their decays. The α decays of the ground state of 160Os (Eα = 7092(15) keV, t1/2 = 97−32+97 μs) and its isomeric state (Eα = 8890(10) keV, t1/2 = 41−9+15 μs) were measured, allowing the excitation energy of the isomer to be determined as 1844(18) keV. These α-decay properties and the excitation energy of the isomer are compared with systematics. The α decays were correlated with subsequent decays to investigate the β decays of the ground state of 156W, revealing that unlike its isotones, both low-lying isomers were populated in its daughter nuclide, 156Ta. An improved value for the half-life of the proton-decaying high-spin isomeric state in 73156Ta83 of 333−22+25 ms was obtained in a separate experiment using the same experimental systems with a 102Pd target. This result was employed to improve the precision of the half-life determined for 156W, which was measured as 157−34+57 ms