Structural trends in atomic nuclei from laser spectroscopy of tin

Tin is the chemical element with the largest number of stable isotopes. Its complete proton shell, comparable with the closed electron shells in the chemically inert noble gases, is not a mere precursor to extended stability; since the protons carry the nuclear charge, their spatial arrangement also drives the nuclear electromagnetism. We report high-precision measurements of the electromagnetic moments and isomeric differences in charge radii between the lowest 1/2(+), 3/2(+), and 11/2(-) states in Sn117-131, obtained by collinear laser spectroscopy. Supported by state-of-the-art atomic-structure calculations, the data accurately show a considerable attenuation of the quadrupole moments in the closed-shell tin isotopes relative to those of cadmium, with two protons less. Linear and quadratic mass-dependent trends are observed. While microscopic density functional theory explains the global behaviour of the measured quantities, interpretation of the local patterns demands higher-fidelity modelling. Measurements of the hyperfine structure of chemical elements isotopes provide unique insight into the atomic nucleus in a nuclear model-independent way. The authors present collinear laser spectroscopy data obtained at the CERN ISOLDE and measure hyperfine splitting along a long chain of odd-mass tin isotopes.Peer reviewe

Nuclear charge radii of ⁶²⁻⁸⁰Zn and their dependence on cross-shell proton excitations

Nuclear charge radii of ⁶²⁻⁸⁰Zn have been determined using collinear laser spectroscopy of bunched ion beams at CERN-ISOLDE. The subtle variations of observed charge radii, both within one isotope and along the full range of neutron numbers, are found to be well described in terms of the proton excitations across the Z = 28 shell gap, as predicted by large-scale shell model calculations. It comprehensively explains the changes in isomer-to-ground state mean square charge radii of ⁶⁹⁻⁷⁹Zn, the inversion of the odd-even staggering around N = 40 and the odd-even staggering systematics of the Zn charge radii. With two protons above Z = 28, the observed charge radii of the Zn isotopic chain show a cumulative effect of different aspects of nuclear structure including single particle structure, shell closure, correlations and deformations near the proposed doubly magic nuclei, ⁶⁸Ni and ⁷⁸Ni

Relativistic configuration interaction calculations of energy levels, isotope shifts, hyperfine structures, and transition rates in the 2s22p2–2s2p3 transition array for the carbon-like sequence

Energy levels, fine-structure separations, specific mass shift parameters, isotope shifts, hyperfine interaction constants, Landé gJ -factors and transition probabilities are reported forthe 2s22p2–2s2p3 transition array in N II, O III, F IV, Ne V and Ti XVII. Wavefunctions were determined using the multiconfiguration Dirac–Hartree–Fock method with account forvalence, core-valence and core–core correlation effects. The transition energies and rates are compared with experimental data and with values from other calculations

Are MCDF calculations 101 % correct in the superheavy elements range?

We explore QED and many-body effects in super-heavy elements up to Z = 173 using the multicon- figuration Dirac–Fock method. We study the effect of going beyond the average level approximation on the determination of the ground state of element 140 and compare with the recent work of Pekka Pyykko¨ on the periodic table for super-heavy elements (Pyykko¨, in Phys Chem Chem Phys, 13:161, 2011). We confirm that QED corrections are of the order of 1% on ionization energies. We show that the atomic number at which the 1s shell dives into the negative energy continuum is 173 and is not affected by the approximation employed to evaluate the electron–electron interaction

Ab initio calculations of the hyperfine structure of zinc and evaluation of the nuclear quadrupole moment Q(Zn-67)

The relativistic multiconfiguration Dirac-Hartree-Fock and the nonrelativistic multiconfiguration Hartree-Fock methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the 4s4p P-3(1)degrees and 4s4p P-3(2)degrees states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment Q((67) Zn) = 0.122(10) b. The error bar was evaluated in a quasistatistical approach-the calculations were carried out with 11 different methods, and then the error bar was estimated from the differences between the results obtained with those methods.Peer reviewe

Comment on the magnetic dipole hyperfine interaction in the gold atom ground state

The multiconfiguration Dirac–Hartree–Fock (MCDHF) model has been employed to calculatethe magnetic dipole hyperfine constant A of the 5d106s 2S1/2 ground state of atomic gold.Electron correlation effects contribute more than 20% to the total value of A. We investigatedthe effects of single, double, and a subset of triple substitutions. The calculations reveal strongcancellations between one-, two- and three-particle correlation effects. It is demonstrated thatin the case of the ground state of atomic gold the three-particle effects are comparable in sizeto the one- and two-particle ones

Accurate Transition Probabilities from Large-scale Multiconfiguration Calculations

The quality and resolution of solar, stellar, and other types of plasma observations, has so improved that the accuracy of atomic data is frequently a limiting factor in the interpretation of these new observations. An obvious need is for accurate transition probabilities. Laboratory measurements, e.g. using ion/traps, beam-foil or laser techniques, have been performed for isolated transitions and atoms, but no systematic laboratory study exists or is in progress. Instead the bulk of these atomic data must be calculated. Multiconfiguration methods, either non-relativistic with Breit-Pauli corrections (MCHF+BP) or fully relativistic (MCDHF), are useful to this end. The main advantage of multiconfiguration methods is that they are readily applicable to excited and openshell systems, including open f-shells, across the whole periodic table, thus allowing for mass production of atomic data. The accuracy of these calculations depends on the complexity of the shell structure and on the underlying model for describing electron correlation. By systematically increasing the number of basis functions in large-scale calculations, as well as exploring different models for electron correlation, it is often possible to provide both transition energies and transition probabilities with some error estimate. The success of the calculations also depends on available computer software. In this talk we will describe a collaborative effort to continue the important and acclaimed work of Prof. Charlotte Froese Fischer and to develop state-of-the-art multiconfiguration codes. In the latest versions of the non-relativistic (ATSP2K) and relativistic (GRASP2K) multiconfiguration codes angular integration is performed using second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique that allows open f-shells. In addition it is possible to transform results given in the relativistic j j-coupling to the more useful LSJ-coupling. Biorthogonal transformation techniques are implemented and initial and final states in a transition can be separately optimized. The main parts of the codes are also adapted for parallel execution using MPI. Results from recent large-scale calculations using these codes will be presented for systems of different complexity. Of special interest are spectrum calculations, where all states up to a certain level are computed at the same time. Finally, we look at new computational developments that allow basis functions in multiconfiguration methods to be built on several independent and non-orthogonal sets of one-electron orbitals. Initial calculations indicate that the increased flexibility of the orbital sets allows transition energies, as well as other atomic properties, to be predicted to a much higher accuracy than before

The ATSP2K and GRASP2K Multiconfiguration Atomic Structure Program Packages

Synopsis The ATSP2K and GRASP2K program packages for large scale atomic calculations are presented. Anumber of applications are given to illustrate the potential and restriction of the packages

Computational Atomic Structure

There is an increasing demand for accurate atomic data due to advancements in experimental techniques and investments in large scale research facilities. In astrophysics the quality and resolution of solar and stellar spectra has so improved that the accuracy of atomic data is frequently a limiting factor in the interpretation. Accurate atomic data are also required in plasma physics and in other emerging areas such as laser spectroscopy on isotope separators, X-ray lithography, and lighting research. The needs include accurate transition energies, fine- and hyperfine structures, isotope shifts as well as parameters related to interaction with external magnetic fields. Also there is a constant need for transition rates between excited states. Data are needed for a wide range of elements and ionization stages. To meet the demands for accurate atomic data the COMPutational Atomic Structure (COMPAS) group has been formed. The group is involved in developing state of the art computer codes for atomic calculations in the non-relativistic scheme with relativistic corrections in the Breit-Pauli approximation [1] as well as in the fully relativistic domain. Here we describe new developments of the GRASP2K relativistic atomic structure code [2, 3]. We present results for a number of systems and properties to illustrate the potential and restriction of computational atomic structure. Among the properties are hyperfine structures and hyperfine quenched rates, Zeeman splittings in intermediate fields, isotope shifts and transition rates [4]. We also discuss plans for future code developments