Collinear laser spectroscopy was performed on Zn (Z=30) isotopes at ISOLDE, CERN. The study of hyperfine spectra of nuclei across the Zn isotopic chain, N=33–49, allowed the measurement of nuclear ...spins for the ground and isomeric states in odd-A neutron-rich nuclei up to N=50. Exactly one long-lived (>10 ms) isomeric state has been established in each 69–79Zn isotope. The nuclear magnetic dipole moments and spectroscopic quadrupole moments are well reproduced by large-scale shell–model calculations in the f5pg9 and fpg9d5 model spaces, thus establishing the dominant term in their wave function. The magnetic moment of the intruder Iπ=1/2+ isomer in 79Zn is reproduced only if the νs1/2 orbital is added to the valence space, as realized in the recently developed PFSDG-U interaction. The spin and moments of the low-lying isomeric state in 73Zn suggest a strong onset of deformation at N=43, while the progression towards 79Zn points to the stability of the Z=28 and N=50 shell gaps, supporting the magicity of 78Ni.
Spectral lines from different isotopes display a small separation in energy, commonly referred to as the line isotope shift. The program ris 4 (Relativistic Isotope Shift) calculates normal and ...specific mass shift parameters as well as field shift electronic factors from relativistic multiconfiguration Dirac–Hartree–Fock wave functions. These quantities, together with available nuclear data, determine isotope-dependent energy shifts. Using a reformulation of the field shift, it is possible to study, in a model-independent way, the atomic energy shifts arising from changes in nuclear charge distributions, e.g. deformations.
Program title: ris 4
Program Files doi: http://dx.doi.org/10.17632/8vjpf69zch.1
Licensing provisions: MIT
Programming language: Fortran 77 and Fortran 90
Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 2187
Does the new version supersede the previous version?: Yes
Subprograms used: grasp 2K VERSION 1_1
Nature of problem: Prediction of level and transition isotope shifts in atoms using four-component relativistic wave functions.
Solution method: The nuclear mass shifts and field shifts are treated using first order perturbation theory. The electron density and the normal and specific mass shift parameters can be expressed as ∑μ,νcμcν〈Φ(γμPJMJ)|Vˆ|Φ(γνPJMJ)〉, where Vˆ is the relevant operator and Ψ(γPJMJ)=∑ν=1McνΦ(γνPJMJ) is the configuration state expansion, where P, J and MJ are the parity and angular quantum numbers, respectively. The matrix elements, in turn, can be decomposed as sums over radial integrals multiplied by angular coefficients. The angular coefficients are calculated using routines from the grasp2K version 1_1 package 1.
Reasons for new version: This new version calculates field shift electronic factors resulting from non-constant (varying) electron densities inside the nucleus.
Summary of revisions: This new version uses an expression of the field shift that through a polynomial expansion of the electron density contains higher order radial moments and thus takes the varying electron density within the nuclear volume into account.
Restrictions: The complexity of the cases that can be handled is entirely determined by the grasp2K package 1 used for the generation of the electronic wave functions.
Unusual features: Using a reformulation of the field shift, it is possible to study the atomic energy shifts arising from changes in nuclear charge distributions, e.g. deformations.
References:
1 P. Jönsson, G. Gaigalas, J. Bieroń, C. Froese Fischer, I.P. Grant, New version: Grasp2K relativistic atomic structure package, Comput. Phys. Commun. 184 (9) (2013) 2197–2203.
The present Grasp2018 is an updated Fortran 95 version of the recommended block versions of programs from Grasp2K Version 1_1 for large-scale calculations Jönsson et al. (2013). MPI programs are ...included so that all major tasks can be executed using parallel computers. Tools have been added that simplify the generation of configuration state function expansions for the multireference single- and double computational model. Names of programs have been changed to accurately reflect the task performed by the code. Modifications to the relativistic self-consistent field program have been made that, in some instances, greatly reduce the number of iterations needed for determining the requested eigenvalues and the memory required. Changes have been made to the relativistic configuration interaction program to substantially cut down on the time for constructing the Hamiltonian matrix for configuration state function expansions based on large orbital sets. In the case of a finite nucleus the grid points have been changed so that the first non-zero point is Z-dependent as for the point nucleus. A number of tools have been developed to generate LaTeX tables of eigenvalue composition, energies, transition data and lifetimes. Tools for plotting and analyzing computed properties along an iso-electronic sequence have also been added. A number of minor errors have been corrected. A detailed manual is included that describes different aspects of the package as well as the steps needed in order to produce reliable results.
Program Title:Grasp2018
Program Files doi:http://dx.doi.org/10.17632/x574wpp2vg.1
Licensing provisions: MIT license
Programming language: Fortran 95.
Nature of problem: Prediction of atomic properties – atomic energy levels, isotope shifts, oscillator strengths, radiative decay rates, hyperfine structure parameters, specific mass shift parameters, Zeeman effects – using a multiconfiguration Dirac–Hartree–Fock approach.
Solution method: The computational method is the same as in the previous Grasp2K 1,2 version except that only the latest recommended versions of certain routines are included.
Restrictions: All calculations are for bound state solutions. Instead of relying on packing algorithms for specifying arguments of arrays of integrals, orbitals are designated by a “short integer” requiring one byte of memory for a maximum of 127 orbitals. The tables of reduced coefficients of fractional parentage used in this version are limited to sub-shells with j≤9∕2 3; occupied sub-shells with j>9∕2 are, therefore, restricted to a maximum of two electrons. Some other parameters, such as the maximum number of orbitals are determined in a parameter_def_M.f90 file that can be modified prior to compile time.
Unusual features: Parallel versions are available for several applications.
References•1 P. Jönsson, X. He, C. Froese Fischer, and I. P. Grant, Comput. Phys. Commun. 176, 597 (2007).•2 P. Jönsson, G. Gaigalas, J. Bieroń, C. Froese Fischer, and I. P. Grant, Comput. Phys. Commun. 184, 2197 (2013).•3 G. Gaigalas, S. Fritzsche, Z. Rudzikas, Atomic Data and Nuclear Data Tables 76, 235 (2000).
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.
A new module, RDENSITY, of the GRASP2018 package 1 is presented for evaluating the radial electron density function of an atomic state described by a multiconfiguration Dirac-Hartree-Fock or ...configuration interaction wave function in the fully relativistic scheme. The present module is the relativistic version of DENSITY 2 that was developed for the ATSP2K package 3. The calculation of the spin-angular factors entering in the expression of the expectation value of the density operator is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique 4. The natural orbitals (NOs) are evaluated from the diagonalization of the density matrix, taking advantage of its κ-block structure. The features of the code are discussed in detail, focusing on the advantages and properties of the NOs and on the electron radial density picture as a mean for investigating electron correlation and relativistic effects.
Program title:RDENSITY
CPC Library link to program files:https://doi.org/10.17632/4sdrf5kfzd.1
Licensing provisions: MIT license
Programming language: FORTRAN 95
Nature of problem: This program determines the atomic electron radial density in the MCDHF approximation. It also evaluates the natural orbitals by diagonalizing the density matrix.
Solution method: Building the density operator using second quantization - Spherical symmetry averaging - Evaluating the matrix elements of the one-body excitation operators in the configuration state function (CSF) space using the angular momentum theory in orbital, spin, and quasispin spaces.
Additional comments including restrictions and unusual features: We evaluated the electron radial density and natural orbitals of the lowest states in Mg II. The MCDHF wave functions consisted of four non-interacting blocks and a total of 79 000 CSFs. The calculation took around 2 minutes using a computer with an Intel(R) Xeon(R) Gold 6148 processor @ 2.4 GHz.
1GRASP2018 - A Fortran 95 version of the General Relativistic Atomic Structure Package, C. Froese Fischer, G. Gaigalas, P. Jönsson and J. Bieroń, Comput. Phys. Commun. 237 (2019) 184-187.2Multiconfiguration electron density function for the ATSP2K-package, A. Borgoo, O. Scharf, G. Gaigalas and M. Godefroid, Comput. Phys. Commun. 181 (2010) 426-4393An MCHF atomic-structure package for large-scale calculations, C. Froese Fischer, G. Tachiev, G. Gaigalas, and M. Godefroid, Comput. Phys. Commun. 176 (2007) 559-5794An efficient approach for spin-angular integrations in atomic structure calculations, G. Gaigalas, Z. Rudzikas, and C. Froese Fischer, J. Phys. B: At. Mol. Phys., 30 (1997) 3747-3771
A revised version of Grasp2K P. Jönsson, X. He, C. Froese Fischer, I.P. Grant, Comput. Phys. Commun. 177 (2007) 597 is presented. It supports earlier non-block and block versions of codes as well as ...a new block version in which the njgraf library module A. Bar-Shalom, M. Klapisch, Comput. Phys. Commun. 50 (1988) 375 has been replaced by the librang angular package developed by Gaigalas based on the theory of G. Gaigalas, Z.B. Rudzikas, C. Froese Fischer, J. Phys. B: At. Mol. Phys. 30 (1997) 3747, G. Gaigalas, S. Fritzsche, I.P. Grant, Comput. Phys. Commun. 139 (2001) 263. Tests have shown that errors encountered by njgraf do not occur with the new angular package. The three versions are denoted v1, v2, and v3, respectively. In addition, in v3, the coefficients of fractional parentage have been extended to j=9/2, making calculations feasible for the lanthanides and actinides. Changes in v2 include minor improvements. For example, the new version of rci2 may be used to compute quantum electrodynamic (QED) corrections only from selected orbitals. In v3, a new program, jj2lsj, reports the percentage composition of the wave function in LSJ and the program rlevels has been modified to report the configuration state function (CSF) with the largest coefficient of an LSJ expansion. The bioscl2 and bioscl3 application programs have been modified to produce a file of transition data with one record for each transition in the same format as in Atsp2K C. Froese Fischer, G. Tachiev, G. Gaigalas, M.R. Godefroid, Comput. Phys. Commun. 176 (2007) 559, which identifies each atomic state by the total energy and a label for the CSF with the largest expansion coefficient in LSJ intermediate coupling. All versions of the codes have been adapted for 64-bit computer architecture.
Program title: Grasp2K, version 1_1
Catalogue identifier: ADZL_v1_1
Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZL_v1_1.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 730252
No. of bytes in distributed program, including test data, etc.: 14808872
Distribution format: tar.gz
Programming language: Fortran.
Computer: Intel Xeon, 2.66 GHz.
Operating system: Suse, Ubuntu, and Debian Linux 64-bit.
RAM: 500 MB or more
Classification: 2.1.
Catalogue identifier of previous version: ADZL_v1_0
Journal reference of previous version: Comput. Phys. Comm. 177 (2007) 597
Does the new version supersede the previous version?: Yes
Nature of problem: Prediction of atomic properties — atomic energy levels, oscillator strengths, radiative decay rates, hyperfine structure parameters, Landé gJ-factors, and specific mass shift parameters — using a multiconfiguration Dirac–Hartree–Fock approach.
Solution method: The computational method is the same as in the previous Grasp2K 1 version except that for v3 codes the njgraf library module 2 for recoupling has been replaced by librang 3,4.
Reasons for new version: New angular libraries with improved performance are available. Also methodology for transforming from jj- to LSJ-coupling has been developed.
Summary of revisions: New angular libraries where the coefficients of fractional parentage have been extended to j=9/2, making calculations feasible for the lanthanides and actinides. Inclusion of a new program jj2lsj, which reports the percentage composition of the wave function in LSJ. Transition programs have been modified to produce a file of transition data with one record for each transition in the same format as Atsp2K C. Froese Fischer, G. Tachiev, G. Gaigalas and M.R. Godefroid, Comput. Phys. Commun. 176 (2007) 559, which identifies each atomic state by the total energy and a label for the CSF with the largest expansion coefficient in LSJ intermediate coupling. Updated to 64-bit architecture. A comprehensive user manual in pdf format for the program package has been added.
Restrictions: The packing algorithm restricts the maximum number of orbitals to be ≤214. The tables of reduced coefficients of fractional parentage used in this version are limited to subshells with j≤9/2 5; occupied subshells with j>9/2 are, therefore, restricted to a maximum of two electrons. Some other parameters, such as the maximum number of subshells of a CSF outside a common set of closed shells are determined by a parameter.def file that can be modified prior to compile time.
Unusual features: The bioscl3 program reports transition data in the same format as in Atsp2K 6, and the data processing program tables of the latter package can be used. The tables program takes a name.lsj file, usually a concatenated file of all the .lsj transition files for a given atom or ion, and finds the energy structure of the levels and the multiplet transition arrays. The tables posted at the website http://atoms.vuse.vanderbilt.edu are examples of tables produced by the tables program. With the extension of coefficients of fractional parentage to j=9/2, calculations for the lanthanides and actinides become possible.
Running time: CPU time required to execute test cases: 70.5 s.
References: 1P. Jönsson, X. He, C. Froese Fischer, I.P. Grant, Comput. Phys. Commun. 177 (2007) 597.2A. Bar-Shalom, M. Klapisch, Comput. Phys. Commun. 50 (1988) 375.3G. Gaigalas, Z.B. Rudzikas, C. Froese Fischer, J. Phys. B: At. Mol. Phys. 30 (1997) 3747.4G. Gaigalas, S. Fritzsche, I.P. Grant, Comput. Phys. Commun. 139 (2001) 263.5G. Gaigalas, S. Fritzsche, Z. Rudzikas, At. Data Nucl. Data Tables 76 (2000) 235.6C. Froese Fischer, G. Tachiev, G. Gaigalas, M.R. Godefroid, Comput. Phys. Commun. 176 (2007) 559.
Hyperfine-structure parameters and isotope shifts for the 795-nm atomic transitions in $^{217,218,219}$At have been measured at CERN-ISOLDE, using the in-source resonance-ionization spectroscopy ...technique. Magnetic dipole and electric quadrupole moments, and changes in the nuclear mean-square charge radii, have been deduced. A large inverse odd-even staggering in radii, which may be associated with the presence of octupole collectivity, has been observed. Namely, the radius of the odd-odd isotope $^{218}$At has been found to be larger than the average of its even-$N$ neighbors, $^{217,219}$At. The discrepancy between the additivity-rule prediction and experimental data for the magnetic moment of $^{218}$At also supports the possible presence of octupole collectivity in the considered nuclei.
Multiconfiguration Dirac-Fock models have been employed to compute the electric field gradient in the ground state of the neutral bismuth atom. Combined with the experimental electric quadrupole ...hyperfine interaction constant, one obtains for (209)Bi the nuclear quadrupole moment Q = -516 (15) mb, which is almost 40% away from the previously accepted standard value -370 (26) mb, and narrows by over an order of magnitude the long-standing, extremely broad array of various results ranging from -370 to -710 mb. The recent Q values of (202-208,210(m)-213)Bi by Pearson et al. suffer a consequent change.
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