An efficient approach for spin - angular integrations in atomic structure calculations

Gaigalas, Gediminas; Rudzikas, Zenonas; Fischer, Charlotte Froese

doi:10.1088/0953-4075/30/17/006

Cited by 107 publications

(170 citation statements)

References 21 publications

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“…The executables are automatically moved to the subdirectory grasp2K v1 1/bin. The names of the executables follow the conventions in grasp2K, where the extension 3 indicates that the angular part of the programs are based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique [10,11].…”

Section: Installation Of the Programmentioning

confidence: 99%

“…The electron density at the origin, needed to calculate the FS in the approximation (27), is also the mean value of a one-body operator:…”

Section: The Field Shiftmentioning

confidence: 99%

“…Expectation value of the two-body operator Using Racah's algebra one can express the r.m.e of any two-particle operator as [26,27] […”

Section: The Field Shiftmentioning

confidence: 99%

“…The evaluation of the submatrix elements of these operators is explained in [27]. This general expression is implemented in grasp2K version 1 1, but what is needed for the SMS evaluation is much simpler, since k 1 = k 2 = 1, σ 1 = σ 2 = 0 and k=0, such as all three terms of (10) have the particular form…”

Section: The Field Shiftmentioning

confidence: 99%

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ris3: A program for relativistic isotope shift calculations

Nazé

Gaidamauskas

Gaigalas

et al. 2013

Computer Physics Communications

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An atomic spectral line is characteristic of the element producing the spectrum. The line also depends on the isotope. The program ris3 (Relativistic Isotope Shift) calculates the electron density at the origin and the normal and specific mass shift parameters. Combining these electronic quantities with available nuclear data, isotope-dependent energy level shifts are determined.Keywords: Isotope shift, field shift, mass shift, normal mass shift, specific mass shift, relativistic nuclear recoil, nuclear radius The nuclear motion and volume effects are treated in first order perturbation theory. Taking the zero-order wave function in terms of a configuration state expansion |Ψ P JM J = µ c µ |Φ(γ µ P JM J ) , where P , J and M J are, respectively, the parity and angular quantum numbers, the electron density at the nucleus and the normal and specific mass shift parameters may generally be expressed as µ,ν c µ c ν γ µ P JM J |ϑ|γ ν P JM J where ϑ is the relevant operator. The matrix elements, in turn, can be expressed as sums over radial integrals multiplied by angular coefficients. All the angular coefficients are calculated using routines from grasp2K version 1 1 package [1]. NEW VERSION PROGRAM SUMMARY Reasons for the new version:This new version takes the nuclear recoil corrections into account within the (αZ) 4 m 2 /M approximation [2] and also allows a storage of the angular coefficients for a series of calculations within a given isoelectronic sequence. Furthermore, the program jj2lsj, a module of grasp2K version 1 1 toolkit that allows a transformation of ASFs from a jj-coupled CSF basis into an LSJ-coupled CSF basis, has been especially adapted to present ris3 results using LSJ labels of the states. This additional tool is called ris3 lsj. Summary of revisions:This version is compatible with the new angular approach of grasp2K version 1 1 package [1] and can store necessary angular coefficients. According to the formalism of the relativistic nuclear recoil, the "uncorrected" expression of the normal mass shift has been fundamentally modified compared with its expression in [3]. Restrictions:The complexity of the cases that can be handled is entirely determined by grasp2K package [1] used for the generation of the electronic wave functions. Unusual features: Angular data stored on disc and can be reused. LSJ labels are used for the states. Additional comments: ?? 2Running time:As an example, we evaluated the isotope shifts parameters and the electron density at the origin using the wave functions of Be-like system. We used MCDHF wave function built on a complete active space (CAS) with n = 8 (296 626 CSFs -62 orbitals) that contains 3 non-interacting blocks of given parity and J values involving 6 different eigenvalues in total. Calculations take around 10 hours on one AMD Opteron 6100 @ 2.3GHz CPU with 8 cores (64GB DDR3 RAM 1.333GHz). If angular files are available the time is reduced to 20 minutes. The storage of the angular data takes 139Mb and 7.2Gb for the one-body and the two-body elements, r...

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Section: Installation Of the Programmentioning

confidence: 99%

“…The electron density at the origin, needed to calculate the FS in the approximation (27), is also the mean value of a one-body operator:…”

Section: The Field Shiftmentioning

confidence: 99%

“…Expectation value of the two-body operator Using Racah's algebra one can express the r.m.e of any two-particle operator as [26,27] […”

Section: The Field Shiftmentioning

confidence: 99%

Section: The Field Shiftmentioning

confidence: 99%

See 2 more Smart Citations

ris3: A program for relativistic isotope shift calculations

Nazé

Gaidamauskas

Gaigalas

et al. 2013

Computer Physics Communications

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“…The code of Hibbert et al (1991) has been updated according to the methods presented by Gaigalas et al (1997Gaigalas et al ( , 1998.…”

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confidence: 99%

Atomic Data for Zn Ii: Improving Spectral Diagnostics of Chemical Evolution in High-Redshift Galaxies

Kisielius

Kulkarni

Ferland

et al. 2015

ApJ

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Damped Lyα (DLA) and sub-DLA absorbers in quasar spectra provide the most sensitive tools for measuring the element abundances of distant galaxies. The estimation of abundances from absorption lines depends sensitively on the accuracy of the atomic data used. We have started a project to produce new atomic spectroscopic parameters for optical andUV spectral lines using state-of-the-art computer codes employing a very broad configuration interaction (CI) basis. Here we report our results for Zn II, an ion used widely in studies of the interstellar medium (ISM) as well as DLAs andsub-DLAs. We report new calculations of many energy levels of Zn IIand the line strengths of the resulting radiative transitions. Our calculations use the CI approach within a numerical HartreeFock framework. We use both nonrelativistic and quasi-relativistic one-electron radial orbitals. We have incorporated the results of these atomic calculations into the plasma simulation code Cloudyand applied them to a lab plasma and examples of a DLA and a sub-DLA. Our values of the Zn II λλ 2026, 2062 oscillator strengths are higher than previous values by 0.10 dex. TheCloudy calculations for representative absorbers with the revised Zn atomic data imply ionization corrections lower than calculated earlier by 0.05 dex. The new results imply that Zn metallicities should be lower by 0.1 dex for DLAs and by 0.13-0.15 dex for sub-DLAs than in past studies. Our results can be applied to other studies of Zn II in the Galactic and extragalactic ISM.

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