Reduced Coefficients of Fractional Parentage and Matrix Elements of the Tensor W(kqkj) in jj-Coupling

Gaigalas, Gediminas; Fritzsche, S.; Rudzikas, Zenonas

doi:10.1006/adnd.2000.0844

Cited by 22 publications

(21 citation statements)

References 28 publications

(69 reference statements)

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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%

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%

ris3: A program for relativistic isotope shift calculations

Nazé

Gaidamauskas

Gaigalas

et al. 2013

Computer Physics Communications

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“…In this paper, a new version of the JJ2LSJ program, consistent with the approach described in [7][8][9][10], is presented. The program performs the transformation of ASFs from a jj-to LSJ-coupling and provides the option to assign all level unique labels.…”

Section: Discussionmentioning

confidence: 99%

“…The expressions and values of these coefficients are published in [6,7]. These transformation matrices, which are applied internally by the program JJ2LSJ, are consistent with the definition of the coefficients of fractional parentage [8,9] and with the phase system used in the [10]. So the program presented in the paper supports transformation from jj-to LSJ-coupling if ASF (which needs transformation) was created using the approach [7][8][9][10].…”

Section: Transformation From Jj-to Lsj-couplingmentioning

confidence: 99%

JJ2LSJ Transformation and Unique Labeling for Energy Levels

Gaigalas

Fischer

Rynkun

et al. 2017

Atoms

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Abstract:The JJ2LSJ program, which is important not only for the GRASP2K package but for the atom theory in general, is presented. The program performs the transformation of atomic state functions (ASFs) from a jj-coupled CSF basis into an LSJ-coupled CSF basis. In addition, the program implements a procedure that assigns a unique label to all energy levels. Examples of how to use the JJ2LSJ program are given. Several cases are presented where there is a unique labeling problem.

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“…The codes of the MCHF atomic structure package were later modified for large-scale computation on parallel systems using Message Passing Interface (MPI) [19]. In addition the algebra underlying the angular integration was improved, and 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 made it possible, for the first time, to perform calculations for systems with open f -shells [20,21,22]. The latest release, the ATSP2K package [23], also implements a fast biorthogonal transformation technique that allows the initial and final states in a transition to be independently optimized [24].…”

Section: Computational Atomic Structurementioning

confidence: 99%

Accurate transition probabilities from large-scale multiconfiguration calculations - A tribute to Charlotte Froese Fischer

Jönsson¹,

Godefroid²,

Gaigalas³

et al. 2013

AIP Conference Proceedings

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Abstract. The development of multiconfiguration computer packages for atomic structure calculations is reviewed with special attention to the work of Charlotte Froese Fischer. The underlying theory is described along with methodologies to choose basis expansions of configuration state functions. Calculations of energies and transitions rates are presented and the accuracy of the results is assessed. Limitations of multiconfiguration methods are discussed and it is shown how these limitations can be circumvented by a division of the original large-scale computational problem into a number of smaller problems.

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Reduced Coefficients of Fractional Parentage and Matrix Elements of the Tensor W(kqkj) in jj-Coupling

Cited by 22 publications

References 28 publications

ris3: A program for relativistic isotope shift calculations

ris3: A program for relativistic isotope shift calculations

JJ2LSJ Transformation and Unique Labeling for Energy Levels

Accurate transition probabilities from large-scale multiconfiguration calculations - A tribute to Charlotte Froese Fischer

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