Application of the method of irreducible tensorial operators to study the expansion of stationary perturbation theory

Gaigalas, Gediminas; Merkelis, G V

doi:10.1007/bf03053831

Cited by 5 publications

(13 citation statements)

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“…The procedures described are fairly simple, however, they are sufficient for the majority of cases. The more complete description of this generalized graphical approach may be found in Gaigalas et al 1985, Gaigalas 1985, Gaigalas and Merkelis 1987 4 Quasispin Formalism A wave function with u shells in LS coupling may be denoted in the form…”

Section: Generalized Graphical Methodsmentioning

confidence: 99%

“…In this section we shall sketch the generalized version of the graphical technique, in which not only one-and two-particle operators are presented in tensorial form (such graphs are analogous to Feynman-Goldstone diagrams but they do not depend on magnetic quantum numbers (Merkelis et al 1986a, b)), but which also allows us to represent graphically any tensorial product of the second quantization operators and to perform graphically the operations with the secondly quantized operators as well as with their tensorial products (Gaigalas et al 1985, Gaigalas 1985, Gaigalas and Merkelis 1987. Such a graphical technique is most suitable for representing any one-and two-particle operator already presented in tensorial form and to find general expressions for their matrix elements.…”

Section: Generalized Graphical Methodsmentioning

confidence: 99%

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On the secondly quantized theory of the many-electron atom

Gaigalas¹,

Rudzikas²

1996

J. Phys. B: At. Mol. Opt. Phys.

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Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spinangular coefficients of radial integrals appearing in the expressions of matrix elements of arbitrary physical operators of atomic quantities has two main disadvantages: (i) The numerical codes for the calculation of spin-angular coefficients are usually very time-consuming; (ii) f-shells are often omitted from programs for matrix element calculation since the tables for their coefficients of fractional parentage are very extensive.On the secondly quantized theory of many-electron atom PACS: 3110, 3115

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Section: Generalized Graphical Methodsmentioning

confidence: 99%

Section: Generalized Graphical Methodsmentioning

confidence: 99%

On the secondly quantized theory of the many-electron atom

Gaigalas¹,

Rudzikas²

1996

J. Phys. B: At. Mol. Opt. Phys.

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“…( 2). Only one of them [9,10] is formulated in an irreducible tensorial form which gives the opportunity to include core-valence correlations with any number of valence electrons. This allows us to apply it to various applications using the combination [4] of the angular momentum theory [17], as described in Ref.…”

Section: Rayleigh-schrödinger Perturbation Theory In Irreducible Tens...mentioning

confidence: 99%

“…Here we present such an implementation of MBPT to the GRASP code [8] in which core-valence correlations can be taken into account with the help of MBPT and the rest of correlations are included in the ordinary way (RCI) by GRASP package. We use the most suitable for these systems irreducible tensorial form of Rayleigh-Schrödinger stationary many-body perturbation theory [9,10]. This allows us to divide the calculation of terms of the perturbation series into the calculation of spin-angular terms by using Racah algebra [4,5,11] and into the accompanying radial integrals.…”

Section: Introductionmentioning

confidence: 99%

Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core–valence correlations

Gaigalas,

Rynkun,

Kitovienė

2024

physics

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The General Relativistic Atomic Structure package [GRASP2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, and J. Bieroń, Comput. Phys. Commun. (2019), DOI: 10.1016/j.cpc.2018.10.032] is based on multiconfiguration Dirac– Hartree–Fock and relativistic configuration interaction (RCI) methods for energy structure calculations. The atomic state function used in the program is built from the set of configuration state functions (CSFs). The valence–valence, core–valence and core–core correlations are explicitly included through expansions over CSFs in RCI. We present a combination of RCI and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form to account for electron core–valence correlations when an atom or ion has any number of valence electrons. This newly developed method, which offers two ways of use, allows a significant reduction of the CSF space for complex atoms and ions. We also demonstrate how the method and program works for the energy structure calculation of Cl III ion.

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“…The phase factor À1 NNÀ1=2 appears when we restore the order of the operators ãl in jnl N a L M L which corresponds to the order of the operators a l in jnl N a L M L . The diagram 10 A 2 is associated with the operator À1 NNÀ1=2 jnl N a L M L : Note, that in the present paper, di¡erently from [23] and [25], we include the phase factor À1 NNÀ1=2 in the de¢nition of the diagram 10 A 2 : Such a de¢nition of 10 A 2 reduces the number of phase factors which must be presented explicitly.…”

Section: Graphical Evaluation Of Matrix Elementsmentioning

confidence: 99%

Graphical Method of Evaluation of Matrix Elements in the Second Quantization Representation

Merkelis

2001

Phys. Scr.

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A correlation velocity log (CVL) is an acoustic navigation aid that estimates the velocity of a maritime vehicle using a transmitter and a receiving array. The CVL discussed here operates by calculating the correlation coefficient between the echoes from a pair of consecutive acoustic pulses transmitted towards the seafloor, across all combinations of receiver pairings in the array. A correlation surface is constructed by plotting the correlation coefficients versus the spatial separation vector of all the receiver pairings. The coordinates of the peak of this surface provide an estimate of the velocity vector of the vessel. However, the correlation coefficient surface exhibits high variance within a modest distance from the peak position, and individual datasets tend to be asymmetric about the peak position. Since each dataset consists of a sparsely sampled set of discrete measurements, the variance makes the task of peak estimation very challenging. This paper outlines the operating principles of CVLs and describes peak-finding techniques that are used to improve the accuracy and precision of the instrument. Three peak estimation techniques are considered, namely the highest point, and fitting of an axisymmetric quadratic model using either least squares or a nonlinear implementation of maximum likelihood estimation. It is shown that the maximum likelihood approach offers some advantages when the peak is controlled to lie near the centre of the receiver array, but the advantages are small compared to the additional computational load required.

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Application of the method of irreducible tensorial operators to study the expansion of stationary perturbation theory

Cited by 5 publications

References 0 publications

On the secondly quantized theory of the many-electron atom

On the secondly quantized theory of the many-electron atom

Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core–valence correlations

Graphical Method of Evaluation of Matrix Elements in the Second Quantization Representation

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