Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

Jursenas, Rytis; Merkelis, Gintaras

doi:10.2478/s11534-009-0126-5

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…The phase multiplier Υ is optional. Usually it is chosen to be equal to 15 In general, the two-particle interaction operator g 12 acts on H × H. However, g γ is reduced and it acts on irreducible tensor space H γ , obtained by reducing 25 (Sec. 2, Eq.…”

Section: The Third-order Effective Hamiltonianmentioning

confidence: 99%

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Development of algebraic techniques for the atomic open-shell MBPT(3)

Jursenas¹,

Merkelis²

2010

Journal of Mathematical Physics

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The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of occupation-number representation and intermediate normalization, the third-order deviations are worked out by employing a computational software program that embodies the generalized Bloch equation. We prove that in the most general case, the terms of effective interaction operator on the proposed complete model space are generated by not more than eight types of the $n$-body ($n\geq2$) parts of the wave operator. To compose the effective Hamiltonian matrix elements handily, the operators are written in irreducible tensor form. We present the reduction scheme in a versatile disposition form, thus it is suited for the coupled-cluster approach

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Section: The Third-order Effective Hamiltonianmentioning

confidence: 99%

“…In Ref. 25 , it was showed that v μαζ β may be constructed in two distinct ways: (i) reducing the Kronecker product (…”

Section: The Third-order Effective Hamiltonianmentioning

confidence: 99%

Development of algebraic techniques for the atomic open-shell MBPT(3)

Jursenas¹,

Merkelis²

2010

Journal of Mathematical Physics

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“…In MBPT this coefficient denotes miscellaneous products of one-or two-particle matrix elements (with energy denominator included). The systematic study of two-particle matrix elements can be found in [12][13][14]. The application of this methodology for the second-order effective Hamiltonian one can find in [15].…”

Section: Introductionmentioning

confidence: 99%

Irreducible tensor form of three-particle operator for open-shell atoms

Jursenas

Merkelis

2011

Open Physics

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Abstract:A three-particle operator in a second quantized form is studied systematically and comprehensively. The operator is transformed into irreducible tensor form. Possible coupling schemes, identified by the classes of symmetric group S 6 , are presented. Recoupling coefficients that make it possible to transform a given scheme into another are produced by using the angular momentum theory combined with quasispin formalism. The classification of the three-particle operator which acts on = 1 2 6 open shells of equivalent electrons of atom is considered. The procedure to construct three-particle matrix elements are examined. PACS

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