We have developed symbolic-numeric algorithms implemented in the Wolfram Mathematica to compute the orthonormal canonical Gel’fand–Tseitlin (G-T), non-canonical Bargmann-Moshinsky (B-M) and Elliott (E) bases of irreducible representations SU(3) ⊃ SO(3) ⊃ SO(2) group for a given orbital of angular momentum. The algorithms resolve the missing label problem by solving eigenvalue problem for the “labeling” B-M operator X(3 ). The effective numeric algorithm for construction of the G-T basis provides a unique capability to perform large scale calculations even with 8 byte real numbers. The algorithms for the construction of B-M and E bases implemented very fast modified Gramm–Schmidt orthonormalization procedure. In B-M basis, a very effective formula for calculation of the matrix X(3 ) is derived by graphical method. The implemented algorithm for construction of the B-M basis makes it possible to perform large scale exact as well as arbitrary precision calculations. The algorithm for the construction of the E basis resolves the missing label problem by calculation of the matrix X(3 ) in an orthogonal basis from this matrix previously built in non-orthogonal basis. The implementation of this algorithm provides large scale calculations with arbitrary precision. © 2021, Springer Nature Switzerland AG.

Authors

Deveikis A.^{1}
,
Gusev A.^{2}
,
Vinitsky S.
^{2,}
^{3}
,
Góźdź A.
^{4}
,
Pȩdrak A.
^{5}
,
Burdik Č.^{6}
,
Pogosyan G.^{7}

Conference proceedings

Publisher

Springer Science and Business Media Deutschland GmbH

Language

English

Pages

100-120

Status

Published

Volume

12865 LNCS

Year

2021

Organizations

^{1}Vytautas Magnus University, Kaunas, Lithuania^{2}Joint Institute for Nuclear Research, Dubna, Russian Federation^{3}RUDN University, 6 Miklukho-Maklaya, Moscow, 117198, Russian Federation^{4}Institute of Physics, Maria Curie-Skłodowska University, Lublin, Poland^{5}National Centre for Nuclear Research, Warsaw, Poland^{6}Czech Technical University, Prague, Czech Republic^{7}Yerevan State University, Yerevan, Armenia

Keywords

Bargmann–Moshinsky basis; Elliott basis; Gel’fand–Tseitlin basis; Gram–Schmidt orthonormalization; Irreducible representations; Missing label problem; Orthonormal non-canonical basis; SU(3) ⊃ SO(3) ⊃ SO(2)

Date of creation

16.12.2021

Date of change

16.12.2021

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Article

Lecture Notes in Networks and Systems.
Springer Science and Business Media Deutschland GmbH.
Vol. 280.
2021.
P. 383-392

Lecture Notes in Networks and Systems.
Springer Science and Business Media Deutschland GmbH.
Vol. 280.
2021.
P. 760-767