https://doi.org/10.1140/epjp/s13360-024-05581-6
Regular Article
Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry
1
Department of Physics and Astronomy, Louisiana State University, 70803-4001, Baton Rouge, LA, USA
2
Quantum CodeX, Baton Rouge, USA
3
Department of Physics, Liaoning Normal University, 116029, Dalian, China
4
Nuclear Physics Institute, Academy of Sciences of the Czech Republic, 25068, Řež, Czech Republic
5
Department of Computer Systems, Faculty of Information Technology, Czech Technical University, 16000, Prague, Czech Republic
Received:
12
July
2024
Accepted:
21
August
2024
Published online:
25
October
2024
A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group–subgroup chains is presented. The canonical 
coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical 
coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single 
irreducible representation is obtained from the dimension of the null space of the 
raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on 
. It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).
© The Author(s) 2024
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