SU(3) ⊃ R(3) Wigner coefficients in the 2s-1d shell

Vergados, J.D.

doi:10.1016/0375-9474(68)90249-2

SU(3) ⊃ R(3) Wigner coefficients in the 2s-1d shell

J.D. Vergados

1968

74 pages

Published in:

Nucl.Phys.A 111 (1968) 681-754

Published: 1968

DOI:

10.1016/0375-9474(68)90249-2

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Abstract: (Elsevier)

Explicit algebraic expressions are given for SU(3) ⊃ R(3) Wigner coefficients, which are of particular interest in p-shell and 2s-1d shell-model calculations. An orthogonal basis tied closely to Elliott's basis is chosen according to a systematic recipe. The Wigner coefficients are those involving the Kronecker products ( λ 1 μ 1 ) × ( λ 2 μ 2 ) → ( λ 3 μ 3 ) in the following cases: 1. (i) ( λ 2 μ 2 ) = (10), (01) and μ 1 ≦ 4 (arbitrary λ i ), i = 1, 3. (For the case μ i = 4, only auxillary coefficients are tabulated whenever the angular momentum multiplicity is 3. From these the final Wigner coefficients can be calculated for any specific case of interest.) 2. (ii) ( λ 2 μ 2 ) = (20), (02) and μ i ≦ 3 (arbitrary λ i ), or λ i ≦ 3 (arbitrary μ i ) i = 1, 3. 3. (iii) ( λ 2 μ 2 = (11) and μ i ≦ 3 (arbitrary λ i ), or λ i ≦ 3 (arbitrary μ i ) i = 1, 3 except for ( λ 3) × (11) → ( λ 3) which is not given.

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