A general yet simple and hence practical algorithm for calculating SV, ::l SV 2 X V, Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. Ii is shown that SV 3 Racah coefficients can be obtained as a solution to a set of simultaneous equations with unknown coefficients given as a by-product of the initial steps in the SV3 ::l SV2 X VI Wigner coefficient construction algorithm. A general expression for evaluating SV3 ::l R3 Wigner coefficients as a sum over a simple subset of the corresponding SU 3 ::l SV 2 X VI Wigner coefficients is also presented. State conjugation properties are discussed and symmetry relations for both the SV3::l SV 2 X VI and SV 3 ::l R3 Wigner coefficients are given. Machine codes based on the results are available.

High speed storage required: SU3 3 SU2 x U1 Wigner coefficients, 13008 words SU3 Racahcoefficients, 14654 words; SU3 3R3 Wigner coefficients, 14202 words SU3 Racah coefficients, 14654 words. SU3~R~Wigner coefficients, 14 202 words No. of bits in a word: 32 Is the program overlaid? No. No. of magnetic tapes required: None. Otherperipherals used: Card reader, line printer No. of cards in combinedprogram and test deck: 2046 Card punching code: EBCDIC.

The shell model with the phenomenologic~l effective interaction is applied to study level structures of 2°Ne, Z~Ne, 2~-Nc, 22Na and 24Mg. The full basis in the sd shell is taken in 2°Ne to diagonalize the energy matrices. This example confirms that SUn symmetry and the supermultiplet provide a very good way of truncation. This truncation is used to calculate level schemes of many nuclei beyond 2°Ne. Even though deviations of the effective interaction from the pure Q-Q interaction and the spin-orbit interaction break the SU3 symmetry and the supermultiplct, the main components of calculated wave functions in low-lying energies can be very well labelled by these two symmetries. Generally, good agreement with observations is found. Particularly, the lowest rotational bands are nicely explained. Exceptions are the level structure of 22Na and ½+ in tPO and 2~Ne, which are too low in the calculation, and the K = 2 bandsin 22Ne and 2~'Mg, which are again too low in the calculation.

The sdg interacting-boson model is applied to 168 Er. Energy levels and E2 transitions are calculated. This model is shown to solve the problem of anharmonicity regarding the excitation energy of the first # w = 4"*" band relative to that of the first K n = 2* one. The level scheme including the K w = 3 + band is well reproduced and the calculated B(E2Y § are consistent with the experimental data.

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