Central and noncentral components of the effectivesd-shell interaction

The contributions of central as well as noncentral two-body interactions to the matrix elements of various effective interactions for the $\mathrm{sd}$ shell are studied in an SU(3) two-particle basis. The results show that their central parts agree rather well and exhibit an approximate SU(3) symmetry. However, large differences are found between the noncentral parts of microscopic and phenomenological interactions, respectively. The influence of noncentral components of the matrix elements of Glaudemans et al. on experimental data is investigated for the case of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, with the result that the $\mathrm{LS}$ component is very important to reproduce the correct ground state binding energy. Some effects introduced by higher order two-body interactions and many-body interactions are discussed.