Abstract
The angular momentum projected deformed particle-hole model (projected Tamm-Dancoff) is applied to the positive parity states of the nuclei $^{20}\mathrm{Ne}$ and $^{24}\mathrm{Mg}$. For the single particle states a large basis containing three major shells is used. The effects of a truncation of this basis to the $1s\ensuremath{-}0d$ shell only are studied, and the possibility of describing these effects by a perturbation expansion is investigated. It turns out that a perturbation expansion in terms of self-consistent projected Tamm-Dancoff states yields a very good agreement already in lowest order, while the usual renormalization of the interaction in terms of spherical one particle-one hole states fails to reproduce the result obtained in the large model space. The reliability of the projected Tamm-Dancoff model is confirmed by a comparison to an exact shell model calculation.NUCLEAR STRUCTURE Angular momentum projected particle-hole model, effective interactions, $^{20}\mathrm{Ne}$, $^{24}\mathrm{Mg}$.
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