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 $1s-0d$ 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, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$.

• Received 7 April 1977

DOI:https://doi.org/10.1103/PhysRevC.16.2050