We examine the prescription for obtaining single-particle splittings at a closed minor shell, i.e., $\epsilon -{\epsilon }^{\prime }=E(N+1,Z)+E(N-1,Z)-2E(N,Z)\mathrm{}$. We find that to understand the value obtained, especially if the minor shell nucleus is deformed, e.g., ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, we have to introduce many-particle-many-hole correlations. These correlations are less important although not negligible in the vicinity of a good closed shell, like ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$.

NUCLEAR STRUCTURE The influence of many particle-many hole correlations on single particle energies, especially for closed minor shells.

• Received 25 June 1976

DOI:https://doi.org/10.1103/PhysRevC.14.1662