The effective interactions between nucleons in the $s-d$ shells are investigated from an exact shell-model calculation via a least-squares fit of the experimental energy spectra of the normal-parity states in the ${}_{}{}^{18,19,20}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18,19,20}{}_{}{}^{}\mathrm{F}$, and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ nuclei. The effects of the $d_{\frac{3}{2}}$ single-particle orbit in shell-model calculations of light $s-d$-shell nuclei are discussed briefly. The two-body matrix elements are compared with those calculated by Kuo and by Arima et al.

• Received 20 December 1971

DOI:https://doi.org/10.1103/PhysRevC.5.2013