We discuss the equation of motion $〈{\psi }_{\hat{B}}\left|\right[H,a_{\alpha }\left]\right|{\psi }_0〉=(E_{\hat{B}}-E_0) 〈{\psi }_{\hat{B}}\left|a_{\alpha }\right|{\psi }_0〉$ in the subspace of states $|{\psi }_{\hat{B}}〉=\Sigma {\alpha }^{}{\beta }_{\alpha }{a}_{\alpha }|{\psi }_0〉$, where $|{\psi }_0〉$ is the correlated ground state of a double magic nucleus. It is shown that this equation can be solved with high accuracy if some low-order correlation functions of the $\exp S$ theory are known. Preliminary results are given for ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ for four different nucleon-nucleon interactions, i.e., the Reid-soft-core potential with and without the three-body correction of Blatt and McKellar, the Hamada-Johnston potential, and the de Toureill-Sprung supersoft-core potential. The connection with shell model states is discussed.

NUCLEAR STRUCTURE ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ calculated hole states ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. Centroid energies from microscopic theory.

• Received 16 July 1976

DOI:https://doi.org/10.1103/PhysRevC.16.1650