Following Brandow's suggestion of setting $QUQ=0\mathrm{}$, where $U$ is the single-particle potential, the Bethe-Goldstone equation becomes $\Psi =\Phi -\left[\frac{Q}{(QTQ-\omega }\right]v\Psi$. This equation has been approximated by replacing $Q$ with the Eden-Emery Pauli operator and by neglecting $\hat{T}\chi$, where $\hat{T}$ is the off-diagonal part of the c.m. kinetic energy operator in the oscillator representation. Care has been taken to retain $\hat{T}\Phi$, which is a large term. The approximate equation has been solved iteratively. It yields defect functions with the bulk of the effect of $Q$ built in. Correction terms to our approximate results have been estimated. A very satisfactory feature of the present approach is that there is considerable cancellation between the so-called spectral and Pauli correction terms. The biggest correction term is $〈\chi \left|\hat{T}\right|\chi 〉$, which can be as large as 0.5 MeV in the triplet even case.

• Received 15 July 1971

DOI:https://doi.org/10.1103/PhysRevC.5.75