It is emphasized that the propagator-renormalized Brueckner-Hartree-Fock self-consistent field theory (RBHF) is an improvement over the unrenormalized Brueckner approximation plus rearrangement energy corrections for two main reasons: (i) through the renormalization of the off-diagonal matrix elements of the single-particle potential in a fixed basis the shape and size of the field are modified, leading to increased nuclear radii and improved density distributions which affect the expectation values of all observables; (ii) through the solution of coupled equations for the "true" occupation probabilities, occupancy-rearrangement effects are calculated self-consistently rather than merely to lowest order. For an accurate test of the RBHF approximation in light nuclei, center-of-mass (c.m.) corrections to the calculated properties are quite important. Two ways of making the c.m. corrections, discussed earlier, are applied and compared in calculations with the Reid soft-core and Hamada-Johnston interactions for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The RBHF equations are solved by matrix diagonalization in the harmonic-oscillator basis. The well depth of the oscillator reference potential for virtual "particle" states is determined by requiring self-consistency, for the low-lying "particle" states, with an average off-energy-shell RBHF self-energy. The binding energies are in good agreement with experiment, as is the radius of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, while the radius of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is about 8% too small. A careful comparison of separation energies with experiment is made; c.m. corrections, the effect of spuriosity (presence of excited c.m. components) in the $0s_{\frac{1}{2}}$ hole state in ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ or ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, and second- and third-order rearrangement energies calculated earlier, are included. Details of density distributions and electron elastic scattering form factors are given. The possible existence of a dip in the proton density at the center of the $\alpha$ particle is discussed. The need for higher dimensionality in the calculation of form factors and properties of unbound single-particle states is established.

[NUCLEAR STRUCTURE Renormalized Brueckner-Hartree-Fock method; c.m., rearrangement corrections. ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$; calculated binding, SP $E$'s, separation $E$'s, true occupation probabilities, $\rho$, $e$-scattering form factor.]

• Received 24 September 1973

DOI:https://doi.org/10.1103/PhysRevC.9.1221