In this paper we present a nonrelativistic microscopic mean-field framework for finite nuclei in which the nucleus is described as a collection of nucleons and $\Delta (3, 3)$ resonances. The ground-state properties of the nuclei ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are determined within the spherical Hartree-Fock approximation using a realistic effective no-core Hamiltonian in a basis consisting of up to six major oscillator shells. A detailed study of the zero-temperature properties of these nuclei under compression and dilation is presented in order to gain insight into the nuclear equation of state. Under certain conditions, a transition to a mixture of nucleons and deltas is found in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ but not in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The transition is reminiscent of a first-order phase transition.

• Received 27 May 1987

DOI:https://doi.org/10.1103/PhysRevC.36.2180