Abstract
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 $\ensuremath{\Delta}(3, 3)$ 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.
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