Excitation of theΔ(3,3) resonance in compressed finite nuclei from a constrained mean-field method

In this paper we present a nonrelativistic microscopic mean-field framework for finite nuclei in which the nucleus is described as a system of A baryons where each baryon is a dynamically determined superposition of a nucleon (N) and a Δ(3,3) resonance. The N-N interaction is a Brueckner G matrix based on the Reid soft-core interaction while the N-Δ transition potentials and Δ-Δ interactions are one-boson-exchange potentials. The ground-state properties of the nuclei ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are determined within the spherical Hartree-Fock approximation in a no-core 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.