This dissertation presents a non-relativistic microscopic mean field theory of finite nuclei in which the nucleus is described as a collection of nucleons and delta resonances. The ground state properties of the nuclei ¹⁶O and ⁴⁰Ca are determined within the spherical Hartree-Fock (SHF) approximation using a realistic effective no-core Hamiltonian in basis spaces 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. The transition is reminiscent of a first order phase transition.

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