Properties of ${}^{12}C$ in the Ab Initio Nuclear Shell Model

We obtain properties of ${}^{12}\mathrm{C}$ in the ab initio no-core nuclear shell model. The effective Hamiltonians are derived microscopically from the realistic CD Bonn and the Argonne $\mathrm{V}{8}^{\prime }$ nucleon-nucleon $\left(\mathrm{NN}\right)$ potentials as a function of the finite harmonic oscillator basis space. Binding energies, excitation spectra, and electromagnetic properties are presented for model spaces up to $5ħ\Omega$. The favorable comparison with available data is a consequence of the underlying $\mathrm{NN}$ interaction rather than a phenomenological fit.