Large-basis ab initio no-core shell model and its application to ${}^{12}\mathbf{C}$

We present the framework for the ab initio no-core nuclear shell model and apply it to obtain properties of ${}^{12}\mathrm{C}.$ We derive two-body effective interactions microscopically for specific model spaces from the realistic CD-Bonn and the Argonne V8’ nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ potentials. We then evaluate binding energies, excitation spectra, radii, and electromagnetic transitions in the $0ħ\Omega ,$ $2ħ\Omega ,$ and $4ħ\Omega$ model spaces for the positive-parity states and the $1ħ\Omega ,$ $3ħ\Omega ,$ and $5ħ\Omega$ model spaces for the negative-parity states. Dependence on the model-space size, on the harmonic-oscillator frequency, and on the type of the $\mathrm{NN}$ potential, used for the effective interaction derivation, are studied. In addition, electromagnetic and weak neutral elastic charge form factors are calculated in the impulse approximation. Sensitivity of the form-factor ratios to the strangeness one-body form-factor parameters and to the influence of isospin-symmetry violation is evaluated and discussed. Agreement between theory and experiment is favorable for many observables, while others require yet larger model spaces and/or three-body forces. The limitations of the present results are easily understood by virtue of the trends established and previous phenomenological results.

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