Large-basis ab initio no-core shell model and its application to ¹²C

We present the framework for the ab initio no-core nuclear shell model and apply it to obtain properties of ¹²C. We derive two-body effective interactions microscopically for specific model spaces from the realistic CD-Bonn and the Argonne V8’ nucleon-nucleon (NN) potentials. We then evaluate binding energies, excitation spectra, radii, and electromagnetic transitions in the 0ħΩ, 2ħΩ, and 4ħΩ model spaces for the positive-parity states and the 1ħΩ, 3ħΩ, and 5ħΩ model spaces for the negative-parity states. Dependence on the model-space size, on the harmonic-oscillator frequency, and on the type of the 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.