Effective interactions and operators in nuclei within the no-core shell model

We review the application of effective operator formalism to the ab initio no core shell model (NCSM). For short-range operators, such as the nucleon-nucleon potential, the unitary-transformation method works extremely well at the two-body cluster approximation and good results are obtained for the binding energies and excitation spectra of light nuclei (A ≤ 16). However, for long-range operators, such as the radius or the quadrupole moment, performing this unitary transformation at the two-body cluster level does not include the higher-order correlations needed to renormalize these long-range operators adequately. Usually, such correlations can be obtained either by increasing the order of the cluster approximation or by increasing the model space. We will discuss the difficulties of these approaches as well as alternate possible solutions for including higher-order correlations in small model spaces.