Ab initio study of 40Ca with an importance-truncated no-core shell model

We propose an importance truncation scheme for no-core shell model or configuration interaction approaches, which enables converged calculations for nuclei well beyond the p shell. It is based on an a priori measure for the importance of individual basis states constructed by means of many-body perturbation theory. Only the physically relevant states of the no-core model space are considered, which leads to a dramatic reduction of the basis dimension. We analyze the validity and efficiency of this truncation scheme using different realistic nucleon-nucleon interactions and compare to conventional no-core shell model calculations for 4He and 16O. Then, we present first converged calculations for the ground state of 40Ca within no-core model spaces including up to 16 PlanckOmega excitations using realistic low-momentum interactions. The scheme is universal and can be easily applied to other quantum many-body problems.