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.
Close-coupling calculations have been performed to investigate the formation of three-particle bound states in a model collinear system. A generalization of Levinson's theorem (1966) is employed to determine the critical potential strengths necessary for the existence of the triatomic states. The system consists of an atom interacting through a Morse potential with a diatomic molecule bound by a harmonic potential. Comparisons are made with classical phase-space and S-matrix theory and with quantum-mechanical variational and perturbation calculations. When only a few bound states are involved it is shown that the quantal approximations are more accurate than the classical results.