Importance Truncated No-Core Shell Model

One of the most universal tools for the ab initio solution of the nuclear many-body problem is the No-Core Shell Model (NCSM). It is widely used for the description of ground states and low-lying excited states of nuclei throughout the p-shell [1]. Apart from energies, detailed spectroscopic information and form-factors can be extracted from the resulting many-body eigenstates. The limitation of converged NCSM calculations to the p-shell results solely from the dimension of the Nmaxh̄ω model space, which grows factorially with the number of particles and the truncation parameter Nmax. However, for the description of an individual eigenstate, e.g. the ground state, many of the basis states are irrelevant, i.e., their amplitude in the expansion of the eigenstates is extremely small or zero. If these irrelevant states were known beforehand one could restrict the model space to the important basis states and thus reduce the dimension significantly. Such an a priori measure for the importance of individual basis states for the description of a selected target state can be derived within many-body perturbation theory [2]. Starting from an initial approximation of the target state |Ψref〉, the importance of a basis state |Φν〉 can be estimated through its amplitude in the first-order perturbative expansion of the target state,