Monopole and Seniority Truncations in the Large-Scale Configuration Interaction Shell Model Approach

Abstract: This paper addresses the challenges of solving the quantum many-body problem, particularly within nuclear physics, through the configuration interaction (CI) method. Large-scale shell model calculations often become computationally infeasible for systems with a large number of valence particles, requiring truncation techniques. We propose truncation methods for the nuclear shell model, in which angular momentum is conserved and rotational symmetry is restored. We introduce the monopole-interaction-based truncation and seniority truncation strategies, designed to reduce the dimension of the calculations. These truncations can be established by considering certain partitions based on their importance and selecting physically meaningful states. We examine these truncations for Sn, Xe, and Pb isotopes, demonstrating their effectiveness in overcoming computational limits. These truncations work well for systems with either a single type of valence nucleon or with both types. With these truncations, we are able to achieve good convergence for the energy at a very small portion of the total dimension.