Infrared Length Scale and Extrapolations for the No-Core Shell Model

Abstract

We precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the A-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of A nucleons in the NCSM space to that of A nucleons in a 3(A - 1)-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for Li-6. We apply our result and perform accurate IR extrapolations for bound states of He-4, He-6, Li-6, and Li-7. We also attempt to extrapolate NCSM results for B-10 and O-16 with bare interactions from chiral effective field theory over tens of MeV.