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 $3(A\ensuremath{-}1)$-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 $^{6}\mathrm{Li}$. We apply our result and perform accurate IR extrapolations for bound states of $^{4}\mathrm{He},^{6}\mathrm{He},^{6}\mathrm{Li}$, and $^{7}\mathrm{Li}$. We also attempt to extrapolate NCSM results for $^{10}\mathrm{B}$ and $^{16}\mathrm{O}$ with bare interactions from chiral effective field theory over tens of MeV.