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

Comments: 8 pages, 4 figures. Updated to address issues fixed during publication. We have prepared a python (v2.7) script that will compute the IR scales (both full scale and intrinsic scale). This script depends only on numpy and scipy and can be found at http://github.com/KyleWendt/ncsm_ho_ir_scale