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.

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

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• Physics of nuclei: Key role of an emergent symmetry
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• Power counting in chiral effective field theory and nuclear binding
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• Jacobi no-core shell model for $p$-shell hypernuclei
• Fast & rigorous predictions for $A=6$ nuclei with Bayesian posterior sampling
• Infrared extrapolations of quadrupole moments and transitions
• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory
• Natural orbital description of the halo nucleus 6He
• Machine Learning for the Prediction of Converged Energies from Ab Initio Nuclear Structure Calculations
• Precise neural network predictions of energies and radii from the no-core shell model
• Nuclear physics uncertainties in light hypernuclei
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• Systematic Nuclear Uncertainties in the Hypertriton System
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• Corrections to nucleon capture cross sections computed in truncated Hilbert spaces
• Two-dimensional extrapolation procedure for ab initio study of nuclear size parameters and the properties of halo nucleus 6He
• Spectroscopic factor calculations in the \textit{ab initio} no-core shell model
• Hypertriton lifetime
• Perturbative $\chi$EFT calculations of the deuteron and triton up to N${}^2$LO
• Current Status of Very-Large-Basis Hamiltonian Diagonalizations for Nuclear Physics
• Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions
• Lifetime of the hypertriton