Pion-less effective field theory for atomic nuclei and lattice nuclei

Abstract

We compute the medium-mass nuclei $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ using pion-less effective field theory (EFT) at next-to-leading order (NLO). The low-energy coefficients of the EFT Hamiltonian are adjusted to experimental data for nuclei with mass numbers $A=2$ and 3, or alternatively to results from lattice quantum chromodynamics at an unphysical pion mass of 806 MeV. The EFT is implemented through a discrete variable representation in the harmonic oscillator basis. This approach ensures rapid convergence with respect to the size of the model space and facilitates the computation of medium-mass nuclei. At NLO the nuclei $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ are bound with respect to decay into alpha particles. Binding energies per nucleon are $9\text{--}10$ MeV and $21\text{--}40$ MeV at pion masses of 140 and 806 MeV, respectively.