Initial four-body forces in many-body calculations

For the ab-initio description of light and medium-mass nuclei, chiral effective field theory is used successfully. Improving the precision and uncertainty estimation of chiral forces, especially an improved description of medium-mass nuclei, requires consistent order-by-order calculations. Starting at N³LO, chiral four-body forces play a role and their impact on nuclei beyond few-body systems is currently unknown. Even without initial four-body forces, transformations such as the similarity renormalization group induce many-body forces. We model the four-body forces using a simple contact interaction and investigate its effect on nuclear many-body observables, especially ground-state energies and radii, as well as correlations between them. The four-body forces are evaluated in a Jacobi harmonic oscillator (HO) basis and subsequently used in no-core shell model and Hartree-Fock calculations for light- and medium mass nuclei. Handling of chiral forces is identical to a contact interaction, once they are evaluated in a HO basis.