Three-nucleon forces in nuclear physics simulations
Licentiate thesis, 2019
The aim of this licentiate thesis is to evaluate the normal-ordered two-body (NO2B)-approximation as a computationally promising way to incorporate realistic three-nucleon forces (3NFs) in nuclear many-body simulations using the no-core-shell-model. The existence and importance of 3NFs is predicted in chiral effective field theories of the strong-nuclear force. However, the inclusion of 3NFs renders simulations computationally demanding and this severely limits the size of nuclei that can be studied. Clearly, approximation schemes are needed. In the specific version of the NO2B-approximation that is studied here, the 3NF is normal-ordered with respect to a single Slater-determinant reference state constructed from harmonic-oscillator states, yielding an expansion with zero-, one-, two- and three-nucleon terms. The irreducible three-nucleon part of the original 3NF is assumed to be small and therefore discarded, thus leaving an effective two-nucleon potential. It is found that the predicted ground-state energy of 4-He in the NO2B-approximation depends strongly on the choice of many-body basis. The NO2B-approximation breaks the translational symmetry of the Hamiltonian and therefore introduces strong center-of-mass (CM)-mixing in the 4-He ground-state. This CM-mixing is shown to be an important reason for the observed basis dependence. Thus, the NO2B approximation is most likely more useful for studies of heavier nuclei. Indeed, the approximation error for the ground-state energy of 16-O is observed to be smaller and the results exhibit a weaker dependence on the choice of many-body basis. Finally, it is recommended that CM mixing should be used as a diagnostic to assess the reliability of the NO2B approximation.