JupiterNCSM: A Pantheon of Nuclear Physics —an implementation of three-nucleon forces in the no-core shell model—

Doctoral thesis, 2021

It is well established that three-nucleon forces (3NFs) are necessary for achieving realistic and accurate descriptions of atomic nuclei. In particular, such forces arisenaturally when using chiral effective field theories (χEFT). However, due to the huge computational complexity associated with the inclusion of 3NFs in many-body methods they are often approximated or neglected completely. In this thesis, three different methods to include the physics of 3NFs in the ab initio no-core shell-model(NCSM) have been implemented and tested. In the first method, we approximate the 3NFs as effective two-body operators by exploiting Wick’s theorem to normal order the 3NF relative a harmonic-oscillator Slater determinant reference state and discarding the remaining three-body term. We explored the performance of this single-reference normal-ordered two-body approximation on the ground-state energies of the two smallest closed-core nuclei, 4He and 16O, in particular focusing on consequences of the breaking of translational symmetry. The second approach is a full implementation of 3NFs in a new NCSM code, named JupiterNCSM, that we provide as an open-source research software. We have validated and benchmarked JupiterNCSM against other codes and we have specifically used it to investigate theeffects of different 3NFs on light p-shell nuclei 6He and 6Li. Finally, we implement the eigenvector continuation (EVC) method to emulate the response of ground-state energies of the aforementioned A = 6 nuclei to variations in the low-energy constants of χEFT that parametrize the 3NFs. In this approach, the full Hamiltonian is projected onto a small subspace that is constructed from a few selected eigenvectors. These training vectors are computed with JupiterNCSM in a large model space for a small set of parameter values. This thesis provides the first EVC-based emulation of nuclei computed with a Slater-determinant basis. After the training phase, we find that EVC predictions offer a very high accuracy and more than seven orders
of magnitude computational speedup. As a result we are able to perform rigorous statistical inferences to explore the effects of 3NFs in nuclear many-body systems.