Chiral Three-Nucleon Interactions in Ab-Initio Nuclear Structure and Reactions

Abstract

The prediction of nuclear structure and reaction observables based on nuclear Hamil- tonians including two- and three-nucleon (NN+3N) interactions derived from chiral effective field theory constitutes a challenging task for ab-initio nuclear theory. In particular, the consistent inclusion of 3N interactions requires formal extensions of the many-body methods and, at the same time, causes a significant increase of the computational cost. This work presents the necessary steps for the inclusion and the subsequent application of 3N interactions in different ab-initio nuclear structure and reaction approaches. The first part is dedicated to the preparation of the chiral nuclear forces before they enter the many-body methods. It addresses the similarity renormalization group (SRG) as a tool to soften the initial chiral interactions and its generalization to consistently include 3N interactions. Moreover, the technically important 3N matrix-element management in a convenient basis for the subsequent many-body methods including an efficient storage scheme is discussed. In addition, a possibility to derive approximative schemes for 3N interactions using normal ordering is presented. In the second part the SRG-evolved chiral NN+3N Hamiltonians are applied in nuclear structure calculations using the importance truncated no-core shell model (IT-NCSM) as well as coupled-cluster theory. The impact of SRG-induced and chiral 3N interactions on ground-state energies and low-energy spectra of different p -shell nuclei is studied, includ- ing a sensitivity analysis concerning uncertainties of the chiral interactions in the 12C and 10B spectra. Furthermore, the first ab-initio study of even oxygen isotopes with explicit 3N interactions is presented, and by means of the normal-ordered two-body approximation the ground-state energy systematics of selected closed-shell nuclei throughout the calcium, nickel, and tin isotopic chains are obtained in qualitative agreement with experiment. The third part of this work focuses on 3N interactions in ab-initio nuclear scattering approaches. This includes a detailed discussion of the inclusion of 3N interactions in the no-core shell model combined with the resonating-group method (NCSM/RGM) with emphasis on the ability to treat targets beyond the lightest nuclei. The extended formalism is then applied to nucleon-4He scattering, where the 3N interaction overall improves scattering phase shifts, differential cross sections and analyzing powers. Finally, the no-core shell model with continuum approach, which constitutes a unified ab-initio approach to bound and scattering states resulting from the combination of the NCSM and the NCSM/RGM, is generalized to 3N interactions and applied to the neutron-8Be system to study the impact of the continuum on the 9Be energy levels. The results demonstrate the importance of the consistent treatment of continuum states.