Feasibility study of a three-nucleon force in the no-core shell model:3Hbinding energy

Abstract

We investigate the three-nucleon system with a realistic nucleon-nucleon potential and the Tucson-Melbourne (TM) two-pion exchange three-body interaction using a translationally invariant harmonic oscillator basis. In the calculations, the no-core shell-model two-body effective interaction replaces the nucleon-nucleon potential, while the three-nucleon interaction is added without any renormalization. We study the convergence of the approach by changing the basis size. Also the dependence of the binding energies on the TM cutoff parameter $\ensuremath{\Lambda}$ is examined. The results show promise for the construction of three-body effective interactions including a three-nucleon interaction, for use in future ab initio no-core shell-model nuclear structure calculations for $A>3$ systems.