A Hyperspherical Treatment of Reaction Pathways in Few-Nucleon Systems

The adiabatic hyperspherical representation has been extensively applied to few–body systems, in which hyperspherical potentials and couplings describe all possible reaction pathways on an equal footing through an adiabatic collective coordinate, the hyperradius. In addition to providing qualitative insight about the pathways controlling key reaction and resonance phenomena, the hyperspherical potentials plus non–adiabatic couplings can provide a quantitative description of reaction rates, bound states and resonances. In this work, reaction pathways for the three–body nnp, npp (J^π=1/2⁺,T=1/2) and four–body nnpp (J^π=0⁺,T=0) systems are visualized through a spectrum of hyperspherical potential curves, which show the different ways these interacting systems can fragment into bound and continuum channels. Calculations are preformed using adiabatic hyperspherical methods that implement an explicitly–correlated Gaussian basis (Suzuki et. al., Few Body Syst. (2008) 42: 33–72). Two different nucleon–nucleon (NN) interactions are considered, the Minnesota NN interaction, and the realistic AV8' NN interaction with a spin–independent three–nucleon force (Hiyama, E. et al., Phys. Rev. C. 70, 031001(2004)). In addition, three– and four–nucleon binding energies and resonances are computed.