Studying Omega-nucleon-nucleon three-body states by realistic nucleon-nucleon and first principles Lattice QCD Omega-nucleon potentials in the cluster model

Abstract

The Faddeev equations in coordinate space are solved to study the Omega-nucleon-nucleon and Omega-Omega-nucleon three-body systems using the latest Omega-nucleon and Omega-Omega interactions developed by the HAL QCD Collaboration (Omega is a decouplet baryon consists three strange quark). We calculate the binding energy of the Omega-nucleon-nucleon system by examining three nucleon-nucleon (NN) potentials, i.e., modern realistic AV18 potential, Yukawa-type Malfliet-Tjon (MT) interaction, and Gogny-Pires-Tourreil (GPT) soft and local potential. We take into account the contribution of the Coulomb potential. Our numerical calculations for Omega-deuteron in maximum spin 5/2+ leads to ground state binding energy of 20.953, 19.368, and 20.439 MeV and matter radius of 1.097, 1.373, and 1.309 fm using MT, GPT, and AV18 NN potentials, respectively. In the case of Omega-deuteron (0)5/2+ system, our numerical analysis shows that considering higher partial waves than s wave in NN interactions leads to an increase of about 0.2 MeV using GPT and about 0.1 MeV reduction with AV18 potentials. We study the convergence of three-body binding energies in a cluster model using the hyperspherical harmonics method and investigate the geometrical properties of Omega-deuteron (0)5/2+ ground states.