Geometrical properties of ΩNN three-body states by realistic NN and first principles Lattice QCD ΩN potentials

Abstract

The Faddeev equations in coordinate space are solved to study the NN and N three-body sys- tems using the latest N 5S2 and 1S0 interactions developed by the HAL QCD Collaboration. We recalculate the binding energy of the NN system by examining three NN potentials, i.e., modern real- istic 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 cal- culations for d (T = 0 ) in maximum spin 5 / 2+ confirm ground state binding energy of 20 . 953, 19 . 368, and 20 . 439 MeV and a matter radius of 1 . 097, 1 . 373, and 1 . 309 fm using MT, GPT, and AV18 NN po- tentials, respectively. In the case of d ( 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 . 2MeV 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 d ( 0 ) 5 / 2+ ground states.