$\Omega$-deuteron Interaction in Folding Model

Abstract

A simple single folding model for $\Omega$-deuteron with maximal spin $\left(I\right)J^{P}=\left(0\right)5/2^{+}$ is investigated. $\Omega$ is assumed to orbit an unperturbed deuteron in a $\Omega$-deuteron potential based on a separable $\Omega$-nucleon potential from lattice QCD. We show that the effective central folding potential of $\Omega d$ in the $^{5}S_{2}$ channel has a simple Wood-Saxon form, and approximate the upper bound for the binding energy of $\Omega$ particle on a deuteron. In order to investigate how changes in the wave functions affect the results, we consider four analytical forms for $S$-state deuteron wave functions, i.e., two widely used Hulth\'en forms, as well as the modified Reid93 and Argonne v18 forms. Our calculations of binding energy from simple two-body approximation are compared with the results reported for the three-body problem; it is confirmed that the $\Omega d$ system is deeply bound. Although the single folding model reduces the three-body problem to a two-body problem, this simplification is inadequate.