Probing the existence of \eta^3He mesic nucleus with a few-body approach

TL;DR

This study investigates the existence of an eta-3He mesic nucleus using a few-body approach, constructing energy-dependent and independent eta-N potentials to predict binding energies and decay widths.

Contribution

It introduces a comprehensive few-body method with various eta-N potentials to analyze eta-3He bound states, providing new predictions for binding energies and decay widths.

Findings

Predicted eta-3He bound states with decay widths around 5-10 MeV.

Constructed energy-dependent and independent eta-N potentials consistent with theoretical models.

Identified conditions under which eta-3He can form a bound state.

Abstract

Motivated by the two recent observations in the WASA-at-COSY detector, we investigate the $\eta^3$He nucleus with the $\eta NNN$ few body method. We construct the effective $s$-wave energy dependent $\eta N$ potential which reproduce the $\eta N$ subthreshold scattering amplitude in the 2005 Green-Wycech model. It gives the $\eta$ separation energy and decay width of 0.19 MeV and 1.71 MeV, respectively. We also construct various sets of effective $s$-wave energy independent $\eta N$ potentials where the corresponding complex scattering lengths (a) are within the range given in most theoretical models. We obtain the bound $\eta^3$He nucleus with decay width of about 5 MeV when a is (1.0 fm, 0.3 fm), and of about 10 MeV when a is (1.0 fm, 0.5 fm).