Binding vs. scattering length: $\eta$ in light nuclei

TL;DR

This paper explores the relationship between binding energy, width, and complex scattering length in light nuclei, aiming to aid the search for eta-mesic bound states through final state interaction analysis.

Contribution

It establishes a connection between binding energy, width, and scattering length for light nuclei, providing a new approach to identify eta-mesic bound states.

Findings

Derived formulas linking binding energy and width to scattering length

Proposed a method to use final state interactions in bound state searches

Clarified the role of scattering length in eta-mesic nuclei detection

Abstract

The possibility of etamesic nuclei remains an open problem in nuclear physics until now. Various calculations give contradictory predictions even for the lightest real nucleus $^3$He. In this paper we present the connection of the binding energy and width to the complex scattering length for heavier nuclei than this in the hope that, with knowledge of the final state interaction this could be useful in searches of possible bound states.