Level shifts of exotic deuterium atoms from effective range parameters

TL;DR

This paper evaluates methods for calculating energy level shifts in exotic hadronic atoms caused by short-range interactions, comparing indirect formulas with direct calculations, and emphasizing the importance of Coulomb and electromagnetic effects.

Contribution

It systematically assesses the accuracy of effective range formulas for level shifts in exotic atoms, including Coulomb and multipole effects, validating their reliability against direct bound-state calculations.

Findings

Effective range formulas provide reliable estimates when Coulomb effects are included.

Including multipole electromagnetic terms improves the accuracy of the indirect approach.

Direct calculations confirm the validity of the perturbative corrections in the indirect method.

Abstract

We discuss various methods for determining the level shifts induced by short-range interactions in exotic atoms which are formed by a hadron and a nucleus of opposite charge. The energy shifts can be related to the effective range parameters through Deser or Trueman formulas. In order to assess the accuracy and the reliability of this indirect approach, its predictions are compared with direct bound-state calculations. Notably, the importance of including the Coulomb potential in scattering calculations is highlighted. Finally, the impact of multipole terms in the asymptotic electromagnetic interaction is examined. It is demonstrated that an indirect approach remains relevant by accounting for these effects perturbatively.