Relativistic levels of mesic atoms

TL;DR

This paper refines the theoretical description of mesic atoms by deriving a covariant two-body equation akin to the Dirac equation, enabling precise calculations of energy levels and QED corrections for pionic and kaonic atoms.

Contribution

It presents a new derivation of a covariant two-body scalar-fermion equation with Coulomb interaction, and introduces a mixed analytic-numerical method for accurate energy level calculations.

Findings

Accurate lowest energy levels for pionic and kaonic atoms.

Effective method for including QED corrections.

Comparison with experimental data shows good agreement.

Abstract

We revisit the derivation of the covariant two-body scalar-fermion equation with a Coulomb interaction, presented in a previous paper. We show that it can be given the formal aspect of a Dirac equation, but for the fact that the eigenvalue is also contained in one of the coefficients and thus it is not linearly included. The discussion of the boundary value problem is therefore different, although some properties of the Dirac equation can be recovered in an approximation bringing back to the concept of reduced mass. We discuss a mixed analytic-numerical method of solution which allows to obtain very accurate results and we calculate the lowest levels, states and QED corrections for pionic and kaonic atoms.