Analytical matrix elements of the Uehling potential in three-body systems, and applications to exotic molecules

TL;DR

This paper derives exact analytical formulas for the Uehling potential matrix elements in three-body systems and applies them to improve the accuracy of vacuum polarization corrections in exotic molecules, including muonic and pionic ones.

Contribution

It provides new analytical expressions for matrix elements of the Uehling potential and applies them to calculate corrections in exotic molecular systems with higher precision.

Findings

Improved accuracy in vacuum polarization energy corrections for exotic molecules

Analytical formulas enable efficient computation of matrix elements

First study of resonant states below the n=2 threshold in these systems

Abstract

Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum polarization correction to the binding energy of muonic and pionic molecules, both in a first-order perturbative treatment and in a nonperturbative approach. The first resonant states lying below the n=2 threshold are also studied, by means of the stabilization method with a real dilatation parameter.