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

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