On the α2(Zα)2-vacuum polarisation contribution to the muonic atom energy levels

A derivation of the relativistic, quantum electrodynamical expression for the α2(Zα)2 vacuum polarisation correction to muonic energy levels is presented. Using this derivation based on the bound-state interaction picture, the expression for the other radiative corrections such as the Lamb shift, α(Zα)3-vacuum polarisation, etc are obtained. This shows that the resulting expression for the α2 (Zα)2 vacuum polarisation contribution is consistent with those used in other calculations which are rigorously based on quantum electrodynamics. Furthermore, this approach avoids the problem of double counting. (author)