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

A derivation of the relativistic, quantum electrodynamical expression for the alpha ²(Z alpha )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 alpha (Z alpha )³-vacuum polarisation, etc are obtained. This shows that the resulting expression for the alpha ²(Z alpha )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.