indicates that the bulk of the result is relatively model independent and can be obtained non-relativistically. However, there remain significant energy shifts that are obtained non-relativistically using a potential model. One would like a calculation by an alternative method to verify the results.

We here explore a fully relativistic dispersive calculation of the two-photon corrections to $\mu$-$D$. In this type of calculation, the energy shift is obtained from the real part of an amplitude whose imaginary part is related without approximation to physical elastic and inelastic $e$-$D$ scattering. To the extent that the data is accurate and sufficient, the result follows just from the data and the calculation is model independent. The calculation resembles the generally accepted work for the $\mu$-$H$ system [@Pachucki:1996zza; @Martynenko:2005rc; @Carlson:2011zd; @Birse:2012eb; @fesr]. However, for the proton case the corrections are much smaller, and the proton data in the relevant kinematic regions is itself very good. Furthermore, good analytic fits, useful for doing integrals, are already available in the literature [@bostedchristy].

For the deuteron we need elastic and inelastic data over a wide range of energies, including the low energy region, where the data is sparse. There are good analytic fits [@bostedchristy] to the deuteron data 