the Coulomb contribution 17.24 kHz, the magnetic contribution 2.28 kHz and the magnetic polarizability correction -0.27 kHz.

Our evaluation for the $1S-2S$ splitting in deuterium is E\_[2S-1S]{}\^[e-D]{}&=&28.812.0[kHz]{}, that is the sum of the elastic (0.53(1) kHz), inelastic (33.4(12.0) kHz) and subtraction (-4.60(3) kHz) contributions. The uncertainty is about a half of the full result. Since for the electronic deuterium the integrals over structure functions are even more strongly weighted at low values of $Q^2$ where no experimental information is available, the large uncertainty does not come unexpectedly. We show in Table \[tab3\] (fourth column) how future electron-deuteron scattering measurements can help improving on this estimate.

Note that this uncertainty estimate exceeds the one in Eq. (34) by two orders of magnitude. However, the main uncertainty in the isotope shift given in [@Parthey:2010] is actually due to uncertainties in other theoretical corrections, largely caused by uncertainties in parameters such as particle masses. The total radius-related energy uncertainty in [@Parthey:2010] is $0.89$ kHz. The uncertainty from the dispersive polarizability calculation is still an order of magnitude larger; using it would change the radius difference result to r\_E\^2(d) - r\_E\^2(p) = 3.8274(88) [fm]{}\^2, increasing the uncertainty by a factor of $\sim10$ as compared 