to Eq. (1). Using the CODATA value for the proton charge radius $r_E(p)=0.8775(51)$ fm leads us to a new extracted value of the deuteron radius, r\_E(d)=2.1442(29) [fm]{}, that should be compared to the previous extraction [@Mohr:2012tt], $r_E(d)=2.1424(21)$ fm. Thus, in the electron case the increase in the polarizability uncertainty for the isotope shift makes it comparable to the existing uncertainty in the proton radius-squared. Using it merely increases the uncertainty in the inferred deuteron radius by a factor of $\sqrt2$.

Conclusion
==========

We conclude that in the case of deuterium, model independence that is the main objective of our approach comes at a high price. Scattering data do not constrain the behavior of structure functions, especially the longitudinal one, at low values of the momentum transfer. Microscopical nuclear calculations do a much better job in terms of intrinsic precision that typically is of order of fractions of a per cent. However, in absence of data this claimed precision is not warranted, and once new low-$Q^2$ electrodisintegration data will be available they will serve as a useful cross check for nuclear calculations, as well.

We are grateful to M. Distler, Z.-E. Meziani, V. Pascalutsa, S. Karshenboim, D.R. Phillips, J. Yang, H. 