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We present a comprehensive analysis of the deuteron charge and quadrupoleform factors based on the latest two-nucleon potentials and charge densityoperators derived in chiral effective field theory. The single- and two-nucleoncontributions to the charge density are expressed in terms of the proton andneutron form factors, for which the most up-to-date empirical parametrizationsare employed. By adjusting the fifth-order short-range terms in the two-nucleoncharge density operator to reproduce the world data on the momentum-transferdependence of the deuteron charge and quadrupole form factors, we predict thevalues of the structure radius and the quadrupole moment of the deuteron:$r_{\rm str}=1.9729\substack{+0.0015\\ -0.0012}\ \text{fm},\Q_d=0.2854\substack{+0.0038\\ -0.0017}\ \text{fm}^2. $ A comprehensive andsystematic analysis of various sources of uncertainty in our predictions isperformed. Following the strategy advocated in our recent publication Phys.Rev. Lett. 124, 082501 (2020), we employ the extracted structure radiustogether with the accurate atomic data for the deuteron-proton mean-squarecharge radii difference to update the determination of the neutron chargeradius, for which we find: $r_n^2=-0.105\substack{+0.005\\ -0.006} \,\text{fm}^2$. Given the observed rapid convergence of the deuteron form factorsin the momentum-transfer range of $Q \simeq 1-2.5$ fm$^{-1}$, we argue thatthis intermediate-energy domain is particularly sensitive to the details of thenucleon form factors and can be used to test different parametrizations.

High-accuracy calculation of the deuteron charge and quadrupole form factors in chiral effective field theory